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.
@article{10_37236_3440,
author = {Jean-Christophe Aval and Adrien Boussicault and Philippe Nadeau},
title = {Tree-like tableaux},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {4},
doi = {10.37236/3440},
zbl = {1295.05004},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3440/}
}
TY - JOUR
AU - Jean-Christophe Aval
AU - Adrien Boussicault
AU - Philippe Nadeau
TI - Tree-like tableaux
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/3440/
DO - 10.37236/3440
ID - 10_37236_3440
ER -
Jean-Christophe Aval; Adrien Boussicault; Philippe Nadeau. Tree-like tableaux. The electronic journal of combinatorics, Tome 20 (2013) no. 4. doi: 10.37236/3440
