Transformation à la Foata for special kinds of descents and excedances

01/06/2021

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by   Jean-Luc Baril, et al.

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A pure excedance in a permutation π=π_1π_2…π_n is a position i<π_i such that there is no j<i with i≤π_j<π_i. We present a one-to-one correspondence on the symmetric group that transports pure excedances to descents of special kind. As a byproduct, we prove that the popularity of pure excedances equals those of pure descents on permutations, while their distributions are different.