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

Raghavendra Tripathi

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~\cite{abdesselam2023log} that $A(p,…