bluuebunny/crossref_metadata_2025_split huggingface dataset:
Extending from bijections between marked occurrences of patterns to all occurrences of patterns
Authors: Remmel Jeffrey , Tiefenbruck Mark 
Published: August 2021

We consider two recent open problems stating that certain statistics on various sets of combinatorial objects are equidistributed. The first, posed by Anders Claesson and Svante Linusson, relates nestings in matchings on $\{1,2,\ldots,2n\}$ to occurrences of a certain pattern in permutations in $S_n$. The second, posed by Miles Jones and Jeffrey Remmel, relates occurrences of a large class of consecutive permutation patterns to occurrences of the same pattern in the cycles of permutations. We develop a general method that solves both of these problems and many more. We further employ the Garsia-Milne involution principle to obtain purely bijective proofs of these results.
Nous considérons deux derniers problèmes ouverts indiquant que certaines statistiques sur les divers ensembles d'objets combinatoires sont équiréparties. La première, posée par Anders Claesson et Svante Linusson, concerne les imbrications dans des filtrages sur $\{1,2,\ldots,2n\}$ pour les occurrences d'un certain modèle de permutations dans $S_n$. La seconde, posée par Miles Jones et Jeffrey Remmel, concerne les occurrences d'une large classe de schémas de permutation consécutive aux évènements du même modèle dans les cycles de permutations. Nous développons une méthode générale qui résout ces deux problèmes et beaucoup plus. Nous avons également utiliser le principe d'involution Garsia-Milne pour obtenir des preuves purement bijectives de ces résultats.
Quasisymmetric Schur functions
Authors: Haglund James , Mason Sarah , Luoto Kurt , van Willigenburg Steph 
Published: August 2021

We introduce a new basis for the algebra of quasisymmetric functions that naturally partitions Schur functions, called quasisymmetric Schur functions. We describe their expansion in terms of fundamental quasisymmetric functions and determine when a quasisymmetric Schur function is equal to a fundamental quasisymmetric function. We conclude by describing a Pieri rule for quasisymmetric Schur functions that naturally generalizes the Pieri rule for Schur functions.
Nous étudions une nouvelle base des fonctions quasisymétriques, les fonctions de quasiSchur. Ces fonctions sont obtenues en spécialisant les fonctions de Macdonald dissymétrique. Nous décrivons les compositions que donne une simple fonction quasisymétriques. Nous décrivons aussi une règle par certaines fonctions de Schur.
Double Schubert polynomials for the classical Lie groups
Authors: Ikeda Takeshi , Mihalcea Leonardo , Naruse Hiroshi 
Published: August 2021

For each infinite series of the classical Lie groups of type $B$, $C$ or $D$, we introduce a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank. These polynomials represent the Schubert classes in the equivariant cohomology of the corresponding flag variety. They satisfy a stability property, and are a natural extension of the (single) Schubert polynomials of Billey and Haiman, which represent non-equivariant Schubert classes. When indexed by maximal Grassmannian elements of the Weyl group, these polynomials are equal to the factorial analogues of Schur $Q$- or $P$-functions defined earlier by Ivanov.
Pour chaque série infinie des groupe de Lie classiques de type $B$,$C$ ou $D$, nous présentons une famille de polynômes indexées par de éléments de groupe de Weyl correspondant de rang infini. Ces polynômes représentent des classes de Schubert dans la cohomologie équivariante des variétés de drapeaux. Ils ont une certain propriété de stabilité, et ils étendent naturellement des polynômes Schubert (simples) de Billey et Haiman, que représentent des classes de Schubert dans la cohomologie non-équivariante. Quand ils sont indexées par des éléments Grassmanniennes de groupes de Weyl, ces polynômes sont égaux à des analogues factorielles de fonctions $Q$ et $P$ de Schur, étudiées auparavant par Ivanov.
Skew domino Schensted algorithm and sign-imbalance
Authors: Kim Jang Soo 
Published: August 2021

