Corners in tree-like tableaux

Pawel Hitczenko, Amanda Lohss

Published 2015-11-16Version 1

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 corners in tree--like tableaux and the total number of corners in symmetric tree--like tableaux. In this paper, we prove both conjectures. Our proofs are based off of the bijection with permutation tableaux or type--B permutation tableaux and consequently, we also prove results for these tableaux. In addition, we derive the limiting distribution of the number of occupied corners in random tree--like tableaux and random symmetric tree--like tableaux.