Refined Enumeration of Corners in Tree-like Tableaux

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 t...

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Published in:Discrete mathematics and theoretical computer science 2017-09, Vol.19 no. 3 (Combinatorics)
Main Authors: Sherry H. F. Yan, Robin D. P. Zhou
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description 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.
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title Refined Enumeration of Corners in Tree-like Tableaux
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