row polynomial matrices of riordan arrays abstract let r r n k n k 0 be a riordan array define the row polynomials r n q k 0 n r n k q k and the row polynomial matrix r q r n k q n k 0 by r n k q j k n r n j q j k then r q is also a riordan array with the r n q located on the leftmost column of r q in this paper we investigate combinatorial properties of the matrix r q and the sequence r n q n 0 including their characterizations the q total positivity of r q and the q log convexity of r n q n 0

hopf algebra of the planar binary trees is a sub hopf algebra there is a basis qn of soln such that the composite map k qn soln k sn has the following property its linear dual k sn k qn is induced by a set theoretic map sn qn in between sn and qn there is an intermediate set yn which is made of planar binary trees with n vertices for instance for n 3 the number of elements in s3 y3 and q3 is 6 5 and 4 respectively the projection from sn to qn is the composite of two maps sn w yn w qn article no ai981759

row sums and alternating sums of riordan arrays abstract here we use row sum generating functions and alternating sum generating functions to characterize riordan arrays and subgroups of the riordan group numerous applications and examples are presented which include the construction of girard waring type identities we also show the extensions to weighted sum generating functions called the expected value generating functions of riordan arrays

rayleigh quotients for coupled free vibrations abstract based upon the general thin shell theory and basic equations in fluid mechanics three kinds of rayleigh s quotients for coupled fluid structure free vibrations are developed for arbitrary tanks fully or partially filled with i inviscid irrotational and incompressible fluid with the effects of free surface waves neglected ii inviscid irrotational and incompressible fluid with the effects of free surface waves considered and iii inviscid irrotational and compressible fluid respectively theorems concerning stationary values of the respective rayleigh quotients are proved by utilizing the generalized orthogonality relationships for the wet modes of these three kinds of liquid containing tank models thus the mathematical foundations for calculating approximately the eigenvalues and eigenvectors in fluid structure interaction systems are presented an example of applying the rayleigh quotient to predicting a natural frequency of a cylindrical tank partially filled with fluid is provided and the result is compared with that available

twisted descent algebras and the solomon tits algebra abstract the notion of descent algebra of a bialgebra is lifted to the barratt joyal setting of twisted bialgebras the new twisted descent algebras share many properties with their classical counterparts for example there are twisted analogs of classical lie idempotents and of the peak algebra moreover the universal twisted descent algebra is equipped with two products and a coproduct and there is a fundamental rule linking all three this algebra is shown to be naturally related to the geometry of the coxeter complex of type a

shuffle compatible permutation statistics abstract since the early work of richard stanley it has been observed that several permutation statistics have a remarkable property with respect to shuffles of permutations we formalize this notion of a shuffle compatible permutation statistic and introduce the shuffle algebra of a shuffle compatible permutation statistic which encodes the distribution of the statistic over shuffles of permutations this paper develops a theory of shuffle compatibility for descent statistics statistics that depend only on the descent set and length which has close connections to the theory of p partitions quasisymmetric functions and noncommutative symmetric functions we use our framework to prove that many descent statistics are shuffle compatible and to give explicit descriptions of their shuffle algebras thus unifying past results of stanley gessel stembridge aguiar bergeron nyman and petersen

free vibration analysis of cylindrical tanks partially filled with liquid abstract a simple but effective modal solution based on the underlying ideas of the hierarchical finite element method is presented for evaluating the free vibration characteristics of vertical thin circular cylindrical shells partially or completely filled with liquid and subjected to any variationally consistent set of boundary conditions on the lower and upper boundaries effects of static liquid pressure in plane inertias and liquid free surface motions are taken into account the solution of the shell problem is obtained through a procedure in which sander s shell equations are transformed into a new system of first order ordinary differential equations which are solved by the galerkin error minimization procedure the system variables are those quantities which appear in the boundary conditions on a rotationally symmetric edge of a cylindrical shell the liquid is taken as non viscous and incompressible and the coupling between the deformable shell and this medium is taken into account the solution for the liquid velocity potential is assumed as a sum of two sets of linear combinations of suitable harmonic functions which satisfy laplace equation and the relevant boundary conditions this procedure leads to a determinantal equation for the determination of the shell and liquid natural frequencies and the associated mode shapes application of the method to a few selected cases and comparisons of the numerical results with those obtained by other theories and from experiments are found to be good and demonstrate the effectiveness and accuracy of the present methodology

