Related papers: Centrosymmetric Permutations and Involutions Avoid…

We show that cyclic permutations avoiding $321$ are precisely those permutations whose image under the fundamental bijection avoid a set of vincular patterns. We do this by using pattern functions and arrow patterns, in combination with the…

Multidimensional permutations, or $d$-permutations, are represented by their diagrams on $[n]^d$ such that there exists exactly one point per hyperplane $x_i$ that satisfies $x_i= j$ for $i \in [d]$ and $j \in [n]$. Bonichon and Morel…

We investigate permutations and involutions that avoid a pattern of length three and have a {\em unique} longest increasing subsequence.

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…

Let $\pi$ be a cyclic permutation that can be expressed in its one-line form as $\pi = \pi_1\pi_2 \cdot\cdot\cdot \pi_n$ and in its standard cycle form as $\pi = (c_1,c_2, ..., c_n)$ where $c_1=1$. Archer et al. introduced the notion of…

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 characterize discrete (anti-)unitary symmetries and their non-invertible generalizations in $2+1$d topological quantum field theories (TQFTs) through their actions on line operators and fusion spaces. We explain all possible sources of…

In this paper, we compute the distributions of the statistic number of crossings over permutations avoiding one of the pairs $\{321,231\}$, $\{123,132\}$ and $\{123,213\}$. The obtained results are new combinatorial interpretations of two…

We consider asymptotics of set partition pattern avoidance in the sense of Klazar. One of the results of this paper extends work of Alweiss, and finds a classification for set partitions $\pi$ such that the number of set partitions of $[n]$…

Recall that an excedance of a permutation $\pi$ is any position $i$ such that $\pi_i > i$. Inspired by the work of Hopkins, McConville and Propp (Elec. J. Comb., 2017) on sorting using toppling, we say that a permutation is toppleable if it…

Combinatorial aspects of multivariate diagonal invariants of the symmetric group are studied. As a consequence it is proved the existence of a multivariate extension of the classical Robinson-Schensted correspondence. Further byproduct are…

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.

An $n\times n$ matrix $C$ is said to be {\it centrosymmetric} if it satisfies the relation $JCJ=C$, where $J$ is the $n\times n$ counteridentity matrix. Centrosymmetric matrices have a rich eigenstructure that has been studied extensively…

We study the spectrum of the Markov matrix of the totally asymmetric exclusion process (TASEP) on a one-dimensional periodic lattice at ARBITRARY filling. Although the system does not possess obvious symmetries except translation…

The concept of centrally symmetric configurations of integer matrices is introduced. We study the problem when the toric ring of a centrally symmetric configuration is normal as well as is Gorenstein. In addition, Gr\"obner bases of toric…

We investigate a supersymmetric generalisation of topological recursion from two perspectives: algebraic and geometric. The algebraic side concerns a recursive structure encoded in modules of a super Virasoro algebra, and the geometric…

We consider square matrices A that commute with a fixed square matrix K, both with entries in a field F not of characteristic 2. When K^2=I, Tao and Yasuda defined A to be generalized centrosymmetric with respect to K. When K^2=-I, we…

We show that the principal order ideal below an element w in the Bruhat order on involutions in a symmetric group is a Boolean lattice if and only if w avoids the patterns 4321, 45312 and 456123. Similar criteria for signed permutations are…

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…

We consider a symmetric quiver with relations. Its (symmetric) representations of a fixed symmetric dimension vector are encoded in the (symmetric) representation varieties. The orbits by a (symmetric) base change group action are the…