asymptotics and random sampling for bci and bck lambda terms this paper presents a bijection between combinatorial maps and a class of enriched trees corresponding to a class of expression trees in some logical systems constrained lambda terms starting from two alternative definitions of combinatorial maps the classical definition by gluing half edges and a definition by non ambiguous depth first traversal we derive non trivial asymptotic expansions and efficient random generation of logic formulae syntactic trees in the bci or bck systems

combinatorial approach to generalized bell and stirling numbers and boson normal ordering problem we consider the numbers arising in the problem of normal ordering of expressions in boson creation a and annihilation a operators a a 1 we treat a general form of a boson string a rnasn a r2as2 a r1as1 which is shown to be associated with generalizations of stirling and bell numbers the recurrence relations and closed form expressions dobinski type formulas are obtained for these quantities by both algebraic and combinatorial methods by extensive use of methods of combinatorial analysis we prove the equivalence of the aforementioned problem to the enumeration of special families of graphs this link provides a combinatorial interpretation of the numbers arising in this normal ordering problem

a simple precoding based blind channel estimation for space time block coded single carrier with frequency domain equalization systems we propose a blind channel estimation method for space time block coded single carrier with frequency domain equalization sc fde systems based on a simple nonredundant precoding this method of precoding allows us to better structure the relation between the covariance matrices of the received data and the products of channel coefficients using this structure we can easily obtain the products of channel coefficients by using only subtraction and division then each of the two channel impulse response vectors is obtained by computing the eigenvector that is associated with the maximal eigenvalue of a hermitian matrix formed from the corresponding products of channel coefficients the proposed framework guarantees the unique recovery of all the products of channel coefficients for colored or white noise cases the impact of the precoding on channel estimation and equalization is also discussed simulations are used to demonstrate the performance of the proposed method

null surgery on knots in l spaces let k be a knot in an l space y with a dehn surgery to a surface bundle over s 1 we prove that k is rationally fibered that is the knot complement admits a fibration over s 1 as part of the proof we show that if k c y has a dehn surgery to s 1 x s 2 then k is rationally fibered in the case that k admits some s 1 x s 2 surgery k is floer simple that is the rank of hfk y k is equal to the order of h 1 y by combining the latter two facts we deduce that the induced contact structure on the ambient manifold y is tight in a different direction we show that if k is a knot in an l space y then any thurston norm minimizing rational seifert surface for k extends to a thurston norm minimizing surface in the manifold obtained by the null surgery on k i e the unique surgery on k with b 1 0

a combinatorial approach to nonlinear functional expansions an introduction with an example in this paper we present a new approach to causal functionals we introduce combinatorial interpretations of the solutions of nonlinear differential equations with forcing terms this theory parallels the algebraic approach with formal power series in noncommutative variables developed by fliess lamnabhi and lamnabhi lagarrigue this theory makes use of certain combinatorial objects called weighted increasing trees weighted paths and histories we can deduce very efficient algorithms for the computation of the corresponding volterra kernels we present an introduction to our combinatorial theory an example with a nonlinear circuit gives the flavor of our approach the complete proofs and general theory will be discussed in a further paper

analytic functors between presheaf categories over groupoids the paper studies analytic functors between presheaf categories generalising results of a joyal 11 and r hasegawa 9 for analytic endofunctors on the category of sets we give two characterisations of analytic functors between presheaf categories over groupoids i as functors preserving filtered colimits quasi pullbacks and cofiltered limits and ii as functors preserving filtered colimits and wide quasi pullbacks the development establishes that small groupoids analytic functors between their presheaf categories and quasi cartesian natural transformations between them form a 2 category

an optimal algorithm to generate rooted trivalent diagrams and rooted triangular maps a trivalent diagram is a connected two colored bipartite graph parallel edges allowed but not loops such that every black vertex is of degree 1 or 3 and every white vertex is of degree 1 or 2 with a cyclic order imposed on every set of edges incident to the same vertex a rooted trivalent diagram is a trivalent diagram with a distinguished edge its root we shall describe and analyze an algorithm giving an exhaustive list of rooted trivalent diagrams of a given size number of edges the list being non redundant in that no two diagrams of the list are isomorphic the algorithm will be shown to have optimal performance in that the time necessary to generate a diagram will be seen to be bounded in the amortized sense the bound being independent of the size of the diagrams we call this the cat property one objective of the paper is to provide a reusable theoretical framework for algorithms generating exhaustive lists of complex combinatorial structures with attention paid to the case of unlabeled structures and to those generators having the cat property