peak quasisymmetric functions and eulerian enumeration abstract via duality of hopf algebras there is a direct association between peak quasisymmetric functions and enumeration of chains in eulerian posets we study this association explicitly showing that the notion of cd index long studied in the context of convex polytopes and eulerian posets arises as the dual basis to a natural basis of peak quasisymmetric functions introduced by stembridge thus eulerian posets having a nonnegative cd index for example face lattices of convex polytopes correspond to peak quasisymmetric functions having a nonnegative representation in terms of this basis we diagonalize the operator that associates the basis of descent sets for all quasisymmetric functions to that of peak sets for the algebra of peak functions and study the g polynomial for eulerian posets as an algebra homomorphism

lie idempotent algebras abstract besides the inner product inherited from each symmetric group algebra ksn on the direct sum ks nksn a second convolution product arises from the hopf algebra structure on ks for any subalgebra a of ks for both the inner and the convolution product it is shown that the lie idempotent algebra l a of a generated by all lie idempotents in a with respect to the convolution product is also closed under inner products its nth homogeneous component l n a is thus a subalgebra of ksn for all n provided that a contains a lie idempotent in ksk for all k n solomon s descent algebra d n is a subalgebra of l n a in this case a number of results on the structure of l n a is derived including a description of its jacobson radical its principal indecomposables and its cartan invariants furthermore solomon s epimorphism from d n onto the ring of class functions clk sn of sn extends to an epimorphism of algebras c n l n a cl k s n additional results are obtained concerning a bialgebra structure of l a in the particular case of a n d n this amounts to a new approach to several well known results on d n

enriched p partitions and peak algebras abstract we develop a more general view of stembridge s enriched p partitions and use this theory to outline the structure of peak algebras for the symmetric group and the hyperoctahedral group initially we focus on commutative peak algebras spanned by sums of permutations with the same number of peaks where we consider several variations on the definition of peak whereas stembridge s enriched p partitions are related to quasisymmetric functions the dual coalgebra of solomon s type a descent algebra our generalized enriched p partitions are related to type b quasisymmetric functions the dual coalgebra of solomon s type b descent algebra using these functions we move on to explore non commutative peak algebras spanned by sums of permutations with the same set of peaks while some of these algebras have been studied before our approach gives explicit structure constants with a combinatorial description

representation theory of 0 hecke clifford algebras abstract the representation theory of 0 hecke clifford algebras as a degenerate case is not semisimple and also with rich combinatorial meaning bergeron hivert and thibon have proved that the grothendieck ring of the category of finitely generated supermodules of 0 hecke clifford algebras is isomorphic to the algebra of peak quasisymmetric functions defined by stembridge in this paper we further study the category of finitely generated projective supermodules and clarify the correspondence between it and the peak algebra of symmetric groups in particular two kinds of restriction rules for induced projective supermodules are obtained after that we consider the corresponding heisenberg double and its fock representation to prove that the ring of peak quasisymmetric functions is free over its subring of symmetric functions spanned by schur s q functions

hydroelastic vibration of a circular plate submerged in a bounded compressible fluid abstract an analytical method for the linear free vibration of a circular plate submerged in a fluid was developed by the rayleigh ritz method based on the fourier bessel series expansion it is assumed that the plate is clamped at an offcenter location of a rigid cylindrical container and the fluid bisected by the plate in the container is non viscous and compressible since a combination of the dry modal functions of the circular plate can approximate the wet vibration modes the functions were used to form a set of linearly independent functions of the rayleigh ritz method it was found that the theoretical results could predict well the fluid coupled natural frequencies with excellent accuracy compared with the finite element analysis results the effects of the fluid compressibility and the offcenter distance on the natural frequencies were also observed

