Related papers: Pattern Avoidance for Random Permutations

We consider a random permutation drawn from the set of permutations of length $n$ that avoid some given set of patterns of length 3. We show that the number of occurrences of another pattern $\sigma$ has a limit distribution, after suitable…

We present a new approach to the problem of enumerating permutations of length n that avoid a fixed consecutive pattern of length m. We use this idea to give explicit upper and lower bounds on the number of permutations avoiding a pattern…

We study random uniform permutations in an important class of pattern-avoiding permutations: the separable permutations. We describe the asymptotics of the number of occurrences of any fixed given pattern in such a random permutation in…

We use various combinatorial and probabilistic techniques to study growth rates for the probability that a random permutation from the Mallows distribution avoids consecutive patterns. The Mallows distribution behaves like a $q$-analogue of…

There is a deep connection between permutations and trees. Certain sub-structures of permutations, called sub-permutations, bijectively map to sub-trees of binary increasing trees. This opens a powerful tool set to study enumerative and…

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, the authors of a recent paper showed that the expected number of…

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…

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 set up a new notion of local convergence for permutations and we prove a characterization in terms of proportions of \emph{consecutive} pattern occurrences. We also characterize random limiting objects for this new topology introducing a…

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 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…

Permutons are probability measures on the unit square with uniform marginals that provide a natural way to describe limits of permutations. We are interested in the permuton limits for permutations sampled uniformly from certain…

Let $X_1,X_2,...,X_n$ be a sequence of independent or locally dependent random variables taking values in $\mathbb{Z}_+$. In this paper, we derive sharp bounds, via a new probabilistic method, for the total variation distance between the…

We consider permutations avoiding a pattern of length three under the family of Mallows distributions. In particular, for any pattern $\tau\in S_3-\{321\}$, we obtain rather precise results on the asymptotic probability as $n\to\infty$ that…

We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called $\mu$-random permutations. We also introduce and study a new general class of…

We study Mallows random permutations conditioned to avoid a given pattern $\alpha$ of length~$3$. When the bias parameter is of the form $e^{\beta/n}$, we prove that these permutations converge to a non-trivial explicit deterministic…

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…

We consider the approximation of a convolution of possibly different probability measures by (compound) Poisson distributions and also by related signed measures of higher order. We present new total variation bounds having a better…

We prove limit theorems for the number of fixed points occurring in a random pattern-avoiding permutation distributed according to a one-parameter family of biased distributions. The bias parameter exponentially tilts the distribution…

This paper presents a collection of experimental results regarding permutation pattern avoidance, focusing on cases where there are "many" patterns to be avoided.