two bijective proofs for the arborescent form of the good lagrange formula and some applications to colored rooted trees and cacti goulden and kulkarni j combin theory ser a 80 2 1997 295 give a bijective proof of an arborescent form of the good lagrange multivariable inversion formula this formula was first stated explicitly by bender and richmond electron j combin 5 1 1998 4pp but is implicit in goulden and kulkarni 1997 in this paper we propose two new simple bijective proofs of this formula and we illustrate the interest of these proofs by applying them to the enumeration and random generation of colored rooted trees and rooted m ary cacti

a generalized bridge number for links in 3 manifolds in sch schubert introduced a new invariant of knots in the 3 sphere called the bridge number and showed that when reduced by 1 it is an additive invariant under the connected sum operation of knots several generalizations of schubert s theorem can be imagined indeed from schubert s perspective the behaviour of bridge number under addition is only a corollary of a more general theorem about bridge number of satellite knots boileau and lickorish have independently observed b l that the following generalization of schubert s theorem would be useful bridge number as defined by schubert begins with a projection of the knot or link onto a sphere in s 3 project instead onto a higher genus unknotted surface in s 3 one advantage of this approach is that it allows bridge number to be defined for a link in a 3 manifold other than 5 3 by projecting the link onto a heegaard surface for the 3 manifold here we explore how such an invariant behaves under connected sum using a line of argument similar to jaco s proof of haken s theorem that heegaard genus is additive ja a crucial additional ingredient needed is lemma4 6 some of the arguments were motivated by no in which as an aside a different generalization of schubert s theorem is attempted they want to show that the standard bridge number behaves well under knot decomposition even when the knot is decomposed by spheres intersecting the knot more than twice e g under tangle sums l besides recovering a new proof of schubert s theorem more in the spirit of jaco s proof of the haken lemma we are also able to prove an analogous theorem for bridge number defined with respect to genus one heegaard splittings of 5 3 or the lens space and also with respect to irreducible heegaard splittings of closed nonhaken 3 manifolds

self similarity in the combinatorics of orthogonal polynomials resume dans cet article nous construisons des structures combinatoires invariantes sous l action d une permutation donnee dans certains cas le poids de ces dernieres correspon a des polynomes orthogonaux dont on a ajuste convenablement les parametres on examine ici de ces structures associees aux polynomes de hermite laguerre krawtchouk meixner meixner pollaczek et de jacobi

monopoles and lens space surgeries monopole floer homology is used to prove that real projective three space cannot be obtained from dehn surgery on a nontrivial knot in the three sphere to obtain this result we use a surgery long exact sequence for monopole floer homology together with a nonvanishing theorem which shows that monopole floer homology detects the unknot in addition we apply these techniques to give information about knots which admit lens space surgeries and to exhibit families of three manifolds which do not admit taut foliations

weak convergence of random p mappings and the exploration process of inhomogeneous continuum random trees we study the asymptotics of the p mapping model of random mappings on n as n gets large under a large class of asymptotic regimes for the underlying distribution p we encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees this exploration process being derived aldous miermont pitman 2004 from a bridge with exchangeable increments our setting generalizes previous results by allowing a finite number of attracting points to emerge

weighted derangements and the linearization coefficients of orthogonal sheffer polynomials the present paper is devoted to a systematic study of the combinatorial interpretations of the moments and the linearization coefficients of the orthogonal sheffer polynomials i e hermite charlier laguerre meixner and meixner pollaczek polynomials in particular we show that viennot s combinatorial interpretations of the moments can be derived directly from their classical analytical expressions and that the linearization coefficients of meixner pollaczek polynomials have an interpretation in the model of derangements analogous to those of laguerre and meixner polynomials

on gammelgaard s formula for a star product with separation of variables we show that gammelgaard s formula expressing a star product with separation of variables on a pseudo kahler manifold in terms of directed graphs without cycles is equivalent to an inversion formula for an operator on a formal fock space we prove this inversion formula directly and thus offer an alternative approach to gammelgaard s formula which gives more insight into the question why the directed graphs in his formula have no cycles

independent process approximations for random combinatorial structures abstract many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables conditioned on the value of a weighted sum of the variables it is interesting to compare the combinatorial structure directly to the independent discrete process without renormalizing the quality of approximation can often be conveniently quantified in terms of total variation distance for functionals which observe part but not all of the combinatorial and independent processes among the examples are combinatorial assemblies e g permutations random mapping functions and partitions of a set multisets e g polynomials over a finite field mapping patterns and partitions of an integer and selections e g partitions of an integer into distinct parts and square free polynomials over finite fields we consider issues common to all the above examples including equalities and upper bounds for total variation distances existence of limiting processes heuristics for good approximations the relation to standard generating functions moment formulas and recursions for computing densities refinement to the process which counts the number of parts of each possible type the effect of further conditioning on events of moderate probability large deviation theory and nonuniform measures on combinatorial objects and the possibility of getting useful results by overpowering the conditioning

