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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.PR2025
A central limit theorem for a generalization of the Ewens measure to random tuples of commuting permutations
Abdelmalek Abdesselam, Shannon Starr
We prove a central limit theorem (CLT) for the number of joint orbits of random tuples of commuting permutations. In the uniform sampling case this generalizes the classic CLT of G…