matrix characterizations of riordan arrays abstract here we discuss two matrix characterizations of riordan arrays p matrix characterization and a matrix characterization p matrix is an extension of the stieltjes matrix defined in 28 and the production matrix defined in 8 by modifying the marked succession rule introduced in 21 a combinatorial interpretation of the p matrix is given the p matrix characterizations of some subgroups of riordan group are presented which are used to find some algebraic structures of the subgroups we also give the p matrix characterizations of the inverse of a riordan array and the product of two riordan arrays a matrix characterization is defined in 20 and it is proved to be a useful tool for a riordan array while on the other side the a sequence characterization is very complex sometimes by using the fundamental theorem of riordan arrays a method of construction of a matrix characterizations from riordan arrays is given the converse process is also discussed several examples and applications of two matrix characterizations are presented

eigenvalue problems for vibrating structures coupled with quiescent fluids with free surface abstract vibrations of plates shells and plate shell systems coupled with sloshing quiescent and inviscid fluid have been advantageously studied by inserting the sloshing condition into the eigenvalue problem here a formulation of this particular eigenvalue problem for symmetric matrices is obtained in fact in the previous studies this technique has given eigenvalue problems for non symmetric matrices for which the problem of the existence of complex eigenvalues arises the present analysis deals with compressible and incompressible fluids and the discretization of the system is obtained by using the rayleigh ritz method the rayleigh quotient of the system is manipulated to obtain expressions suitable for symmetric formulations of the eigenvalue problem in particular the rayleigh quotient is transformed into a simpler expression where the potential energies of the compressible fluid and free surface waves do not appear the method is applied to a vertical simply supported circular cylindrical shell partially filled by an incompressible sloshing liquid a case with large interaction between sloshing and bulging modes is considered and interesting phenomena are observed

schroder matrix as inverse of delannoy matrix abstract using riordan arrays we introduce a generalized delannoy matrix by weighted delannoy numbers it turns out that delannoy matrix pascal matrix and fibonacci matrix are all special cases of the generalized delannoy matrices meanwhile schroder matrix and catalan matrix also arise in involving inverses of the generalized delannoy matrices these connections are the focus of our paper the half of generalized delannoy matrix is also considered in addition we obtain a combinatorial interpretation for the generalized fibonacci numbers

coupled vibrations of cantilever cylindrical shells partially submerged in fluids with continuous simply connected and non convex domain abstract the approach developed in the present paper is applied for the coupled vibration analysis of a cantilever cylindrical shell partially submerged in a fluid with a continuous simply connected and non convex domain the shell is partially and concentrically submerged in a rigid cylindrical container partially filled by a fluid which is assumed to be incompressible and inviscid the velocity potential for fluid motion is formulated in terms of eigenfunction expansions using the collocation method the interaction between the fluid and the structure takes into account by using the compatibility requirement along the wet surface of the shell and the rayleigh ritz method is used to calculate natural frequencies and modes of the coupled system the validity of the developed theoretical method is verified by comparing the results with those obtained from the finite element analysis furthermore the effects of submergence depth radial distance between shell and container and circumferential wavenumbers on the natural frequencies and modes of the coupled system are investigated

representing polynomials as characteristic polynomials via the stieltjes transform abstract the stieltjes transform s a of an infinite lower triangular matrix a with nonzero diagonal entries is defined by s a a 1 a where a is the matrix obtained from a by deleting its initial row in this paper we express a sequence of polynomials as the characteristic polynomials of the stieltjes transforms using a highly structured infinite lower triangular matrix called a riordan matrix as a result computation of the zeros of such polynomials becomes amenable to iterative methods for computing eigenvalues or to eigenvalue location theorems such as the gersgorin theorem we also describe a finite analog of the polynomial correspondence and its relationship to eigenvalue regions as an application the recurrence relations for several polynomial sequences are obtained using the stieltjes transform

functions and jordan canonical forms of riordan matrices abstract this paper collects results about riordan arrays in the framework of matrix functions actually the following methodology applies to any square matrix m m with exactly one eigenvalue of algebraic multiplicity m n generalized lagrange bases are used to construct hermite polynomials that interpolate a family of functions moreover we show a parallel application of such functions via jordan canonical forms and case studies are given

