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

Abdelmalek Abdesselam, Pedro Brunialti, Tristan Doan +1

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