Related papers: Avoidance of vincular patterns by flattened derang…
Catalan words are particular growth-restricted words counted by the eponymous integer sequence. In this article we consider Catalan words avoiding a pair of patterns of length 3, pursuing the recent initiating work of the first and last…
We develop the technique of reduced word manipulation to give a range of results concerning reduced words and permutations more generally. We prove a broad connection between pattern containment and reduced words, which specializes to our…
In the past decade, a lot of attention has been devoted to the enumera-tion of walks with prescribed steps confined to a convex cone. In two dimensions, this means counting walks in the first quadrant of the plane (possibly after a linear…
A redundant generating function is a generating function having terms which are not part of the solution of the original problem. We use redundant generating functions to study two path problems. In the first application we explain a…
Pattern avoiding machines were introduced recently by Claesson, Cerbai and Ferrari as a particular case of the two-stacks in series sorting device. They consist of two restricted stacks in series, ruled by a right-greedy procedure and the…
We have extended classical pattern avoidance to a new structure: multiple task-precedence posets whose Hasse diagrams have three levels, which we will call diamonds. The vertices of each diamond are assigned labels which are compatible with…
An inversion sequence of length $n$ is an integer sequence $(a_1, \ldots, a_n)$ such that $0 \le a_i < i$ for all $i$. The study of pattern-avoiding inversion sequences was initiated in 2015 by Mansour and Shattuck and in 2016 by Corteel,…
Sergey Kitaev has shown that the exponential generating function for permutations avoiding the generalized pattern $\sigma$-$k$, where $\sigma$ is a pattern without dashes and $k$ is one greater than the biggest element in $\sigma$, is…
In the past 20 years, the enumeration of plane lattice walks confined to a convex cone -- normalized into the first quadrant -- has received a lot of attention, stimulated the development of several original approaches, and led to a rich…
We enumerate the pattern class Av(2143,4231) and completely describe its permutations. The main tools are simple permutations and monotone grid classes.
We prove that any class of permutations defined by avoiding a partially ordered pattern (POP) with height at most two has a regular insertion encoding and thus has a rational generating function. Then, we use Combinatorial Exploration to…
In the last decade a huge amount of articles has been published studying pattern avoidance on permutations. From the point of view of enumeration, typically one tries to count permutations avoiding certain patterns according to their…
We review and extend what is known about the generating functions for consecutive pattern-avoiding permutations of length 4, 5 and beyond, and their asymptotic behaviour. There are respectively, seven length-4 and twenty-five length-5…
A permutation is called Grassmannian if it has at most one descent. In this paper, we investigate pattern avoidance and parity restrictions for such permutations. As our main result, we derive formulas for the enumeration of Grassmannian…
In this thesis, we introduced and carried out a combinatorial study of permutations that avoid one or two patterns of length 3 according to the statistic number of crossings. For this purpose, we manipulated a bijection of Elizalde and Pak…
We study the involutions belonging to the class of 321 avoiding permutations. We calculate the algebraic generating functions of the set containing the involutions avoiding 321 and of some of its subsets. Precisely we determine the…
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…
We solve three enumerative problems concerning families of planar maps. More precisely, we establish algebraic equations for the generating function of non-separable triangulations in which all vertices have degree at least d, for a certain…
We consider a random permutation drawn from the set of 321-avoiding permutations of length $n$ and show that the number of occurrences of another pattern $\sigma$ has a limit distribution, after scaling by $n^{m+\ell}$ where $m$ is the…
Let $\Delta =\{ \delta_1,\delta_2,...,\delta_m \} $ be a finite set of 2-connected patterns, i.e. graphs up to vertex relabelling. We study the generating function $D_{\Delta }(z,u_1,u_2,...,u_m),$ which counts polygon dissections and marks…