nonredundant precoding assisted blind channel estimation for single carrier space time block coded transmission with frequency domain equalization relying on nonredundant diagonal precoding and independent and identically distributed i i d source assumption this paper proposes a blind channel estimation scheme for single carrier frequency domain equalization based space time block coded systems the proposed method exploits the precoding induced linear signal structure in the conjugate cross correlation between the two temporal block received signals as well as the circulant channel matrix property and can yield exact solutions whenever the channel noise is circularly gaussian and the receive data statistic is perfectly obtained the channel estimation formulation builds on rearranging the set of linear equations relating the entries of conjugate cross correlation matrix and products of channel impulse responses into one with a distinctive block circulant with circulant block bccb structure this allows a simple identifiability condition depending on precoder parameters alone and also provides a natural yet effective optimal precoder design framework for improving solution accuracy when imperfect data estimation occurs we consider two models of data mismatch from both deterministic and statistical points of view and propose the associated design criteria the optimization problems are formulated to take advantage of the bccb system matrix property and are solved analytically the proposed optimal precoder aims to optimize solution robustness against deterministic error perturbation and also minimize the mean square error when the data mismatch is modeled as a white noise pairwise error probability analysis is conducted for investigating the equalization performance numerical examples are used to illustrate the performance of the proposed method

two applications of analytic functors we apply the theory of analytic functors to two topics related to theoretical computer science one is a mathematical foundation of certain syntactic well quasi orders and well orders appearing in graph theory the theory of term rewriting systems and proof theory the other is a new verification of the lagrange good inversion formula using several ideas appearing in semantics of lambda calculi especially the relation between categorical traces and fixpoint operators copyright 2002 elsevier science b v

a set theoretic interpretation of the umbral calculus abstract through the notion of enriched species we develop a bijective calculus set theoretic counterpart of the theory of binomial enumeration

a generalized cyclotomic identity abstract in this paper we prove a generalization of the cyclotomic identity for each group g satisfying suitable finiteness conditions we prove this generalized cyclotomic identity by counting coloured g set structures the cyclotomic identity corresponds to taking g the free abelian group of rank one for the free abelian group of rank two for example we get an analogous identity involving the generating function of the partition function interalia we show that studying g set structures gives a unified and conceptually simple approach to other classical combinatorial identities not to the author s knowledge previously linked in the literature

categorical aspects of generating functions i exponential formulas and krull schmidt categories abstract in this paper we study formal power series with exponents in a category for example the generating function of a category e with finite hom sets is defined by e t tx aut x where the summation is taken over all isomorphism classes of objects of e we can use such power series to enumerate the number of e structures along a faithful functor theorem 4 6 our theory is closely related to the theory of species joyal 1981 a species can be identified with a faithful functor from a groupoid to the category of finite sets theorem 3 6 we use mainly the concept of faithful functors with finite fibers instead of species so that we can separate the roles categories and functors play for example the exponential formula e t exp con e t means the unique coproduct decomposition property theorem 5 8 in the final section we give some applications of our theory to rather classical enumerations

heegaard floer correction terms and rational genus bounds given an element in the first homology of a rational homology 3 sphere y one can consider the minimal rational genus of all knots in this homology class this defines a function on h1 y z which was introduced by turaev as an analogue of thurston norm we will give a lower bound for this function using the correction terms in heegaard floer homology as a corollary we show that floer simple knots in l spaces are genus minimizers in their homology classes hence answer questions of turaev and rasmussen about genus minimizers in lens spaces

non redundant precoding based blind and semi blind channel estimation for mimo block transmission with a cyclic prefix by combining multiple input multiple output mimo communication with block transmission using a cyclic prefix cp mimo block transmission systems can not only achieve high data rates but also simplify channel estimation and equalization in this paper to provide a bandwidth efficient solution for channel estimation in mimo block transmission systems with a cp we present a framework for blind channel estimation based on a general non redundant precoding using this framework we propose a blind estimator exploiting a simplified non redundant precoding that is robust against overestimates of a true mimo channel order furthermore in the case with the number of transmit antennas greater than that of receive antennas we show under specific system conditions that the proposed blind algorithms can be used for estimation of the mimo channel without oversampling the received signals with the simplified precoding conditions established in this paper the proposed method does not impose the strict identifiability conditions on the mimo channel which are required for the existing methods furthermore the proposed estimator achieves accurate channel estimation with a small number of symbol blocks in addition we derive a simplified precoder that is optimized in the sense of minimizing the impact of unknown additive noise we discuss the tradeoff between channel estimation accuracy and bit error rate performance associated with the simplified precoder finally we develop a technique for resolving the channel ambiguity in the proposed blind estimator to create a semi blind channel estimator relying on only a few known symbols

