Some Observations about the "Generalized Abundancy Index"

2025/05/11 by Starr, Shannon · 2 citations
Mathematics · #05A19 #11B75 #41A60 #60F05 #Combinatorics (math.CO) #FOS: Mathematics #Holomorphic and Operator Theory #Limits and Structures in Graph Theory #Mathematical Analysis and Transform Methods #Number Theory (math.NT) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2505.07051

openalex publication_date 2025/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A(ℓ,n) ⊂ S_n^ℓ denote the set of all ℓ-tuples (π₁,…,π_ℓ), for π₁,…,π_ℓ ∈ S_n satisfying: ∀ i

Citations

• Asymptotics of commuting ℓ-tuples in symmetric groups and log-concavity
• A bijection for tuples of commuting permutations and a log-concavity conjecture
• Log-concavity with respect to the number of orbits for infinite tuples of commuting permutations
• Orbifold Euler characteristics and the number of commuting n-tuples in symmetric groups

Cited by

• Proof of a conjecture by Starr and log-concavity for random commuting permutations
• A central limit theorem for a generalization of the Ewens measure to random tuples of commuting permutations

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