Counting packings of generic subsets in finite groups

Abstract

A packing of subsets S1,. . . , Sn in a group G is an element (g1,. . . , gn) of Gn such that g1S1,. . . , gn, Sn are disjoint subsets of G. We give a formula for the number of packings if the group G is finite and if the subsets S1,. . . , Sn satisfy a genericity condition. This formula can be seen as a generalization of the falling factorials which encode the number of packings in the case where all the sets Si are singletons.