orthogonality of wet modes in coupled vibrations of cylindrical shells containing liquids abstract on the basis of flugge s thin shell equations and a linear potential flow theory general orthogonality relations of wet modes for cylindrical storage vessels containing liquids are established some applications of these relations to dynamic response analysis under arbitrary excitation are also discussed

random walks on quasisymmetric functions abstract conditions are provided under which an endomorphism on quasisymmetric functions gives rise to a left random walk on the descent algebra which is also a lumping of a left random walk on permutations spectral results are also obtained several important random walks are now realized this way stanley s qs distribution results from endomorphisms given by evaluation maps a shuffles result from the a th convolution power of the universal character and the tchebyshev operator of the second kind introduced recently by ehrenborg and readdy yields traditional riffle shuffles a conjecture of ehrenborg regarding the spectra for a family of random walks on ab words is proven a theorem of stembridge from the theory of enriched p partitions is also recovered as a special case

shift operators defined in the riordan group and their applications abstract in this paper we discuss a linear operator t defined in riordan group r by using the upper shift matrix u and lower shift matrix u t namely for each r r t r u r u t some isomorphic properties of the operator t and the structures of its range sets for different domains are studied by using the operator t and the properties of bell subgroup of r the riordan type chu vandermonde identities and the riordan equivalent identities of format last theorem and beal conjecture are shown the applications of the shift operators to the complementary riordan arrays and to the riordan involutions and riordan pseudo involutions are also presented

the peak algebra and the descent algebras of types b and d we show the existence of a unital subalgebra n of the symmetric group algebra linearly spanned by sums of permutations with a common peak set which we call the peak algebra we show that n is the image of the descent algebra of type b under the map to the descent algebra of type a which forgets the signs and also the image of the descent algebra of type d the algebra n contains a two sided ideal n which is defined in terms of interior peaks this object was introduced in previous work by nyman 2003 we find that it is the image of certain ideals of the descent algebras of types b and d we derive an exact sequence of the form 0 n n n 2 0 we obtain this and many other properties of the peak algebra and its peak ideal by first establishing analogous results for signed permutations and then forgetting the signs in particular we construct two new commutative semisimple subalgebras of the descent algebra of dimensions n and n 2 1 by grouping permutations according to their number of peaks or interior peaks we discuss the hopf algebraic structures that exist on the direct sums of the spaces n and n over n 0 and explain the connection with previous work of stembridge 1997 we also obtain new properties of his descents to peaks map and construct a type b analog

a decomposition of solomon s descent algebra abstract a descent class in the symmetric group sn is the collection of permutations with a given descent set it was shown by l solomon j algebra41 1976 255 264 that the product in the group algebra q sn of two descent classes is a linear combination of descent classes thus descent classes generate a subalgebra of q sn we refer to it here as solomon s descent algebra and denote it by n this algebra is not semisimple but it has a faithul representation in terms of upper triangular matrices the main goal of this paper is a decomposition of its multiplicative structure it develops that n acts in a natural way on the so called lie monomials this action has a purely combinatorial description and is a crucial tool in the construction of a complete set of indecomposable representations of n in particular we obtain a natural basis of irreducible orthogonal idempotents indexed by partitions of n for the quotient n n natural bases of nilpotents and idempotents for the subspaces e ne for two arbitrary partitions and are also constructed and the dimensions of these spaces are given a combinatorial interpretation in terms of the so called decreasing factorization of an arbitary word into a product of lyndon words

a unified approach for the catalan matrices by using riordan arrays abstract we study generalized catalan matrices based on the riordan array and fuss catalan numbers a unified combinatorial interpretation for the entries of the generalized catalan matrices is presented by means of m dyck paths some properties and examples of the generalized catalan matrices are given including a new convolution formula for the generalized catalan numbers finally we present applications of generalized catalan matrices to the problems in counting the hill free and lower peak free m dyck paths