Using growth diagrams, we define a skew domino Schensted algorithm which is a domino analogue of the "Robinson-Schensted algorithm for skew tableaux'' due to Sagan and Stanley. The color-to-spin property of Shimozono and White is extended. As an application, we give a simple generating function for a weighted sum of skew domino tableaux whose special case is a generalization of Stanley's sign-imbalance formula. The generating function gives a method to calculate the generalized sign-imbalance formula.
Nous définissons, à partir de diagrammes de croissances, un algorithme de Schensted pour les dominos gauches. Cet algorithme est un analogue de l'algorithme de Schensted pour les tableaux gauches dû à Sagan et Stanley. Nous généralisons la propriété couleur-à-spin de Shimozono et White. Comme application, nous présentons une fonction génératrice simple pour une somme pondérée de tableaux de dominos gauches qui, dans un cas particulier, généralise la formule de "sign-imbalance'' de Stanley. La fonction génératrice donne aussi lieu à une méthode permettant de calculer la formule de "sign-imbalance''.
New bijective links on planar maps
Authors: Fusy Eric 
Published: August 2021

This article describes new bijective links on planar maps, which are of incremental complexity and present original features. The first two bijections $\Phi _{1,2}$ are correspondences on oriented planar maps. They can be considered as variations on the classical edge-poset construction for bipolar orientations on graphs, suitably adapted so as to operate only on the embeddings in a simple local way. In turn, $\Phi_{1,2}$ yield two new bijections $F_{1,2}$ between families of (rooted) maps. (i) By identifying maps with specific constrained orientations, $\Phi_2 \circ \Phi_1$ specialises to a bijection $F_1$ between 2-connected maps and irreducible triangulations; (ii) $F_1$ gives rise to a bijection $F_2$ between loopless maps and triangulations, observing that these decompose respectively into 2-connected maps and into irreducible triangulations in a parallel way.
Cet article décrit de nouveaux liens bijectifs sur les cartes planaires. Nos constructions sont de complexité croissante et présentent des caractéristiques originales. Les deux premières bijections $\Phi _{1,2}$ portent sur des cartes orientées. Elle peuvent être vues comme des variations sur une construction classique de posets sans $N$ à partir d'orientations bipolaires, adaptées ici pour opérer de manière très simple sur le plongement. Les bijections $\Phi _{1,2}$ entrainent à leur tour deux nouvelles bijections $F_{1,2}$ entre familles de cartes (enracinées). (i) En identifiant les cartes avec certaines orientations contraintes, $\Phi_2 \circ \Phi_1$ se spécialise en une bijection $F_1$ entre cartes 2-connexes et triangulations irréductibles, (ii) $F_1$ induit une bijection $F_2$ entre cartes sans boucles et triangulations, qui se décomposent respectivement en cartes 2-connexes et en triangulations irréductibles de manière parallèle.
Bijections for Permutation Tableaux
Authors: Corteel Sylvie , Nadeau Philippe 
Published: August 2021

In this paper we propose a new bijection between permutation tableaux and permutations. This bijection shows how natural statistics on the tableaux are equidistributed to classical statistics on permutations: descents, RL-minima and pattern enumerations. We then use the bijection, and a related encoding of tableaux by words, to prove results about the enumeration of permutations with a fixed number of 31-2 patterns, and to define subclasses of permutation tableaux that are in bijection with set partitions. An extended version of this work is available in [6].
Dans cet article nous donnons une bijection entre les tableaux de permutations et les permutations. Cette bijection montre comment des statistiques naturelles sur les tableaux sont équidistribuées avec des statistiques classiques sur les permutations: descentes, minima de droite à gauche et motifs. Cette bijection nous sert ensuite, à l'aide d'un certain codage des tableaux par des mots, à donner des résultats sur l'énumération de permutations avec un nombre fixé de motifs 31-2, et à déterminer certaines sous-classes de tableaux en bijection avec les partitions d'ensembles. Une version étendue de ce travail est disponible [6].
On the link pattern distribution of quarter-turn symmetric FPL configurations
Authors: Duchon Philippe 
Published: August 2021

We present new conjectures on the distribution of link patterns for fully-packed loop (FPL) configurations that are invariant, or almost invariant, under a quarter turn rotation, extending previous conjectures of Razumov and Stroganov and of de Gier. We prove a special case, showing that the link pattern that is conjectured to be the rarest does have the prescribed probability. As a byproduct, we get a formula for the enumeration of a new class of quasi-symmetry of plane partitions.
Nous présentons de nouvelles conjectures portant sur la distribution des schémas de couplage des configurations de boucles compactes (FPL) invariantes, ou presque invariantes, par une rotation d'un quart de tour. Ces nouvelles conjectures étendent des conjectures précédentes dues à Razumov et Stroganov et à de Gier. Dans chaque cas, nous prouvons un cas particulier, en démontrant que le schéma de couplage conjecturé pour être le plus rare a effectivement la probabilité prédite. Nous obtenons également une formule pour l'énumération d'une nouvelle classe de quasi-symétrie de partitions planes.
Foreword to the special issue dedicated to the tenth ''Journées montoises d'informatique théorique''
Authors: Bruyère Véronique , Rigo Michel 
Published: August 2021

