Foreword

<abstract xmlns="http://www.w3.org/1999/xhtml"> The excedance number for Sn is known to have an Eulerian distribution. Nevertheless, the classical proof uses descents rather than excedances. We present a direct proof based on a recursion which uses only excedances and extend it to the flag-excedance parameter defined on the group of colored permutations Gr,n = ℤr ≀ Sn. We have also computed the distribution of a variant of the flag-excedance number, and show that its enumeration uses the Stirling number of the second kind. Moreover, we show that the generating function of the flag-excedance number defined on ℤr ≀ Sn is symmetric, and its variant is log-concave on ℤr ≀ Sn.. </abstract>

The Jerusalem College of Technology 93721 Jerusalem, Israel

Department of Applied Mathematics Holon Institute of Technology 58102 Holon, Israel

Department of Mathematics University of Haifa 31905 Haifa, Israel

Department of Computer Sciences and Mathematics Ariel University 40700 Ariel, Israel

Recursions for the flag-excedance number in colored permutations groups

<abstract xmlns="http://www.w3.org/1999/xhtml"> In a recent paper [2], the authors provide enumerating results for equivalence classes of permutations modulo excedances. In this paper we investigate two other equivalence relations based on descents and left-to-right maxima. Enumerating results are presented for permutations, involutions, derangements, cycles and permutations avoiding one pattern of length three.</abstract>

Equivalence classes of permutations modulo descents and left-to-right maxima

<abstract xmlns="http://www.w3.org/1999/xhtml"> We study the construction and the enumeration of bit strings, or binary words in {0, 1}*, having more 1’s than 0’s and avoiding a set of Grand Dyck patterns which form a cross-bifix-free set. We give a particular jumping and marked succession rule which describes the growth of such words according to the number of 1’s. Then, we give the enumeration of the class by means of generating function. </abstract>

A generating function for bit strings with no Grand Dyck pattern matching

<abstract xmlns="http://www.w3.org/1999/xhtml"> We define an order relation over Sn considering the Robinson-Schensted bijection and the dominance order over Young tableaux. This order relation makes Sn(k k - 1...3 2 1) -the set of permutations of length n that avoid the pattern k k - 1...3 2 1, k ≤ n- a principal filter in Sn. We study in detail these order relations on Sn(321) and Sn(4321), finding order-isomorphisms between these sets and sets of lattice paths. </abstract>

The dominance order for permutations

<abstract xmlns="http://www.w3.org/1999/xhtml"> The Sand Pile Model (SPM) and its generalization, the Ice Pile Model (IPM), originate from physics and have various applications in the description of the evolution of granular systems. In this article, we deal with the enumeration and the exhaustive generation of the accessible configuration of the system. Our work is based on a new recursive decomposition theorem for SPM configurations using the notion of staircase bases. Based on this theorem, we provide a recursive formula for the enumeration of SPM(n) and a constant amortized time (CAT) algorithm for the generation of all SPM(n) configurations. The extension of the same approach to the Ice Pile Model is also discussed. </abstract>

roberto.mantaci@liafa.univ-paris-diderot.fr

A recursive structure of sand pile model and its applications

<abstract xmlns="http://www.w3.org/1999/xhtml"> Let λ be a partition of the positive integer n, selected uniformly at random among all such partitions. Corteel et al. (1999) proposed three different procedures of sampling parts of λ at random. They obtained limiting distributions of the multiplicity μn = μn(λ) of the randomly-chosen part as n → ∞. The asymptotic behavior of the part size σn = σn(λ), under these sampling conditions, was found by Fristedt (1993) and Mutafchiev (2014). All these results motivated us to study the relationship between the size and the multiplicity of a randomly-selected part of a random partition. We describe it obtaining the joint limiting distributions of (μn; σn), as n → ∞, for all these three sampling procedures. It turns out that different sampling plans lead to different limiting distributions for (μn; σn). Our results generalize those obtained earlier and confirm the known expressions for the marginal limiting distributions of μn and σn. </abstract>

Sampling parts of random integer partitions: a probabilistic and asymptotic analysis

<abstract xmlns="http://www.w3.org/1999/xhtml"> A sequence (an)n≥0 is k-automatic if there is a finite automaton that, on input n expressed in base k, reaches a state with output an. In this paper I will survey some recent advances concerning enumeration of various aspects of these sequences, such as the recurrence function, and the subword complexity (which counts the number of distinct blocks of length n). </abstract>

Enumeration and Automatic Sequences

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this note, we provide bijective proofs of some recent identities involving Stirling numbers of the second kind, as previously requested. Our arguments also yield generalizations in terms of a well known q-Stirling number.</abstract>

Combinatorial proofs of some Stirling number formulas

AHEAD OF PRINT

Volume 30 (2022): Issue 4 (December 2022)

Volume 30 (2022): Issue 3 (October 2022) Special issue dedicated to 70th anniversary of prof. Peter Tallos

Volume 30 (2022): Issue 2 (August 2022)

Volume 30 (2022): Issue 1 (June 2022)

Volume 29 (2020): Issue 1 (December 2020)

Volume 28 (2019): Issue 1 (October 2019)

Volume 27 (2018): Issue 2 (August 2018)

Volume 27 (2018): Issue 1 (July 2018)

Volume 26 (2017): Issue 1 (June 2017)

Volume 25 (2015): Issue 2 (December 2015)

Volume 25 (2015): Issue 1 (September 2015)

Pure Mathematics and Applications

 Pure Mathematics and Applications - section Algebra and Theoretical Computer Science - publishes original high quality articles of international relevance in the two disciplines of algebra and theoretical computer science. Specific topics include (but are not limited to) group and semigroup theory, commutative algebra, computational algebra, poset and lattice theory, linear algebra, theory of automata and formal languages, computational complexity, analysis of algorithms, game theory. In particular, articles in which interactions between algebra and theoretical computer science play a relevant role (i.e. techniques of either discipline are fundamental in obtaining results of the other) will be privileged. As a natural consequence of this fact, one of the disciplines which are more relevant to the journal is discrete mathematics, and more specifically enumerative and algebraic combinatorics, graph theory, discrete tomography, random and exhaustive generation, combinatorial order theory, bioinformatics, matroid theory, combinatorics on words.Papers about high quality applications of combinatorial methods to computer science (especially algorithms, data structures, and criptography), or special issues, completely devoted to a certain contemporary topic of high interest, are also published.  Pure Mathematics and Applications - section Mathematics of Optimization - publishes original research works, surveys, historical and biographical articles primarily on mathematics of optimization. Papers about high quality applications of mathematical methods to decision sciences (especially operations research, economics, games and control theory, actuarial and financial mathematics), or special issues, completely devoted to a certain contemporary topic of high interest are also published.  The journal contains two sections - one devoted to Algebra and Theoretical Computer Science, and second to Mathematics of Optimization. The published articles of the first section focus on algebra and theoretical computer science, with interactions between algebra and theoretical computer science in particular. The second section publishes research works, surveys, historical and biographical articles primarily on mathematics of optimization.  Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process.  Target group  researchers in the fields of algebra and theoretical computer science 