expansions of chromatic polynomials and log concavity in this paper we present several results and open problems about log concavity properties of sequences associated with graph colorings five polynomials intimately related to the chromatic polynomial of a graph are introduced and their zeros combinatorial and log concavity properties are studied four of these polynomials have never been considered before in the literature and some yield new expansions for the chromatic polynomial

on floer homology and the berge conjecture on knots admitting lens space surgeries we complete the first step in a two part program proposed by baker grigsby and the author to prove that berge s construction of knots in the three sphere which admit lens space surgeries is complete the first step which we prove here is to show that a knot in a lens space with a threesphere surgery has simple in the sense of rank knot floer homology the second conjectured step involves showing that for a fixed lens space the only knots with simple floer homology belong to a simple finite family using results of baker we provide evidence for the conjectural part of the program by showing that it holds for a certain family of knots coupled with work of ni these knots provide the first infinite family of non trivial knots which are characterized by their knot floer homology as another application we provide a floer homology proof of a theorem of berge

holomorphic disks and three manifold invariants properties and applications in 27 we introduced floer homology theories hf y s hf y s hf y t hf y s and hf red y s associated to closed oriented three manifolds y equipped with a spiny structures s spin c y in the present paper we give calculations and study the properties of these invariants the calculations suggest a conjectured relationship with seiberg witten theory the properties include a relationship between the euler characteristics of hf and turaev s torsion a relationship with the minimal genus problem thurston norm and surgery exact sequences we also include some applications of these techniques to three manifold topology

scaling limits of random graphs from subcritical classes we study the uniform random graph c n with n vertices drawn from a subcritical class of connected graphs our main result is that the resealed graph c n root n converges to the brownian continuum random tree t e multiplied by a constant scaling factor that depends on the class under consideration in addition we provide sub gaussian tail bounds for the diameter d c n and height h c n center dot of the rooted random graph c n center dot we give analytic expressions for the scaling factor in several cases including for example the class of outerplanar graphs our methods also enable us to study first passage percolation on c n where we also show the convergence to t e under an appropriate rescaling

behavioural differential equations a coinductive calculus of streams automata and power series we present a theory of streams infinite sequences automata and languages and formal power series in terms of the notions of homomorphism and bisimulation which are the cornerstones of the theory of universal coalgebra this coalgebraic perspective leads to a unified theory in which the observation that each of the aforementioned sets carries a so called final automaton structure plays a central role finality forms the basis for both definitions and proofs by coinduction the coalgebraic counterpart of induction coinductive definitions take the shape of what we have called behavioural differential equations after brzozowski s notion of input derivative a calculus is developed for coinductive reasoning about all of the afore mentioned structures closely resembling calculus from classical analysis

a combinatorial description of knot floer homology given a grid presentation of a knot or link k in the three sphere we describe a heegaard diagram for the knot complement in which the heegaard surface is a torus and all elementary domains are squares using this diagram we obtain a purely combinatorial description of the knot floer homology of k

generalised brownian motion and second quantisation a new approach to the generalised brownian motion introduced by m bouzejko and r speicher is described based on symmetry rather than deformation the symmetrisation principle is provided by joyal s notions of tensorial and combinatorial species any such species v gives rise to an endofunctor fv of the category of hilbert spaces with contractions a generalised brownian motion is an algebra of creation and annihilation operators acting on fv h for arbitrary hilbert spaces h and having a prescription for the calculation of vacuum expectations in terms of a function t on pair partitions the positivity is encoded by a semigroup of broken pair partitions whose representation space with respect to t is v the existence of the second quantisation as functor t from hilbert spaces to noncommutative probability spaces is proved to be equivalent to the multiplicative property of the function t for a certain one parameter interpolation between the fermionic and the free brownian motion it is shown that the field algebras k are type ii1 factors when k is infinite dimensional

the lens space realization problem we determine the lens spaces that arise by integer dehn surgery along a knot in the three sphere specically if surgery along a knot produces a lens space then there exists an equivalent surgery along a berge knot with the same knot floer homology groups this leads to sharp information about the genus of such a knot the arguments rely on tools from floer homology and lattice theory they are primarily combinatorial in nature

intersection theory on the moduli space of curves and the matrix airy function we show that two natural approaches to quantum gravity coincide this identity is nontrivial and relies on the equivalence of each approach to kdv equations we also investigate related mathematical problems

some applications of gabai s internal hierarchy any haken 3 manifold possibly with boundary consisting of tori can be transformed into a surface s 1 by a series of splitting and regluing along incompressible surfaces this fact was proved by gabai as an application of his sutured manifold theory the first half of this paper provides a few technical details in the proof in the second half of this paper some applications of gabai s theorem to heegaard floer homology are given we refine the known results about the thurson norm and fibrations we also give some classification results for floer simple knots in manifolds with positive b 1

