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Combinatorial properties of permutation tableaux

Abstract : We give another construction of a permutation tableau from its corresponding permutation and construct a permutation-preserving bijection between $1$-hinge and $0$-hinge tableaux. We also consider certain alignment and crossing statistics on permutation tableaux that have previously been shown to be equidistributed by mapping them to patterns in related permutations. We give two direct maps on tableaux that prove the equidistribution of those statistics by exchanging some statistics and preserving the rest. Finally, we enumerate some sets of permutations that are restricted both by pattern avoidance and by certain parameters of their associated permutation tableaux.
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Alexander Burstein, Niklas Eriksen. Combinatorial properties of permutation tableaux. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.625-640. ⟨hal-01185149⟩

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