A. Abdesselam

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20242026

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math.CO2025

Proof of a conjecture by Starr and log-concavity for random commuting permutations

Abdelmalek Abdesselam

We prove a conjecture by Shannon Starr regarding the asymptotics for the number of tuples of commuting permutations with given number of joint orbits. These numbers generalize unsi…

math.CO2024

Bessenrodt--Ono inequalities for $ℓ$ -tuples of pairwise commuting permutations

Abdelmalek Abdesselam, Bernhard Heim, Markus Neuhauser

Let $S_{n}$ denote the symmetric group. We consider \begin{equation*} N_{\ell}(n) := \frac{\left\vert Hom\left( \mathbb{Z}^{\ell},S_n\right) \right\vert}{n!} \end{equation*} which al…

math.CO2024

A bijection for tuples of commuting permutations and a log-concavity conjecture

Abdelmalek Abdesselam, Pedro Brunialti, Tristan Doan +1

Let $A (ℓ, n, k)$ denote the number of $ℓ$ -tuples of commuting permutations of $n$ elements whose permutation action results in exactly $k$ orbits or connected components. We pr…

Proof of a conjecture by Starr and log-concavity for random commuting permutations

Bessenrodt--Ono inequalities for ℓ-tuples of pairwise commuting permutations

A bijection for tuples of commuting permutations and a log-concavity conjecture

Bessenrodt--Ono inequalities for $ℓ$ -tuples of pairwise commuting permutations