We compute the cycle index sum of the symmetric group action on the homology of the configuration spaces of points in a Euclidean space with the condition that no $k$ of them are equal.
"Cycle Index Sum for Non-$k$-Equal Configurations." Bull. Belg. Math. Soc. Simon Stevin 25 (1) 129 - 139, march 2018. https://doi.org/10.36045/bbms/1523412060