Related papers: Pattern avoidance in compositions and powers of pe…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
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 introduce a new boundedness condition for affine permutations, motivated by the fruitful concept of periodic boundary conditions in statistical physics. We study pattern avoidance in bounded affine permutations. In particular, we show…
Permutation Pattern Matching (or PPM) is a decision problem whose input is a pair of permutations $\pi$ and $\tau$, represented as sequences of integers, and the task is to determine whether $\tau$ contains a subsequence order-isomorphic to…
Following a question of J. Cooper, we study the expected number of occurrences of a given permutation pattern $q$ in permutations that avoid another given pattern $r$. In some cases, we find the pattern that occurs least often, (resp. most…
Let $F \subset S_k$ be a finite set of permutations and let $C_n(F)$ denote the number of permutations $\sigma$ in $S_n$ avoiding the set of patterns $F$. The Noonan-Zeilberger conjecture states that the sequence ${C_n(F)}$ is P-recursive.…
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 the scaling limits of a random…
The $\sigma$-machine was recently introduced by Cerbai, Claesson and Ferrari as a tool to gain a better insight on the problem of sorting permutations with two stacks in series. It consists of two consecutive stacks, which are restricted in…
We define a class L_{n, k} of permutations that generalizes alternating (up-down) permutations and give bijective proofs of certain pattern-avoidance results for this class. As a special case of our results, we give two bijections between…
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…
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…
A permutation $\sigma\in\mathfrak{S}_n$ is simsun if for all $k$, the subword of $\sigma$ restricted to $\{1,...,k\}$ does not have three consecutive decreasing elements. The permutation $\sigma$ is double simsun if both $\sigma$ and…
We consider the problem of bounding the number of permutations $\sigma\in S_n$ that avoid a fixed permutation $\pi\in S_k$ in specific indices given by a $k$-uniform hypergraph $\Lambda$. We obtain relatively sharp bounds in the case where…
The study of patterns in permutations in a very active area of current research. Klazar defined and studied an analogous notion of pattern for set partitions. We continue this work, finding exact formulas for the number of set partitions…
We say that a word $w$ on a totally ordered alphabet avoids the word $v$ if there are no subsequences in $w$ order-equivalent to $v$. In this paper we suggest a new approach to the enumeration of words on at most $k$ letters avoiding a…
We study groups generated by sets of pattern avoiding permutations. In the first part of the paper we prove some general results concerning the structure of such groups. In the second part we carry out a case-by-case analysis of groups…
We present four constructions of inversion sequences, and use them to compute the enumeration sequences of 24 classes of pattern-avoiding inversion sequences. This completes the enumeration of inversion sequences avoiding one or two…
We completely classify the asymptotic behavior of the number of alternating sign matrices classically avoiding a single permutation pattern, in the sense of [Johansson and Linusson 2007]. In particular, we give a uniform proof of an…
We consider the problem of enumerating permutations in the symmetric group on $n$ elements which avoid a given set of consecutive pattern $S$, and in particular computing asymptotics as $n$ tends to infinity. We develop a general method…
We study the structure of 01-matrices avoiding a pattern P as an interval minor. We focus on critical P-avoiders, i.e., on the P-avoiding matrices in which changing a 0-entry to a 1-entry always creates a copy of P as an interval minor. Let…