%0 Journal Article
%T Tree-like tableaux
%A Jean-Christophe Aval
%A Adrien Boussicault
%A Philippe Nadeau
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1109.0371v2