Zubieta's Conjecture on the Enumeration of Corners in Tree-like Tableaux

Alice L. L. Gao, Emily X. L. Gao, Brian Y. Sun

Published 2015-11-17Version 1

In this paper, we confirm a conjecture of Zubieta on the enumeration of corners in tree-like tableaux. Our proof is based on Aval, Boussicault and Nadean's bijection between tree-like tableaux and permutation tableaux, and Corteel and Nadeau's bijection between permutation tableaux and permutations. We found the relationship of corners in permutation tableaux with descent and ascent statistics in permutations, which enables us to enumerate the number of corners in permutation tableaux, and thus to completely solve Zubieta's conjecture.