Descents and inversions in powers of permutations

2024/08/02 by Stijn Cambie, Jun Yan, Cambie, Stijn +1
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Bayesian Methods and Mixture Models

paper · pdf · doi:10.48550/arxiv.2408.01211

Abstract

In this paper, we generalise several recent results by Archer and Geary on descents in powers of permutations, and confirm all their conjectures. Specifically, for all k∈ℤ⁺, we prove explicit formulas for the expected numbers of descents and inversions in the k-th powers of permutations in S_n for all n≥2k+1. We also compute the number of Grassmanian permutations in S_n whose k-th powers remain Grassmanian, and the number of permutations in S_n whose k-th powers have the maximum number of descents.

Related

• Descents in powers of permutations
• Descent polynomials
• Variations on Descents and Inversions in Permutations
• The number of permutations with k inversions
• Counting subwords in flattened permutations