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arXiv · 2111.11527

Permutations with non-decreasing transposition array and pattern avoidance

Fufa Beyene·Roberto Mantaci
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Abstract

We give some results about a bijection associating each permutation with a subexcedant function. This function is related to a particular decomposition of the permutation as a product of transpositions and therefore it has been called transposition array in the literature. In particular, we identify anti-exceedance positions of the permutation through its transposition array and we give an expression of the bijection in terms of the cycle structure of the permutation. We give a characterization of a family of permutations having a non-decreasing transposition array and study length 3 pattern avoidance therein.

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Fufa Beyene, Roberto Mantaci. 2021-11-22. Permutations with non-decreasing transposition array and pattern avoidance. https://arxiv.org/abs/2111.11527

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