Related papers: On Ascent, Repetition and Descent Sequences
In this article, we provide a bijection between the set of inversion sequences avoiding the pattern 102 and the set of 2-Schr\"{o}der paths having neither peaks nor valleys and ending with a diagonal step. To achieve this, we introduce two…
Inspired by the definition of modified ascent sequences, we introduce a new class of integer sequences called revised ascent sequences. These sequences are defined as Cayley permutations where each entry is a leftmost occurrence if and only…
Let alpha = a_1 a_2 ... a_n be a sequence of nonnegative integers. The ascent set of alpha, Asc(alpha), consists of all indices k where a_{k+1} > a_k. An ascent sequence is alpha where the growth of the a_k is bounded by the elements of…
Catalan words are particular growth-restricted words over the set of non-negative integers, and they represent still another combinatorial class counted by the Catalan numbers. We study the distribution of descents on the sets of Catalan…
We count permutations avoiding a nonconsecutive instance of a two- or three-letter pattern, that is, the pattern may occur but only as consecutive entries in the permutation. Two-letter patterns give rise to the Fibonacci numbers. The…
We initiate a systematic study of pattern avoidance in rectangulations. We give a formal definition of such patterns and investigate rectangulations that avoid $\top$-like patterns - the pattern $\top$ and its rotations. For every $L…
As shown by Bousquet-M\'elou--Claesson--Dukes--Kitaev (2010), ascent sequences can be used to encode $({\bf2+2})$-free posets. It is known that ascent sequences are enumerated by the Fishburn numbers, which appear as the coefficients of the…
Recently, Yan and the first named author investigated systematically the enumeration of inversion or ascent sequences avoiding vincular patterns of length $3$, where two of the three letters are required to be adjacent. They established…
For L-convex polyominoes we give the asymptotics of the generating function coefficients, obtained by analysis of the coefficients derived from the functional equation given by Castiglione et al. \cite{CFMRR7}. For 201-avoiding ascent…
In this article, we study (102,000)-avoiding inversion sequences with a fixed number of distinct elements. By introducing simple H-paths, we derive the trivariate generating function for these inversion sequences with respect to their…
In 2011, Duncan and Steingr\'imsson conjectured that modified ascent sequences avoiding any of the patterns 212, 1212, 2132, 2213, 2231 and 2321 are counted by the Bell numbers. Furthermore, the distribution of the number of ascents is the…
Starting from some considerations we make about the relations between certain difference statistics and the classical permutation statistics we study permutations whose inversion number and excedance difference coincide. It turns out that…
This paper presents a bijection between ascent sequences and upper triangular matrices whose non-negative entries are such that all rows and columns contain at least one non-zero entry. We show the equivalence of several natural statistics…
Vincular and covincular patterns are generalizations of classical patterns allowing restrictions on the indices and values of the occurrences in a permutation. In this paper we study the integer sequences arising as the enumerations of…
The first problem addressed by this article is the enumeration of some families of pattern-avoiding inversion sequences. We solve some enumerative conjectures left open by the foundational work on the topics by Corteel et al., some of these…
We construct an intriguing bijection between $021$-avoiding inversion sequences and $(2413,4213)$-avoiding permutations, which proves a sextuple equidistribution involving double Eulerian statistics. Two interesting applications of this…
The Catalan numbers count many classes of combinatorial objects. The most emblematic such objects are probably the Dyck walks and the binary trees, and, whenever another class of combinatorial objects is counted by the Catalan numbers, it…
In 1916, MacMahon showed that permutations in $S_n$ with a fixed descent set $I$ are enumerated by a polynomial $d_I(n)$. Diaz-Lopez, Harris, Insko, Omar, and Sagan recently revived interest in this descent polynomial, and suggested the…
We consider the distribution of ascents, descents, peaks, valleys, double ascents, and double descents over permutations avoiding a set of patterns. Many of these statistics have already been studied over sets of permutations avoiding a…
A permutation is (1-23-4)-avoiding if it contains no four entries, increasing left to right, with the middle two adjacent in the permutation. Here we give a 2-variable recurrence for the number of such permutations, improving on the…