Related papers: Permutation patterns, Stanley symmetric functions …

We introduce and study a new random permutation model that generalizes the $k$-card minimum model defined by Travers and the Mallows model. We calculate the permuton limit of such a sequence of random permutations. As a corollary, we deduce…

We obtain new connections between permutation patterns and singularities of Schubert varieties, by giving a new characterization of Gorenstein varieties in terms of so called bivincular patterns. These are generalizations of classical…

We introduce the stack-sorting map $\text{SC}_\sigma$ that sorts, in a right-greedy manner, an input permutation through a stack that avoids some vincular pattern $\sigma$. The stack-sorting maps of Cerbai et al. in which the stack avoids a…

Let G be GL_N or SL_N as reductive linear algebraic group over a field k of positive characteristic p. We prove several results that were previously established only when N < 6 or p > 2^N. Let G act rationally on a finitely generated…

We extend classical results on simple varieties of trees (asymptotic enumeration, average behavior of tree parameters) to trees counted by their number of leaves. Motivated by genome comparison of related species, we then apply these…

In this paper we present a new compact expression of the elliptic genus of SL(2)/U(1)-supercoset theory by making use of the `spectral flow method' of the path-integral evaluation. This new expression is written in a form like a Poincare…

R. Stanley has found a nice combinatorial formula for characters of irreducible representations of the symmetric group of rectangular shape. Then, he has given a conjectural generalisation for any shape. Here, we will prove this formula…

Petrie symmetric functions $G(k,n)$, also known as truncated homogeneous symmetric functions or modular complete symmetric functions, form a class of symmetric functions interpolating between the elementary symmetric functions $e_n$ and the…

Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of k-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a…

Let k be an algebraically closed field of characteristic p>2. We compute the Weyl filtration multiplicities in indecomposable tilting modules and the decomposition numbers for the symplectic group over k in terms of cap-curl diagrams under…

We study the combinatorial properties of vexillary signed permutations, which are signed analogues of the vexillary permutations first considered by Lascoux and Sch\"utzenberger. We give several equivalent characterizations of vexillary…

We examine historic formulations of the spin-statistics theorem from a point of view that distinguishes between the observable consequences and the ``symmetrization postulate''. In particular, we make a critical analysis of concepts of…

We consider the well-studied pattern counting problem: given a permutation $\pi \in \mathbb{S}_n$ and an integer $k > 1$, count the number of order-isomorphic occurrences of every pattern $\tau \in \mathbb{S}_k$ in $\pi$. Our first result…

Let $\alpha$ range over the set of compositions. Dual immaculate quasisymmetric functions $\mathfrak{S}_\alpha^*$, introduced by Berg, Bergeron, Saliola, Serrano, and Zabrocki, provide a quasisymmetric analogue of Schur functions. They also…

David Little developed a combinatorial algorithm to study the Schur-positivity of Stanley symmetric functions and the Lascoux-Sch\"{u}tzenberger tree. We generalize this algorithm to affine Stanley symmetric functions.

We show that for any permutation $\pi$ there exists an integer $k_{\pi}$ such that every permutation avoiding $\pi$ as a pattern is a product of at most $k_{\pi}$ separable permutations. In other words, every strict class $\mathcal C$ of…

We introduce new natural generalizations of the classical descent and inversion statistics for permutations, called width-$k$ descents and width-$k$ inversions. These variations induce generalizations of the excedance and major statistics,…

Motivated by Stanley's conjecture on the multiplication of Jack symmetric functions, we prove a couple of identities showing that skew Jack symmetric functions are semi-invariant up to translation and rotation of a $\pi$ angle of the skew…

We prove that the dimension of the Specht module of a forest $G$ is the same as the normalized volume of the matching polytope of $G$. We also associate to $G$ a symmetric function $s_G$ (analogous to the Schur symmetric function…

Symmetric extensions are essential in quantum mechanics, providing a lens to investigate the correlations of entangled quantum systems and to address challenges like the quantum marginal problem. Though semi-definite programming (SDP) is a…