Related papers: Enumeration of standard Young tableaux of shifted …

We consider the problem of counting the occurrences of patterns of the form $xy-z$ within flattened permutations of a given length. Using symmetric functions, we find recurrence relations satisfied by the distributions on $\mathcal{S}_n$…

We show that sequences of skew Schur polynomials obtained from stretched semi-standard Young tableaux satisfy a linear recurrence, which we give explicitly. Using this, we apply this to finding certain asymptotic behavior of these Schur…

Through the following, we establish the conditions which allow us to express recursive sequences of real numbers, enumerated through the recurrence relation a_{n+1} = Aa_n + Ba_{n-1}, by means of algebraic equations in two variables of…

Let $R$ be a polynomial ring in $m$ variables over a field of characteristic zero. We classify all rank $n$ twisted generalized Weyl algebras over $R$, up to $\mathbb{Z}^n$-graded isomorphisms, in terms of higher spin 6-vertex…

Let $n,r,k,s$ be positive integers with $n,k\ge 2$. The generalized Ramsey number $R(n,r;k,s)$ is the smallest positive integer $p$ such that for every graph $G$ of order $p$, either $G$ contains a subgraph induced by $n$ vertices with at…

Fix a sequence of $d$-regular graphs $(G_d)_{d\in \mathbb{N}}$ and denote by $G_{d,p}$ the graph obtained from $G_d$ after edge-percolation with probability $p=c/d$, for a constant $c>0$. We prove a quantitative local convergence of…

We give a solution to a problem posed by Corteel and Nadeau concerning permutation tableaux of length n and the number of occurrences of the dashed pattern 32--1 in permutations on [n]. We introduce the inversion number of a permutation…

The expectation of the descent number of a random Young tableau of a fixed shape is given, and concentration around the mean is shown. This result is generalized to the major index and to other descent functions. The proof combines…

We study vectors formed by entries on the diagonal of standard Young tableaux of shifted shapes. Such vectors are in bijection with integer lattice points of certain integral polytopes, which are Minkowski sums of simplices. We also…

Young diagrams are fundamental combinatorial objects in representation theory and algebraic geometry. Many constructions that rely on these objects depend on variations of a straightening process that expresses a filling of a Young diagram…

Let $(X_{k})_{k\geq 1}$ and $(Y_k)_{k\geq 1}$ be the sequence of $X$ and $Y$-coordinates of the positive integer solutions $(x, y)$ of the equation $x^2 - dy^2 = t$. In this paper we completely describe those recurrence sequences such that…

Given a digraph $G$, we propose a new method to find the recurrence equation for the number of vertices $n_k$ of the $k$-iterated line digraph $L^k(G)$, for $k\geq0$, where $L^0(G)=G$. We obtain this result by using the minimal polynomial…

The weighted Delannoy numbers are defined by the recurrence relation $f_{m,n}=\alpha f_{m-1,n}+ \beta f_{m,n-1}+ \gamma f_{m-1,n-1}$ if $m n>0 $, with $f_{m,n}=\alpha^m \beta^n$ if $n m=0$. In this work, we study a generalization of these…

We show that the subgraph induced in Young's graph by the set of partitions with an odd number of standard Young tableaux is a binary tree. This tree exhibits self-similarities at all scales, and has a simple recursive description.

The classical hook length formula counts the number of standard tableaux of straight shapes. In 1996, Okounkov and Olshanski found a positive formula for the number of standard Young tableaux of a skew shape. We prove various properties of…

Given two vectors $u$ and $v$, their outer sum is given by the matrix $A$ with entries $A_{ij} = u_{i} + v_{j}$. If the entries of $u$ and $v$ are increasing and sufficiently generic, the total ordering of the entries of the matrix is a…

We consider two partial orders on standard Young tableaux. The first one is induced from the weak right Bruhat order on symmetric group by Robinson-Schensted algorithm. The second one is induced from the order on Young diagrams by…

Refined canonical stable Grothendieck polynomials were introduced by Hwang, Jang, Kim, Song, and Song. There exist two combinatorial models for these polynomials: one using hook-valued tableaux and the other using pairs of a semistandard…

We introduce balanced shifted tableaux, as an analogue of balanced tableaux of Edelman and Greene, from the perspective of root systems of type B and C. We show that they are equinumerous to standard Young tableaux of the corresponding…

We introduce the notion of "type" of a tableau, that allows us to define new families of tableaux including both balanced and standard Young tableaux. We use these new objects to describe the set of reduced decompositions of any…