the campbell hausdorff near ring over n a topological view abstract the famous baker campbell hausdorff series defines a group composition on the set of the so called grouplike elements of a completed free lie algebra as we can find in p cartier s paper on the campbell hausdorff formula in 1956 according to a baider and r c churchill we call this group the campbell hausdorff group over the alphabet x of the free lie algebra by a certain coproduct and certain bialgebra endomorphisms of the free associative algebra over a set x which should be at most countably infinite we get an alternative realisation of this campbell hausdorff group this realisation is much more comfortable to deal with than the classical one the usual composition of endomorphisms gives a near ring structure to this group in this paper we consider a metric on the campbell hausdorff near ring over the alphabet n and the compatibility of this metric with the near ring compositions and we make some topological remarks

parametric catalan numbers and catalan triangles abstract here presented a generalization of catalan numbers and catalan triangles associated with two parameters based on the sequence characterization of bell type riordan arrays among the generalized catalan numbers a class of large generalized catalan numbers and a class of small generalized catalan numbers are defined which can be considered as an extension of large schroder numbers and small schroder numbers respectively using the characterization sequences of bell type riordan arrays some properties and expressions including the taylor expansions of generalized catalan numbers are given a few combinatorial interpretations of the generalized catalan numbers are also provided finally a generalized motzkin numbers and motzkin triangles are defined similarly an interrelationship among parametrical catalan triangle pascal triangle and motzkin triangle is presented based on the sequence characterization of bell type riordan arrays

identities induced by riordan arrays historically there exist two versions of the riordan array concept the older one better known as recursive matrix consists of bi infinite matrices d n k n k is an element of z k n implies d n k 0 deals with formal laurent series and has been mainly used to study algebraic properties of such matrices the more recent version consists of infinite lower triangular arrays d n k n k is an element of n k n implies d n k 0 deals with formal power series and has been used to study combinatorial problems here we show that every riordan array induces two characteristic combinatorial sums in three parameters n k m is an element of z these parameters can he specialized and generate an indefinite number of other combinatorial identities which are valid in the hi infinite realm of recursive matrices

the shifted poirier reutenauer algebra based on the shifted schensted correspondence and the shifted knuth equivalence a shifted analog of the poirier reutenauer algebra is introduced it is a right coideal subalgebra of the poirier reutenauer algebra and turns out to be a higher lift of schur s p functions its close relations with the peak subalgebra and the stembridge algebra of peak functions are also uncovered

free vibration of a partially liquid filled and submerged horizontal cylindrical shell abstract the dynamic characteristics i e natural frequencies and mode shapes of a partially filled and or submerged horizontal cylindrical shell are examined in this investigation it is assumed that the fluid is ideal and fluid forces are associated with inertial effects only namely the fluid pressure on the wetted surface of the structure is in phase with the structural acceleration the in vacuo dynamic characteristics of the cylindrical shell are obtained using standard finite element software in the wet part of the analysis it is assumed that the shell structure preserves its in vacuo mode shapes when in contact with the contained and or surrounding fluid and that each mode shape gives rise to a corresponding surface pressure distribution of the shell the fluid structure interaction effects are calculated in terms of generalized added masses using a boundary integral equation method together with the method of images in order to impose an appropriate boundary condition on the free surface to assess the influence of the contained and or surrounding fluid on the dynamic behaviour of the shell structure the wet natural frequencies and associated mode shapes were calculated and compared with available experimental measurements

some algebraic structure of the riordan group abstract in this paper we highlight some of the algebraic properties of the riordan group we present some new properties and provide proofs for some known properties for instance proofs of properties of the power bell and derivative subgroups are presented we also give a new property for generating stochastic riordan matrices which are elements of the stochastic riordan subgroup centralizers stabilizers and certain riordan group isomorphisms are also given and proved we conclude by proving some properties connecting similar riordan matrices and pseudo involutions in the riordan group

riordan arrays and related polynomial sequences abstract in this paper we generalize the results due to luzon and moron and present a characterization of the generalized riordan arrays using this characterization we establish a recurrence for the generalized sheffer sequences and study some special types of polynomial sequences including the generalized lucas u sequence and v sequence and the generalized humbert polynomial sequence in particular by appealing to the factorizations of riordan arrays the umbral composition of polynomial sequences and the hadamard product of series we establish various relations among these polynomial sequences thus we give a unified approach to some well known polynomial sequences appeared in combinatorics and the theory of special functions