Held at the Institute of Mathematics of the University of Liège, Liège, September 8―11, 2004
This special issue of Discrete Mathematics & Theoretical Computer Science is dedicated to the tenth "Journées montoises d'informatique théorique" conference (Mons theoretical computer science days) which was held, for the first time, at the Institute of Mathematics of the University of Liège, Belgium, From 8th to 11th September 2004. Previous editions of this conference took place in Mons 1990, 1992, 1994, 1998, in Rouen 1991, in Bordeaux 1993, Marseille 1995, Marne-La-Vallée 2000 and Montpellier 2002.<p> This tenth edition can be considered as a widely international one. We were lucky to have almost 85 participants from fourteen different countries: Austria, Belgium, Burkina Faso, Canada, Czech republic, Finland, France, Germany, Israel, Italy, Japan, Norway, Poland and Portugal. The main proportion of researchers participating to this event was coming from France and Italy where a long tradition of combinatorics on words is well established. During four days, 42 contributed talks and 7 invited talks were given, the main topics being combinatorics on words, numeration systems, automata and formal languages theory, coding theory, verification, bio-informatics, number theory, grammars, text algorithms, symbolic dynamics and tilings. The invited speakers were: J. Cassaigne (CNRS, Luminy-Marseille), D. Caucal (IRISIA-CNRS, Rennes), C. Frougny (LIAFA, Université Paris 8), T. Helleseth (University of Bergen), S. Langerman (FNRS, Université Libre de Bruxelles), F. Neven (Limburgs Universitair Centrum, Diepenbeek), M.-F. Sagot (Inria Rhône-Alpes, Université Lyon I).<p> We would like to thanks all the participants, the invited speakers and the anonymous referees who made possible this event and special issue. Each paper has been refereed using high scientific standard by two independent referees. Readers of this special issue may wonder why it took so long to obtain it. We have encountered some problems with the formerly chosen journal and for the benefit of the contributors to this issue, we have chosen Discrete Mathematics & Theoretical Computer Science to publish their work.
On the critical exponent of generalized Thue-Morse words
Authors: Massé Alexandre B. , Brlek Srečko , Glen Amy , Labbé Sébastien 
Published: August 2021

Automata, Logic and Semantics
For certain generalized Thue-Morse words t, we compute the critical exponent, i.e., the supremum of the set of rational numbers that are exponents of powers in t, and determine exactly the occurrences of powers realizing it.
Interaction properties of relational periods
Authors: Halava Vesa , Harju Tero , Kärki Tomi 
Published: August 2021

Automata, Logic and Semantics
We consider relational periods where the relation is a compatibility relation on words induced by a relation on letters. We introduce three types of periods, namely global, external and local relational periods, and we compare their properties by proving variants of the theorem of Fine and Wilf for these periods.
On symmetric structures of order two
Authors: Bousquet Michel , Lamathe Cédric 
Published: August 2021

Combinatorics
Let (w_n)0 < n be the sequence known as Integer Sequence A047749 In this paper, we show that the integer w_n enumerates various kinds of symmetric structures of order two. We ﬁrst consider ternary trees having a reflexive symmetry and we relate all symmetric combinatorial objects by means of bijection. We then generalize the symmetric structures and correspondences to an infinite family of symmetric objects.
A determinant of Stirling cycle numbers counts unlabeled acyclic single-source automata
Authors: Callan David 
Published: August 2021

Combinatorics
We show that a determinant of Stirling cycle numbers counts unlabeled acyclic single-source automata. The proof involves a bijection from these automata to certain marked lattice paths and a sign-reversing involution to evaluate the determinant. We also give a formula for the number of acyclic automata with a given set of sources.
On quadratic residue codes and hyperelliptic curves
Authors: Joyner David 
Published: August 2021

Combinatorics
For an odd prime p and each non-empty subset S ⊂ GF(p), consider the hyperelliptic curve X_S deﬁned by y^2 = f_s(x), where f_s(x) = \P_{a2S} (x-a). Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p), this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufﬁciently large primes p there exists a subset S ⊂ GF(p) for which the bound |X_S(GF(p))| > 1.39p holds. We also use the quasi-quadratic residue codes deﬁned below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the "Riemann hypothesis."
Sufficient conditions for labelled 0-1 laws
Authors: Burris Stanley N. , Yeats Karen A. 
Published: August 2021

