Séminaire Lotharingien de Combinatoire, 86B.15 (2022), 11 pp.

Per Alexandersson and Olivia Nabawanda

Peaks Are Preserved Under Run-Sorting (Extended Abstract)

Abstract. We study a sorting procedure (run-sorting) on permutations, where runs are rearranged in lexicographic order. We describe a rather surprising bijection on permutations of length n, with the property that it sends the set of peak-values to the set of peak-values after run-sorting. We further show that the descent generating polynomials, A_n(t) for run-sorted permutations, RSP(n) are real rooted, and satisfy an interlacing property similar to that satisfied by the Eulerian polynomials.

Received: November 25, 2021. Accepted: March 4, 2022. Final version: April 1, 2022.

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