Related papers: Inversions of Semistandard Young Tableaux

Permutations that avoid given patterns have been studied in great depth for their connections to other fields of mathematics, computer science, and biology. From a combinatorial perspective, permutation patterns have served as a unifying…

Let $SYT_{n}$ be the set of all standard Young tableaux with $n$ cells and $\leq_{weak}$ be Melnikov's the weak order on $SYT_n$. The aim of this paper is to introduce a conjecture, called the {\it property of inner tableau translation} and…

Let $\delta=(\delta_1,\ldots,\delta_n)$ be a string of letters $h$ and $v$. We define a Young tableau to be $\delta$-semistandard if the entries are weakly increasing along rows and columns, and the entries $i$ form a horizontal strip if…

Let $S$ be a $*$-semigroup and let $a,w,v\in S$. The initial goal of this work is to introduce two new classes of generalized inverses, called the $w$-core inverse and the dual $v$-core inverse in $S$. An element $a\in S$ is $w$-core…

Inversion sequences of length $n$, $\mathbf{I}_n$, are integer sequences $(e_1, \ldots, e_n)$ with $0 \leq e_i < n$ for each $i$. The study of patterns in inversion sequences was initiated recently by Mansour-Shattuck and…

A notion of cyclic descents on standard Young tableaux (SYT) of rectangular shape was introduced by Rhoades, and extended to certain skew shapes by the last two authors. The cyclic descent set restricts to the usual descent set when the…

In the paper we investigate two partial orders on standard Young tableaux and show their applications in the theory of invariant subspaces of nilpotent linear operators.

The number of inversions is a statistic on permutation groups measuring the degree to which the entries of a permutation are out of order. We provide a generalization of that statistic by introducing the statistic number of pseudoinversions…

We derive new combinatorial identities which may be viewed as multivariate analogs of summation formulas for hypergeometric series. As in the previous paper [Re], we start with probability distributions on the space of the infinite Young…

Let $G = \mathrm{SL}(n,\mathbb{C})$, let $B$ be a fixed Borel subgroup, and let $P \supset B$ be a parabolic subgroup determined by a composition $(c_1,\dots,c_k)$ of $n$. Write $P'$ for the derived group of $P$ and $\mathfrak{m}$ for the…

We give new bounds and asymptotic estimates on the number of standard Young tableaux of skew shape in a variety of special cases. Our approach is based on Naruse's hook-length formula. We also compare our bounds with the existing bounds on…

Combinatorial spiders are a model for the invariant space of the tensor product of representations. The basic objects, webs, are certain directed planar graphs with boundary; algebraic operations on representations correspond to…

We provide an algebraic-geometrical interpretation of the classical semistandard Young-tableaux via the notion of Seshadri stratifications. The columns appearing in such a tableau correspond to vanishing multiplicities of certain rational…

Barely set-valued tableaux are a variant of Young tableaux in which one box contains two numbers as its entry. It has recently been discovered that there are product formulas enumerating certain classes of barely set-valued tableaux. We…

We curry the elementary arithmetic operations of addition and multiplication to give monotone injections on N, and describe & study the inverse monoids that arise from also considering their generalised inverses. This leads to well-known…

In the first part of the paper, we study the inversion statistic of random permutations under the family $(\mathbb{P}_\theta^{(n)})_{\theta \ge 0}$ of Ewens sampling distributions on $S_n$. We obtain a rather simple exact formula for the…

Nonlinear inverse problems have complicated landscapes. Hence the calculation with naive iterative schemes (e.g., Gauss-Newton or conjugate gradients) is trapped in local minima. The (first) Born approximation can avoid this trapping but…

We introduce an infinite family of lower triangular matrices $\Gamma^{(s)}$, where $\gamma_{n,i}^s$ counts the standard Young tableaux on $n$ cells and with at most $s$ columns on a suitable subset of shapes. We show that the entries of…

The RSK correspondence is a bijection between permutations and pairs of standard Young tableaux with identical shape, where the tableaux are commonly denoted $P$ (insertion) and $Q$ (recording). It has been an open problem to demonstrate $$…

The celebrated hook-length formula gives a product formula for the number of standard Young tableaux of a straight shape. In 2014, Naruse announced a more general formula for the number of standard Young tableaux of skew shapes as a…