Related papers: Permutations that strongly avoid 132

A frequent topic in the study of pattern avoidance is identifying when two sets of patterns $\Pi, \Pi'$ are Wilf equivalent, that is, when $|\text{Av}_n(\Pi)| = |\text{Av}_n(\Pi')|$ for all $n$. In recent work of Dokos et al. the notion of…

We initiate the study of limit shapes for random permutations avoiding a given pattern. Specifically, for patterns of length 3, we obtain delicate results on the asymptotics of distributions of positions of numbers in the permutations. We…

This short paper is concerned with the enumeration of permutations avoiding the following four patterns: $2431$, $4231$, $1432$ and $4132$. Using a bijective construction, we prove that these permutations are counted by the central binomial…

There are several versions of permutation pattern avoidance that have arisen in the literature, and some known examples of two different types of pattern avoidance coinciding. In this paper, we examine barred patterns and vincular patterns.…

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 distributions of the lengths of the longest monotone and alternating subsequences in classes of permutations of size $n$ that avoid a specific pattern or set of patterns, with respect to the uniform distribution on each such…

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…

We continue our study of a new boundedness condition for affine permutations, motivated by the fruitful concept of periodic boundary conditions in statistical physics. We focus on bounded affine permutations of size $N$ that avoid the…

The large Schroder numbers are known to count several classes of permutations avoiding two 4-letter patterns. Here we show they count another family of permutations, those whose left to right minima decomposition, when reversed, is…

We define a variation of Stirling permutations, called quasi-Stirling permutations, to be permutations on the multiset $\{1,1,2,2,\ldots, n,n\}$ that avoid the patterns 1212 and 2121. Their study is motivated by a known relationship between…

Let $\pi_n$ be a uniformly chosen random permutation on $[n]$. Using an analysis of the probability that two overlapping consecutive $k$-permutations are order isomorphic, we show that the expected number of distinct consecutive patterns in…

The Permutation Pattern Matching problem, asking whether a pattern permutation $\pi$ is contained in a permutation $\tau$, is known to be NP-complete. In this paper we present two polynomial time algorithms for special cases. The first…

We consider the distribution of the length of the longest subsequence avoiding a given pattern in a random permutation of length n. The well-studied case of a longest increasing subsequence corresponds to avoiding the pattern 21. We show…

We consider a few special cases of the more general question: How many permutations $\pi\in\mathcal{S}_n$ have the property that $\pi^2$ has $j$ descents for some $j$? In this paper, we first enumerate Grassmannian permutations $\pi$ by the…

We study a subset of permutations, where entries are restricted to having the same remainder as the index, modulo some integer $k \geq 2$. We show that when also imposing the classical 132- or 213-avoidance restriction on the permutations,…

We study the descent distribution over the set of centrosymmetric permutations that avoid the pattern of length 3. Our main tool in the most puzzling case, namely, $\tau=123$ and $n$ even, is a bijection that associates a Dyck prefix of…

We study pattern avoidance by combinatorial objects other than permutations, namely by ordered partitions of an integer and by permutations of a multiset. In the former case we determine the generating function explicitly, for integer…

Higher dimensional permutations are tuples of d-1 permutations that can be identified with a point set in a d-dimensional grid. In N. Bonichon and P.-J. Morel, {\it J. Integer Sequences} 25 (2022), several conjectures regarding the…

In the set of all patterns in $S_n$, it is clear that each k-pattern occurs equally often. If we instead restrict to the class of permutations avoiding a specific pattern, the situation quickly becomes more interesting. Mikl\'os B\'ona…

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…