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arXiv · 1109.0371

Tree-like tableaux

Jean-Christophe Aval·Adrien Boussicault·Philippe Nadeau
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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.

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Jean-Christophe Aval, Adrien Boussicault, Philippe Nadeau. 2013-06-10. Tree-like tableaux. https://arxiv.org/abs/1109.0371

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