Refined Enumeration of Corners in Tree-like Tableaux

Tree-like tableaux are certain fillings of Ferrers diagrams originallyintroduced by Aval et al., which are in simple bijections with permutationtableaux coming from Postnikov's study of totally nonnegative Grassmanian andalternative tableaux introduced by Viennot. In this paper, we confirm twoc...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science 2017-01, Vol.19 (3)
Main Authors: Yan, Sherry H F, Zhou, Robin D P
Format: Article
Language:English
Subjects:
Corners
Enumeration
Mathematics
Partitions (mathematics)
Permutations
Online Access:Get full text
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Summary:Tree-like tableaux are certain fillings of Ferrers diagrams originallyintroduced by Aval et al., which are in simple bijections with permutationtableaux coming from Postnikov's study of totally nonnegative Grassmanian andalternative tableaux introduced by Viennot. In this paper, we confirm twoconjectures of Gao et al. on the refined enumeration of non-occupied corners intree-like tableaux and symmetric tree-like tableaux via intermediate structuresof alternative tableaux, linked partitions, type BB alternative tableaux andtype BB linked partitions.
ISSN:1365-8050