une theorie combinatoire des series formelles abstract this paper presents a combinatorial theory of formal power series the combinatorial interpretation of formal power series is based on the concept of species of structures a categorical approach is used to formulate it a new proof of cayley s formula for the number of labelled trees is given as well as a new combinatorial proof due to g labelle of lagrange s inversion formula polya s enumeration theory of isomorphism classes of structures is entirely renewed recursive methods for computing cycle index polynomials are described a combinatorial version of the implicit function theorem is stated and proved the paper ends with general considerations on the use of coalgebras in combinatorics

bilinear approach to multiuser second order statistics based blind channel estimation we present a bilinear approach to multiple input multiple output mimo blind channel estimation where products of the channel parameters are first estimated from the covariance of the received data the channel parameters are then obtained as the dominant eigenvectors of the outer product estimate necessary and sufficient identifiability conditions are presented for a single channel and extended to the multichannel case it is found that this technique can identify the channel to within a subspace ambiguity as long as the basis functions for the channel satisfy certain constraints regardless of the left invertability of the channel matrix one important requirement for identifiability is that the number of channel parameters is small compared with the channel length advantageously this is exactly the situation in which this algorithm has significantly lower complexity than competing parametric multiuser blind algorithms simulations show that the technique is applicable in situations where typical identifiability conditions fail common nulls a single symbol spaced channel and more users than channels these simulations are for the almost flat faded situation when the propagation delay spread is a fraction of the transmission pulse duration as might be found in current tdma systems comparisons are made when possible to a subspace method incorporating knowledge of the basis functions the bilinear approach requires significantly less computation but performs better than the subspace method at low snr especially for multiple users

floer simple manifolds and l space intervals abstract an oriented three manifold with torus boundary admits either no l space dehn filling a unique l space filling or an interval of l space fillings in the latter case which we call floer simple we construct an invariant which computes the interval of l space filling slopes from the turaev torsion and a given slope from the interval s interior as applications we give a new proof of the classification of seifert fibered l spaces over s 2 and prove a special case of a conjecture of boyer and clay 6 about l spaces formed by gluing three manifolds along a torus

blind identification with periodic modulation a time domain approach we propose a method for blind identification of finite impulse response fir channels with periodic modulation the time domain formulation in terms of block signals is simple compared with existing frequency domain formulations it is shown that the linear equations relating the products of channel coefficients and the autocorrelation matrix of the received signal can be further arranged into decoupled groups the arrangement reduces computations and improves accuracy of the solution it also leads to very simple identifiability conditions and a very natural formulation of the optimal modulating sequence selection problem the proposed optimal selection minimizes the effects of channel noise and error in autocorrelation matrix estimation it results in a consistent channel estimate when the channel noise is white simulation results show that the method yields good performance it compares favorably with an existing subspace modulation induced cyclostationarity method and it is robust with respect to channel order overestimation the effect of modulation period and threshold of the modulating sequence are also discussed

exceptional and cosmetic surgeries on knots we show that the bridge distance of a knot determines a lower bound on the genera of essential surfaces and heegaard surfaces in the manifolds that result from non trivial dehn surgeries on the knot in particular knots with high bridge distance do not admit non trivial non hyperbolic surgeries or non trivial cosmetic surgeries we further show that if a knot has bridge distance at least 3 then its bridge number is bounded above by a function of seifert genus or indeed by the genus of almost any essential surface or heegaard surface in the surgered manifold

combinatorial proofs of symmetry formulas for the generalized hypergeometric series abstract in this paper we introduce the notion of weakly isomorphic combinatorial models several symmetry formulas involving the generalized hypergeometric series for example the pfaff saalchutz identity which was first proved combinatorially by d foata are then proved by finding weak isomorphisms between models for the two sides of the identity this is applied to combinatorial models for hypergeometric orthogonal polynomials such as laguerre charlier meixner krawtchouk meixner pollaczek jacobi and hahn polynomials

context free grammars differential operators and formal power series abstract in this paper we introduce the concepts of a formal function over an alphabet and a formal derivative based on a set of substitution rules we call such a set of rules a context free grammar because these rules act like a context free grammar in the sense of a formal language given a context free grammar we can associate each formal function with an exponential formal power series in this way we obtain grammatical interpretations of addition multiplication and functional composition of formal power series a surprising fact about the grammatical calculus is that the composition of two formal power series enjoys a very simple grammatical representation we apply this method to obtain simple demonstrations of faa di bruno s formula and some identities concerning bell polynomials stirling numbers and symmetric functions in particular the lagrange inversion formula has a simple grammatical representation from this point of view one sees that cayley s formula on labeled trees is equivalent to the lagrange inversion formula