Combinatorics
If F(x) = e^G(x), where F(x) = \Sum f(n)x^n and G(x) = \Sum g(n)x^n, with 0 ≤ g(n) = O(n^θn/n!), θ ∈ (0,1), and gcd(n : g(n) > 0) = 1, then f(n) = o(f(n − 1)). This gives an answer to Compton's request in Question 8.3 [Compton 1987] for an "easily verifiable sufficient condition" to show that an adequate class of structures has a labelled first-order 0-1 law, namely it sufﬁces to show that the labelled component count function is O(n^θn) for some θ ∈ (0,1). It also provides the means to recursively construct an adequate class of structures with a labelled 0-1 law but not an unlabelled 0-1 law, answering Compton's Question 8.4.
Total domination in K₅- and K₆-covered graphs
Authors: Favaron Odile , Karami H. , Sheikholeslami S. M. 
Published: August 2021

Graphs and Algorithms
A graph G is Kr-covered if each vertex of G is contained in a Kr-clique. Let $\gamma_t(G)$ denote the total domination number of G. It has been conjectured that every Kr-covered graph of order n with no Kr-component satisﬁes $\gamma_t(G) \le \frac{2n}{r+1}$. We prove that this conjecture is true for r = 5 and 6.
Leftmost derivations of propagating scattered context grammars: a new proof
Authors: Masopust Tomáš , Techet Jiří 
Published: August 2021

Automata, Logic and Semantics
In 1973, V. Virkkunen proved that propagating scattered context grammars which use leftmost derivations are as powerful as context-sensitive grammars. This paper brings a significantly simplified proof of this result.
Analysis of some parameters for random nodes in priority trees
Authors: Panholzer Alois 
Published: August 2021

Analysis of Algorithms
Priority trees are a certain data structure used for priority queue administration. Under the model that all permutations of the numbers 1, . . . , n are equally likely to construct a priority tree of size n we study the following parameters in size-n trees: depth of a random node, number of right edges to a random node, and number of descendants of a random node. For all parameters studied we give limiting distribution results.
Gray codes avoiding matchings
Authors: Dimitrov Darko , Dvořák Tomáš , Gregor Petr , Škrekovski Riste 
Published: August 2021

Graphs and Algorithms
A (cyclic) n-bit Gray code is a (cyclic) ordering of all 2(n) binary strings of length n such that consecutive strings differ in a single bit. Equivalently, an n-bit Gray code can be viewed as a Hamiltonian path of the n-dimensional hypercube Q(n), and a cyclic Gray code as a Hamiltonian cycle of Q(n). In this paper we study (cyclic) Gray codes avoiding a given set of faulty edges that form a matching. Given a matching M and two vertices u, v of Q(n), n >= 4, our main result provides a necessary and sufficient condition, expressed in terms of forbidden configurations for M, for the existence of a Gray code between u and v that avoids M. As a corollary. we obtain a similar characterization for a cyclic Gray code avoiding M. In particular, in the case that M is a perfect matching, Q(n) has a (cyclic) Gray code that avoids M if and only if Q(n) - M is a connected graph. This complements a recent result of Fink, who proved that every perfect matching of Q(n) can be extended to a Hamiltonian cycle. Furthermore, our results imply that the problem of Hamilionicity of Q(n) with faulty edges, which is NP-complete in general, becomes polynomial for up to 2(n-1) edges provided they form a matching.
Adjoint functors and tree duality
Authors: Foniok Jan , Tardif Claude 
Published: August 2021

Graphs and Algorithms
A family T of digraphs is a complete set of obstructions for a digraph H if for an arbitrary digraph G the existence of a homomorphism from G to H is equivalent to the non-existence of a homomorphism from any member of T to G. A digraph H is said to have tree duality if there exists a complete set of obstructions T consisting of orientations of trees. We show that if H has tree duality, then its arc graph delta H also has tree duality, and we derive a family of tree obstructions for delta H from the obstructions for H. Furthermore we generalise our result to right adjoint functors on categories of relational structures. We show that these functors always preserve tree duality, as well as polynomial CSPs and the existence of near-unanimity functions.
Ore and Erdős type conditions for long cycles in balanced bipartite graphs
Authors: Adamus Janusz , Adamus Lech 
Published: August 2021

