Related papers: Greek letters in random staircase tableaux
Up-down permutations are counted by tangent resp. secant numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all…
Given a positive integer $n$ and a partitioning $n=r_1s_1+\dots+ r_ts_t$, $t,r_i,s_i$ positive integers, such that $r_1>\dots>r_t$ (for $t\ge 2$), we can write $n$ symbols $1,\dots,n$ in the form of a staircase matrix having $r_1$ rows…
Taking up a suggestion of David Gale from 1956, we generate sets of combinatorially isomorphic polytopes by choosing their Gale diagrams at random. We find that in high dimensions, and under suitable assumptions on the growth of the…
The question about maximal size of independent system of word equations is one of the most striking problems in combinatorics on words. Recently, Aleksi Saarela has introduced a new approach to the problem that is based on linear-algebraic…
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
We study combinatorial structures arising from finite-time transition probabilities of the Totally Asymmetric Simple Exclusion Process with open boundary conditions. While much of the existing combinatorial theory regarding the TASEP…
As suggested by Currie, we apply the probabilistic method to problems regarding pattern avoidance. Using techniques from analytic combinatorics, we calculate asymptotic pattern occurrence statistics and use them in conjunction with the…
We utilize the technique of staircases and jagged partitions to provide analytic sum-sides to some old and new partition identities of Rogers-Ramanujan type. Firstly, we conjecture a class of new partition identities related to the…
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…
The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…
A discretization of the peakons lattice is introduced, belonging to the same hierarchy as the continuous--time system. The construction examplifies the general scheme for integrable discretization of systems on Lie algebras with $r$--matrix…
Set-valued tableaux, introduced by Buch to express the tableaux-sum formula for stable Grothendieck polynomials, generalize semistandard tableaux. We provide a new recursive proof that the number of set-valued tableaux of a given shape is…
Generalizing the notion of staircase words, introduced by Knopfmacher et.\ al, we define staircase graph words. These are functions $w$ from the vertex set $V$ of a graph into the set $\{1,2,\ldots,k\}$, such that $|w(x)-w(y)|\leq 1$, for…
We investigate two closely related setups. In the first one we consider a TASEP-style system of particles with specified initial and final configurations. The probability of each history of the system is assumed to be equal. We show that…
Tree-like tableaux are combinatorial objects that appear in a combinatorial understanding of the PASEP model from statistical mechanics. In this understanding, the corners of the Southeast border correspond to the locations where a particle…
Vacillating tableaux are sequences of integer partitions that satisfy specific conditions. The concept of vacillating tableaux stems from the representation theory of the partition algebra and the combinatorial theory of crossings and…
In this note, we explicitly compute the probability that a given cell in a random standard Young tableau of the shifted staircase shape $(2n-1, 2n-3, \ldots, 3,1)$ contains the maximal label. We also show that the asymptotic distribution of…
We prove several combinatorial properties of suffix arrays, including a characterization of suffix arrays through a bijection with a certain well-defined class of permutations. Our approach is based on the characterization of…
In this paper, we study tree--like tableaux, combinatorial objects which exhibit a natural tree structure and are connected to the partially asymmetric simple exclusion process (PASEP). There was a conjecture made on the total number of…
A randomisation of the Berele insertion algorithm is proposed, where the insertion of a letter to a symplectic Young tableau leads to a distribution over the set of symplectic Young tableaux. Berele's algorithm provides a bijection between…