functors of white noise associated to characters of the infinite symmetric group the characters of the infinite symmetric group are extended to multiplicative positive definite functions on pair partitions by using an explicit representation due to versik and kerov the von neumann algebra generated by the fields with f in an infinite dimensional real hilbert space is infinite and the vacuum vector is not separating for a family depending on an integer n 1 an exclusion principle is found allowing at most identical particles on the same state the algebras are type factors functors of white noise are constructed and proved to be non equivalent for different values of n

object grammars and bijections a new systematic approach for the specification of bijections between sets of combinatorial objects is presented it is based on the notion of object grammars object grammars give recursive descriptions of objects and generalize context free grammars the study of a particular substitution in these object grammars confirms once more the key role of dyck words in the domain of enumerative and bijective combinatorics

decomposition spaces incidence algebras and mobius inversion i basic theory abstract this is the first in a series of papers devoted to the theory of decomposition spaces a general framework for incidence algebras and mobius inversion where algebraic identities are realised by taking homotopy cardinality of equivalences of groupoids a decomposition space is a simplicial groupoid satisfying an exactness condition weaker than the segal condition expressed in terms of active and inert maps in just as the segal condition expresses composition the new exactness condition expresses decomposition and there is an abundance of examples in combinatorics after establishing some basic properties of decomposition spaces the main result of this first paper shows that to any decomposition space there is an associated incidence coalgebra spanned by the space of 1 simplices and with coefficients in groupoids we take a functorial viewpoint throughout emphasising conservative ulf functors these induce coalgebra homomorphisms reduction procedures in the classical theory of incidence coalgebras are examples of this notion and many are examples of decalage of decomposition spaces an interesting class of examples of decomposition spaces beyond segal spaces is provided by hall algebras the waldhausen s construction of an abelian or stable infinity category is shown to be a decomposition space in the second paper in this series we impose further conditions on decomposition spaces to obtain a general mobius inversion principle and to ensure that the various constructions and results admit a homotopy cardinality in the third paper we show that the lawvere menni hopf algebra of mobius intervals is the homotopy cardinality of a certain universal decomposition space two further sequel papers deal with numerous examples from combinatorics note the notion of decomposition space was arrived at independently by dyckerhoff and kapranov 17 who call them unital 2 segal spaces our theory is quite orthogonal to theirs the definitions are different in spirit and appearance and the theories differ in terms of motivation examples and directions

periodic modulation based blind channel identification for single carrier block transmission with frequency domain equalization this paper proposes a periodic modulation based blind channel identification scheme for single carrier sc block transmission with frequency domain equalization fde the proposed approach relies on the block system model and exploits the circulant channel matrix structure after the cyclic prefix is removed it is shown that the set of linear equations relating the autocorrelation matrix of the block received signal and the product channel coefficients can be rearranged into one with a distinctive block circulant structure the identification equations thus obtained lead to a very simple identifiability condition as well as a natural formulation of the optimal modulating sequence design problem which based on the block circulant signal structure can be cast as a constrained quadratic problem that allows for a simple closed form solution the impact of the optimal modulating sequence on the peak to average power ratio papr is investigated also it is shown that the optimal sequence results in a consistent channel estimate irrespective of white noise perturbation pairwise error probability analysis is used to examine the equalization performance and based on which several design tradeoffs are discussed simulation results are used for illustrating the performance of the proposed method

holomorphic disks and knot invariants abstract we define a floer homology invariant for knots in an oriented three manifold closely related to the heegaard floer homologies for three manifolds defined in an earlier paper we set up basic properties of these invariants including an euler characteristic calculation and a description of the behavior under connected sums then we establish a relationship with hf for surgeries along the knot applications include calculation of hf of three manifolds obtained by surgeries on some special knots in s 3 and also calculation of hf for certain simple three manifolds which fiber over the circle

decomposable functors and the exponential principle abstract we develop a combinatorial theory for the operation of forming the logarithm of generating functions associated with covariant functors on the category of finite sets and bijective maps this leads to a rather general and flexible exponential principle for labeled combinatorial structures we also introduce the concept of a topos like category which turns out to be a convenient framework for the discussion of a wide range of applications a few of which are studied in detail

the q t gaussian process the q t fock space fq t h introduced in this paper is a deformation of the q fock space of bozejko and speicher the corresponding creation and annihilation operators now satisfy the commutation relation aq t f aq t g qaq t g aq t f f g htn turn mathjax off a defining relation of the chakrabarti jagannathan deformed quantum oscillator algebra the moments of the deformed gaussian element sq t h aq t h aq t h are encoded by the joint statistics of crossings and nestings in pair partitions the q 0 t specialization yields a natural single parameter deformation of the full boltzmann fock space of free probability with the corresponding semicircular measure variously encoded via the rogers ramanujan continued fraction the t airy function the t catalan numbers of carlitz riordan and the first order statistics of the reduced wigner process

