Corners in tree-like tableaux
© 2016, Australian National University. All rights reserved. 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 on 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.
Hitczenko, Paweł and Lohss, Amanda, "Corners in tree-like tableaux" (2016). Educator Scholarship & Departmental Newsletters. 70.