duality between quasi symmetrical functions and the solomon descent algebra abstract the ring qsym of quasi symmetric functions is naturally the dual of the solomon descent algebra the product and the two coproducts of the first extending those of the symmetric functions correspond to a coproduct and two products of the second which are defined by restriction from the symmetric group algebra a consequence is that qsym is a free commutative algebra

an algebraic structure for faber polynomials abstract let be the set of functions convergent for all z 1 with a laurent series of the form f z z n 0 a n z n in this paper we prove that the set of faber polynomial sequences over and the set of their normalized kth derivative sequences form groups which are isomorphic to the hitting time subgroup and the bell k subgroup of the riordan group respectively further a relationship between such faber polynomial sequences and lucas and sheffer polynomial sequences is derived

linearized formulation for fluid structure interaction application to the linear dynamic response of a pressurized elastic structure containing a fluid with a free surface abstract to control the linear vibrations of structures partially filled with liquids is of prime importance in various industries such as aerospace naval civil and nuclear engineering it is proposed here to investigate a linearized formulation adapted to a rational computation of the vibrations of such coupled systems its particularity is to be fully lagrangian since it considers the fluid displacement field with respect to a static equilibrium configuration as the natural variable describing the fluid motion as classically done in structural dynamics as the coupled system considered here is weakly damped in the low frequency domain low modal density the analysis of the vibrations of the associated undamped conservative system constitutes the main objective of this paper one originality of the present formulation is to take into account the effect of the pressurization of the tank on the dynamics of the system particularly in the case of a compressible liquid we propose here a new way of deriving the linearized equations of the coupled problem involving a deformable structure and an inner inviscid liquid with a free surface a review of the classical case considering a heavy incompressible liquid is followed by an application to the new case involving a light compressible liquid a solution procedure in the frequency domain is proposed and a numerical discretization using the finite element method is discussed in order to reduce the computational costs an appropriate reduced order matrix model using modal synthesis approach is also presented

a proof of solomon s rule abstract we put forward a proof of solomon s rule in terms of matrices for multiplication in the descent algebra of the symmetric group our proof exploits the graphs that we can obtain from all the subsets of the set of transpositions i i 1 n 1i 1

orthogonality of wet modes in coupled vibration abstract the orthogonality property of wet modes for arbitrary storage vessels filled or partially filled with compressible fluid is investigated by means of love s thin shell equations and a linear potential flow theory the proof shows that the wet modes do possess the orthogonality property for all kinds of fluid filled tanks with zero boundary energy conditions when incompressible fluid is considered and the effect of free surface waves is neglected it is pointed out that there is another kind of orthogonality relationship among wet modes when a compressible fluid is contained or and the effect of the free surface waves is considered

the peak algebra of the symmetric group revisited abstract the linear span p n of the sums of all permutations in the symmetric group sn with a given set of peaks is a sub algebra of the symmetric group algebra due to nyman this peak algebra is a left ideal of the descent algebra d n and the direct sum p of all p n is a hopf sub algebra of the direct sum d of all d n dual to the stembridge algebra of peak functions in our self contained approach peak counterparts of several results on the descent algebra are established including a simple combinatorial characterization of the algebra p n an algebraic characterization of p n based on the action on the poincare birkhoff witt basis of the free associative algebra the display of peak variants of the classical lie idempotents an eulerian type sub algebra of p n a description of the jacobson radical of p n and its nil potency index of the principal indecomposable and irreducible p n modules and of the cartan matrix of p n furthermore it is shown that the primitive lie algebra of p is free and that p is its enveloping algebra