a physicist s proof of the lagrange good multivariable inversion formula we provide a new proof inspired by quantum field theory of the lagrange good multivariable inversion formula

holomorphic disks and topological invariants for closed three manifolds the aim of this article is to introduce certain topological invariants for closed oriented three manifolds y equipped with a spiny structure given a heegaard splitting of y u 0o u u 1 these theories are variants of the lagrangian floer homology for the g fold symmetric product of relative to certain totally real subspaces associated to u 0 and u 1

a calculus for the random generation of labelled combinatorial structures a systematic approach to the random generation of labelled combinatorial objects is presented it applies to structures that are decomposable i e formally specifiable by grammars involving set sequence and cycle constructions a general strategy is developed for solving the random generation problem with two closely related types of methods for structures of size n the boustrophedonic algorithms exhibit a worst case behaviour of the form o n log n the sequential algorithms have worst case o n2 while offering good potential for optimizations in the average case the complexity model is in terms of arithmetic operations and both methods appeal to precomputed numerical table of linear size that can be computed in time o n2 a companion calculus permits systematically to compute the average case cost of the sequential generation algorithm associated to a given specification using optimizations dictated by the cost calculus several random generation algorithms of the sequential type are developed most of them have expected complexity 1 2n log n and are thus only slightly superlinear the approach is exemplified by the random generation of a number of classical combinatorial structures including cayley trees hierarchies the cycle decomposition of permutations binary trees functional graphs surjections and set partitions

cayley continuants in 1858 cayley considered a particular kind of tridiagonal determinants or continuants by a direct inspection of the first cases he conjectured an identity expressing these determinants in terms of certain other determinants considered by sylvester in 1854 then cayley proved the conjectured identity by induction but as he wrote he felt unsatisfied with his proof the main aim of this paper is to give a straightforward proof of cayley s identity using the method of formal series moreover we use this method and umbral calculus techniques to obtain several other identities cayley continuants appear in several contexts and in particular in enumerative combinatorics mittag leffler polynomials meixner polynomials of the first kind the falling and the raising factorials are just few instances of these continuants they can be interpreted in terms of weighted permutations moreover as we prove in this paper they also appear in the context of hankel determinants generated by certain catalan like numbers

the euler characteristic of the moduli space of curves let fg 1 g 1 be the mapping class group consisting of all isotopy classes of base point and orientation preserving homeomorphisms of a closed oriented surface f of genus g let 1 be its euler characteristic in the sense of wall that is z f i fgl f l z e f where f is any torsion free subgroup of finite index in f 1 and e is a contractible space on which f acts freely and properly discontinuously an example of such a space is the teichmiiller space 1 and g f can be interpreted as the orbifold euler characteristic of f i join the moduli space of curves of genus g with base point the purpose of this paper is to prove the following formula for f i

absolutely graded floer homologies and intersection forms for four manifolds with boundary abstract in ozsvath and szabo holomorphic triangles and invariants for smooth four manifolds math sg 0110169 2001 we introduced absolute gradings on the three manifold invariants developed in ozsvath and szabo holomorphic disks and topological invariants for closed three manifolds math sg 0101206 ann of math 2001 to appear coupled with the surgery long exact sequences we obtain a number of three and four dimensional applications of this absolute grading including strengthenings of the complexity bounds derived in ozsvath and szabo holomorphic disks and three manifold invariants properties and applications math sg 0105202 ann of math 2001 to appear restrictions on knots whose surgeries give rise to lens spaces and calculations of hf for a variety of three manifolds moreover we show how the structure of hf constrains the exoticness of definite intersection forms for smooth four manifolds which bound a given three manifold in addition to these new applications the techniques also provide alternate proofs of donaldson s diagonalizability theorem and the thom conjecture for cp 2

optimal two sided diagonal scaling for filter bank frames two sided diagonal scaling for transfer matrices is formulated an efficient algorithm is proposed to compute globally optimal solutions using the iterated bi section and linear matrix inequality lmi solver it is shown that the two sided scaling of filter bank fb frames can be implemented by the adjustment of channel gains and the periodic precoding of source signal and that the frame bound ratio of fb frames can be effectively improved by such scaling explicit formulas are established for both uniform and nonuniform fb frames including detail formulas for discrete weyl heisenberg frames and tree structured fbs discrete wavelets different examples show the effectiveness of the obtained results

holomorphic triangles and invariants for smooth four manifolds abstract in earlier articles the authors introduced invariants for closed oriented three manifolds defined using a variant of lagrangian floer homology in the symmetric products of riemann surfaces the aim of this article is to introduce invariants of oriented smooth four manifolds built using these floer homology groups this four dimensional theory also endows the corresponding three dimensional theories with additional structure an absolute grading of certain of its floer homology groups

