Sherry H. F. Yan ; Robin D. P. Zhou - Refined Enumeration of Corners in Tree-like Tableaux

dmtcs:3683 - Discrete Mathematics & Theoretical Computer Science, September 26, 2017, Vol. 19 no. 3 -
Refined Enumeration of Corners in Tree-like TableauxArticle

Authors: Sherry H. F. Yan ; Robin D. P. Zhou

    Tree-like tableaux are certain fillings of Ferrers diagrams originally introduced by Aval et al., which are in simple bijections with permutation tableaux coming from Postnikov's study of totally nonnegative Grassmanian and alternative tableaux introduced by Viennot. In this paper, we confirm two conjectures of Gao et al. on the refined enumeration of non-occupied corners in tree-like tableaux and symmetric tree-like tableaux via intermediate structures of alternative tableaux, linked partitions, type $B$ alternative tableaux and type $B$ linked partitions.

    Volume: Vol. 19 no. 3
    Section: Combinatorics
    Published on: September 26, 2017
    Accepted on: September 13, 2017
    Submitted on: September 4, 2017
    Keywords: Mathematics - Combinatorics

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