dmtcs:2891 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2011,
DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
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https://doi.org/10.46298/dmtcs.2891
Tree-like tableauxArticle
Authors: Jean-Christophe Aval 1; Adrien Boussicault 1; Philippe Nadeau 2
1 Laboratoire Bordelais de Recherche en Informatique
2 Faculty of Mathematics [Vienna]
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.
Mark Dukes;Thomas Selig;Jason P. Smith;Einar Steingrímsson, 2019, Permutation Graphs and the Abelian Sandpile Model, Tiered Trees and Non-Ambiguous Binary Trees, The Electronic Journal of Combinatorics, 26, 3, 10.37236/8225, https://doi.org/10.37236/8225.
Amanda Lohss, 2016, The asymptotic distribution of symbols on diagonals of random weighted staircase tableaux, arXiv (Cornell University), 49, 4, pp. 795-818, 10.1002/rsa.20665, https://arxiv.org/abs/1512.00329.