three dimensional manifolds kleinian groups and hyperbolic geometry 1 a conjectural picture of 3 manifolds a major thrust of mathematics in the late 19th century in which poincare had a large role was the uniformization theory for riemann surfaces that every conformai structure on a closed oriented surface is represented by a riemannian metric of constant curvature for the typical case of negative euler characteristic genus greater than 1 such a metric gives a hyperbolic structure any small neighborhood in the surface is isometric to a neighborhood in the hyperbolic plane and the surface itself is the quotient of the hyperbolic plane by a discrete group of motions the exceptional cases the sphere and the torus have spherical and euclidean structures three manifolds are greatly more complicated than surfaces and i think it is fair to say that until recently there was little reason to expect any analogous theory for manifolds of dimension 3 or more except perhaps for the fact that so many 3 manifolds are beautiful the situation has changed so that i feel fairly confident in proposing the

truncation of unitary operads abstract we introduce truncation ideals of a k linear unitary symmetric operad and use them to study ideal structure growth property and to classify operads of low gelfand kirillov dimension

knot floer homology detects genus one fibred knots ozsv ath and szab o conjectured that knot floer homology detects fibred knots we propose a strategy to approach this conjecture based on contact topology and gabai s theory of sutured manifold decomposition we implement this strategy for genus one knots obtaining as a corollary that if rational surgery on a knot k gives the poincar e homology sphere sigma 2 3 5 then k is the left handed trefoil knot

higher dimensional algebra iii n categories and the algebra of opetopes abstract we give a definition of weak n categories based on the theory of operads we work with operads having an arbitrary set s of types or s operads and given such an operad o we denote its set of operations by elt o then for any s operad o there is an elt o operad o whose algebras are s operads over o letting i be the initial operad with a one element set of types and defining i 0 i i i 1 i i we call the operations of i n 1 the n dimensional opetopes opetopes form a category and presheaves on this category are called opetopic sets a weak n category is defined as an opetopic set with certain properties in a manner reminiscent of street s simplicial approach to weak categories similarly starting from an arbitrary operad o instead of i we define n coherent o algebras which are n times categorified analogs of algebras of o examples include monoidal n categories stable n categories virtual n functors and representable n prestacks we also describe how n coherent o algebra objects may be defined in any n 1 coherent o algebra

on coding labeled trees we consider the problem of coding labeled trees by means of strings of node labels different codes have been introduced in the literature by prufer neville and deo and micikevicius for all of them we show that both coding and decoding can be reduced to integer radix sorting closing several open problems within a unified framework that can be applied both in a sequential and in a parallel setting our sequential coding and decoding schemes require optimal o n time when applied to n node trees yielding the first linear time decoding algorithm for a code presented by neville these schemes can be parallelized on the erew pram model so as to work in o logn time with cost o n or o nlogn depending on the code and on the operation in all cases they either match or improve the performances of the best ad hoc approaches known so far

dual operators and lagrange inversion in several variables the original lagrange inversion formula which gives explicitly the inverse under composition of a formal series was obtained by lagrange in 1770 through formal computations involving logarithms of inlmite products see lagrange 121 there exists an extensive literature on various versions of the inversion formula obtained by algebraic analytic and combinatorial methods comtet 3 gives a survey and an ample bibliography during the last ten years there have appeared several papers on generalizations and new proofs of the inversion formula in 1974 abhyankar obtained an inversion formula using algebraic methods see bass connell and wright 11 several authors have related lagrange inversion with rota s finite operator calculus 151 for example joni 8 garsia and joni 4 hofhauer 7 and roman and rota 14 joyal and labelle used a combinatorial theory of formal series to obtain inversion formulas see 9 l i and viskov 161 used ideas from lie algebra theory to prove formulas similar to abhyankar s in the present paper we use operator methods to obtain inversion formulas in several variables that generalize the formulas of abhyankar joni and viskov we get our results studying an algebra with involution of linear operators on the algebra of formal laurent series in several indeterminates we also show that by means of an anti isomorphism of operator algebras which we call the operator bore1 transform the study of finite operator calculus can be reduced to the study of certain groups of operators on the algebra of formal laurent series our approach may be considered as an algebraic analogue of the complex variable methods used by good 5 to obtain the lagrange inversion formula as a consequence of the change of variables theorem for the

a hopf laboratory for symmetric functions an analysis of symmetric function theory is given from the perspective of the underlying hopf and bi algebraic structures these are presented explicitly in terms of standard symmetric function operations particular attention is focused on laplace pairing sweedler cohomology for 1 and 2 cochains and twisted products rota cliffordizations induced by branching operators in the symmetric function context the latter are shown to include the algebras of symmetric functions of orthogonal and symplectic type a commentary on related issues in the combinatorial approach to quantum field theory is given