Related papers: Pattern avoidance in non-crossing and non-nesting …
In a recent paper, Bona and Smith define the notion of \textit{strong avoidance}, in which a permutation and its square both avoid a given pattern. In this paper, we generalize this idea to what we call \textit{chain avoidance}. We say that…
Permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics, computer science and biology. In this paper we study fixed points of both 123- and…
A permutation $\pi$ strongly avoids the pattern $\tau$ if both $\pi$ and $\pi^2$ avoid $\tau$. In this paper, we enumerate permutations of size $n$ that strongly avoid the pattern 132. This enumeration allows us to prove a conjecture that…
In this paper, we characterize and enumerate pattern-avoiding permutations composed of only 3-cycles. In particular, we answer the question for the six patterns of length 3. We find that the number of permutations composed of $n$ 3-cycles…
We extend earlier work of the same author to enumerate alternating permutations avoiding the permutation pattern 2143. We use a generating tree approach to construct a recursive bijection between the set A_{2n}(2143) of alternating…
Let I_n(\pi) denote the number of involutions in the symmetric group S_n which avoid the permutation \pi. We say that two permutations \alpha,\beta\in\S{j} may be exchanged if for every n, k, and ordering \tau of j+1,...,k, we have…
In this paper we study pattern avoidance for affine permutations. In particular, we show that for a given pattern p, there are only finitely many affine permutations in $\widetilde{S}_n$ that avoid p if and only if p avoids the pattern 321.…
This paper completes a project to enumerate permutations avoiding a triple T of 4-letter patterns, in the sense of classical pattern avoidance, for every T. There are 317 symmetry classes of such triples T and previous papers have…
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…
We find the generating function for the class of all permutations that avoid the patterns 3124 and 4312 by showing that it is an inflation of the union of two geometric grid classes.
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 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…
This paper presents a collection of experimental results regarding permutation pattern avoidance, focusing on cases where there are "many" patterns to be avoided.
We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is itself a Dumont permutation of the second kind. We also consider some combinatorial statistics on Dumont permutations avoiding…
The equidistribution of many crossing and nesting statistics exists in several combinatorial objects like matchings, set partitions, permutations, and embedded labelled graphs. The involutions switching nesting and crossing numbers for set…
How many matchings on the vertex set V={1,2,...,2n} avoid a given configuration of three edges? Chen, Deng and Du have shown that the number of matchings that avoid three nesting edges is equal to the number of matchings avoiding three…
We study the distribution of the statistics 'number of fixed points' and 'number of excedances' in permutations avoiding subsets of patterns of length 3. We solve all the cases of simultaneous avoidance of more than one pattern, giving…
Babson and Steingr\`imsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Subsequently, Claesson presented a complete solution for the…
We consider a random permutation drawn from the set of 132-avoiding permutations of length $n$ and show that the number of occurrences of another pattern $\sigma$ has a limit distribution, after scaling by $n^{\lambda(\sigma)/2}$ where…
We study permutations $p$ such that both $p$ and $p^2$ avoid a given pattern $q$. We obtain a generating function for the case of $q=312$ (equivalently, $q=231$), we prove that if $q$ is monotone increasing, then above a certain length,…