Tree-like tableaux
Combinatorics
2014-04-15 v2
Abstract
In this work we introduce and study tree-like tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux. We exhibit an elementary insertion procedure on our tableaux which gives a clear proof that tree-like tableaux of size n are counted by n!, and which moreover respects most of the well-known statistics studied originally on alternative and permutation tableaux. Our insertion procedure allows to define in particular two simple new bijections between tree-like tableaux and permutations: the first one is conceived specifically to respect the generalized pattern 2-31, while the second one respects the underlying tree of a tree-like tableau.
Cite
@article{arxiv.1109.0371,
title = {Tree-like tableaux},
author = {Jean-Christophe Aval and Adrien Boussicault and Philippe Nadeau},
journal= {arXiv preprint arXiv:1109.0371},
year = {2014}
}