Corners in tree-like tableaux

Document Type

Article

Publication Date

11-10-2016

Abstract

© 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.

Comments

Hitczenko, P., & Lohss, A. (2016). Corners in tree-like tableaux. The Electronic Journal of Combinatorics, 23(4), P4.26. https://doi.org/10.37236/5712

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