Graphs and Algorithms
We conjecture Ore and Erdős type criteria for a balanced bipartite graph of order 2n to contain a long cycle C(2n-2k), where 0 <= k < n/2. For k = 0, these are the classical hamiltonicity criteria of Moon and Moser. The main two results of the paper assert that our conjectures hold for k = 1 as well.
On-line extensible bin packing with unequal bin sizes
Authors: Ye Deshi , Zhang Guochuan 
Published: August 2021

Analysis of Algorithms
In the extensible bin packing problem we are asked to pack a set of items into a given number of bins, each with an original size. However, the original bin sizes can be extended if necessary. The goal is to minimize the total size of the bins. We consider the problem with unequal (original) bin sizes and give the complete analysis on a list scheduling algorithm (LS). Namely we present tight bounds of LS for every collection of original bin sizes and every number of bins. We further show better on-line algorithms for the two-bin case and the three-bin case. Interestingly, it is proved that the on-line algorithms have better competitive ratios for unequal bins than for equal bins. Some variants of the problem are also discussed.
Structure of spanning trees on the two-dimensional Sierpinski gasket
Authors: Chang Shu-Chiuan , Chen Lung-Chi 
Published: August 2021

Combinatorics
Consider spanning trees on the two-dimensional Sierpinski gasket SG(n) where stage n is a non-negative integer. For any given vertex x of SG(n), we derive rigorously the probability distribution of the degree j ∈{1,2,3,4} at the vertex and its value in the infinite n limit. Adding up such probabilities of all the vertices divided by the number of vertices, we obtain the average probability distribution of the degree j. The corresponding limiting distribution φj gives the average probability that a vertex is connected by 1, 2, 3 or 4 bond(s) among all the spanning tree configurations. They are rational numbers given as φ1=10957/40464, φ2=6626035/13636368, φ3=2943139/13636368, φ4=124895/4545456.
Contextual partial commutations
Authors: Choffrut Christian , Mercas Robert 
Published: August 2021

special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications
We consider the monoid T with the presentation < a, b; aab = aba > which is ''close'' to trace monoids. We prove two different types of results. First, we give a combinatorial description of the lexicographically minimum and maximum representatives of their congruence classes in the free monoid \a, b\* and solve the classical equations, such as commutation and conjugacy in T. Then we study the closure properties of the two subfamilies of the rational subsets of T whose lexicographically minimum and maximum cross-sections respectively, are rational in \a, b\*.
Linear Time Recognition Algorithms and Structure Theorems for Bipartite Tolerance Graphs and Bipartite Probe Interval Graphs
Authors: Brown David E. , Busch Arthur H. , Isaak Garth 
Published: August 2021

Graphs and Algorithms
A graph is a probe interval graph if its vertices can be partitioned into probes and nonprobes with an interval associated to each vertex so that vertices are adjacent if and only if their corresponding intervals intersect and at least one of them is a probe. A graph G = (V, E) is a tolerance graph if each vertex v is an element of V can be associated to an interval I(v) of the real line and a positive real number t(v) such that uv is an element of E if and only if vertical bar I(u) boolean AND I(v)vertical bar >= min \t(u), t(v)\. In this paper we present O(vertical bar V vertical bar + vertical bar E vertical bar) recognition algorithms for both bipartite probe interval graphs and bipartite tolerance graphs. We also give a new structural characterization for each class which follows from the algorithms.
Asymptotic variance of random symmetric digital search trees
Authors: Hwang Hsien-Kuei , Fuchs Michael , Zacharovas Vytas 
Published: August 2021

Dedicated to the 60th birthday of Philippe Flajolet
Asymptotics of the variances of many cost measures in random digital search trees are often notoriously messy and involved to obtain. A new approach is proposed to facilitate such an analysis for several shape parameters on random symmetric digital search trees. Our approach starts from a more careful normalization at the level of Poisson generating functions, which then provides an asymptotically equivalent approximation to the variance in question. Several new ingredients are also introduced such as a combined use of the Laplace and Mellin transforms and a simple, mechanical technique for justifying the analytic de-Poissonization procedures involved. The methodology we develop can be easily adapted to many other problems with an underlying binomial distribution. In particular, the less expected and somewhat surprising n (logn)(2)-variance for certain notions of total path-length is also clarified.