Tree-like tableaux

Details Tree-like tableaux Tree-like tableaux

2011-09-02

arxiv.org/abs/1109.0371v1

23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), Iceland (2011)

Mathematics

Combinatorics

Scientific paper

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 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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