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Corners in tree-like tableaux. (English) Zbl 1351.05229

Summary: In this paper, we study tree-like tableaux, combinatorial objects which exhibit a natural tree structure and are connected to the partially asymmetric simple exclusion process (PASEP). There was a conjecture made on the total number of corners in tree-like tableaux and the total number of corners in symmetric tree-like tableaux. In this paper, we prove both conjectures. Our proofs are based off of the bijection with permutation tableaux or type-B permutation tableaux and consequently, we also prove results for these tableaux. In addition, we derive the limiting distribution of the number of occupied corners in random tree-like tableaux and random symmetric tree-like tableaux.

MSC:

05E10 Combinatorial aspects of representation theory
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References:

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