riordan arrays associated with laurent series and generalized sheffer type groups a relationship between a pair of laurent series and riordan arrays is formulated in addition a type of generalized sheffer groups is defined by using riordan arrays with respect to power series with non zero coefficients the isomorphism between a generalized sheffer group and the group of the riordan arrays associated with laurent series is established furthermore appell associated bell and hitting time subgroups of the groups are defined and discussed a relationship between the generalized sheffer groups with respect to different type of power series is presented the equivalence of the defined riordan array pairs and generalized stirling number pairs is given a type of inverse relations of various series is constructed by using pairs of riordan arrays finally several applications involving various arrays polynomial sequences special formulas and identities are also presented as illustrative examples

bijections and the riordan group one of the cornerstone ideas in mathematics is to take a problem and to look at it in a bigger space in this paper we examine combinatorial sequences in the context of the riordan group various subgroups of the riordan group each give us a different view of the original sequence in many cases this leads to both a combinatorial interpretation and to eco rewriting rules in this paper we will concentrate on just four of the subgroups of the riordan group to demonstrate some of the possibilities of this approach

structural properties of riordan matrices and extending the matrices abstract we consider an infinite lower triangular matrix l l n k n k n 0 and a sequence n n n 0 called the a b sequence such that every element l n 1 k 1 except lying in column 0 can be expressed as l n 1 k 1 i 0 n k m i l n ai k bi 0 0 where a and b are integers with a b m 0 and b 0 this concept generalizes the a sequence of a riordan matrix as a result we explore several structural properties of riordan matrices by means of a b sequences in particular if b

log convexity of aigner catalan riordan numbers abstract let t t n k n k 0 be an infinite lower triangular matrix defined by t 0 0 1 t n 1 0 j 0 n z j t n j t n 1 k 1 j k n a j k t n j for n k 0 where all z j a j k are nonnegative and a j k 0 unless j k 0 we show that the sequence t n 0 n 0 is log convex if the coefficient matrix a is tp 2 where z 0 z 1 z 2 and a a i j i j 0 this gives a unified proof of the log convexity of many well known combinatorial sequences including the catalan numbers the motzkin numbers the central binomial coefficients the schroder numbers the bell numbers and so on

addition formulas for polynomials built on classical combinatorial sequences abstract we prove addition formulas for some polynomials built on combinatorial sequences catalan numbers bell numbers or related to classical polynomials hermite these relations give also an explicit computation of several hankel determinants

recurrence relations for the sheffer sequences abstract in this paper using the production matrix of an exponential riordan array g t f t we give a recurrence relation for the sheffer sequence for the ordered pair g t f t we also develop a new determinant representation for the general term of the sheffer sequence as applications determinant expressions for some classical sheffer polynomial sequences are derived

a technique for the systematic choice of admissible functions in the rayleigh ritz method abstract a simple and systematic choice of admissible functions which are the eigenfunctions of the closest simple problem extracted from the one considered is proposed the extracted problem must be less constrained than the original one in other words it must be a problem where some constraints or other complications e g added masses are eliminated elastic constraints replace the eliminated rigid ones the convergence is also analyzed this approach has practical applications when it is possible to extract a problem with eigenfunctions expressed in closed form it also allows a very simple calculation of the potential energy of the system solutions for several cases involving beams are given in order to show the power of the method application of the method to circular plates and shells is also addressed

an algebraic characterization of the set of succession rules qui dedit beneficium taceat narret qui accepit seneca merci maurice in this paper we will give a formal description of succession rules in terms of linear operators satisfying certain conditions this representation allows us to introduce a system of well defined operations into the set of succession rules and then to tackle problems of combinatorial enumeration simply by using operators instead of generating functions finally we will suggest several open problems whose solution should lead to an algebraic characterization of the set of succession rules

total positivity of recursive matrices abstract let a a n k n k 0 be an infinite lower triangular matrix defined by the recurrence a 0 0 1 a n 1 k r k a n k 1 s k a n k t k 1 a n k 1 where a n k 0 unless n k 0 and r k s k t k are all nonnegative many well known combinatorial triangles are such matrices including the pascal triangle the stirling triangle of the second kind the bell triangle the catalan triangles of aigner and shapiro we present some sufficient conditions such that the recursive matrix a is totally positive as applications we give the total positivity of the above mentioned combinatorial triangles in a unified approach