Tree-like Tableaux

Author:

Aval Jean-Christophe,Boussicault Adrien,Nadeau Philippe

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.

Publisher

The Electronic Journal of Combinatorics

Subject

Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics

Cited by 8 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. About the Determinant of Complete non-ambiguous Trees;Electronic Proceedings in Theoretical Computer Science;2024-06-24

2. Non-ambiguous trees: New results and generalisation;European Journal of Combinatorics;2021-06

3. The number of directed k-convex polyominoes;Discrete Mathematics;2020-03

4. An asymptotic distribution theory for Eulerian recurrences with applications;Advances in Applied Mathematics;2020-01

5. Context-free grammars, generating functions and combinatorial arrays;European Journal of Combinatorics;2019-05

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