On log-concavity of the number of orbits in commuting tuples of permutations

2024/08/30 by Raghavendra Tripathi, Tripathi, Raghavendra · 1 citation
Computer Science · Engineering · Mathematics · #05A17 #Advanced Combinatorial Mathematics #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2408.17212

openalex publication_date 2024/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Denote by A(p, n, k) the number of commuting p-tuples of permutations on [n] that have exactly k distinct orbits. It was conjectured in~\citeabdesselam2023log that A(p, n, k) is log-concave with respect to k for every p≥ 2, n≥ 3, and the log-concavity was proved in ``p=∞" case. In this paper, we prove that for k=n-α, the log-concavity for A(p, n, k) holds for every p≥ 2 for sufficiently large n.

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