Stammering tableaux

TL;DR

This paper introduces stammering tableaux, a new combinatorial object linked to the PASEP model, establishing bijections with various existing tableaux and combinatorial structures, enriching the understanding of their interrelations.

Contribution

It defines stammering tableaux within Young's lattice and connects them to multiple combinatorial models, providing new insights and bijections in the study of tableaux.

Findings

Stammering tableaux are introduced as a new combinatorial object.

Bijections are established between stammering tableaux and existing combinatorial structures.

The work links PASEP partition functions to various tableau variants.

Abstract

The PASEP (Partially Asymmetric Simple Exclusion Process) is a probabilistic model of moving particles, which is of great interest in combinatorics, since it appeared that its partition function counts some tableaux. These tableaux have several variants such as permutations tableaux, alternative tableaux, tree- like tableaux, Dyck tableaux, etc. We introduce in this context certain excursions in Young's lattice, that we call stammering tableaux (by analogy with oscillating tableaux, vacillating tableaux, hesitating tableaux). Some natural bijections make a link with rook placements in a double staircase, chains of Dyck paths obtained by successive addition of ribbons, Laguerre histories, Dyck tableaux, etc.