Counting packings of generic subsets in finite groups

Roland Bacher (1)

1 IF - Institut Fourier

A packing of subsets $\mathcal S_1,\dots, \mathcal S_n$ in a group $G$ is a sequence $(g_1,\dots,g_n)$ such that $g_1\mathcal S_1,\dots,g_n\mathcal S_n$ are disjoint subsets of $G$. We give a formula for the number of packings if the group $G$ is finite and if the subsets $\mathcal S_1,\dots,\mathcal S_n$ 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 $\mathcal S_i$ are singletons.

Mots clés: Packings in groups; additive combinatorics; additive number theory; Stirling number; enumeration of hypertrees

Domaines: Combinatoire [math.CO]; Théorie des nombres [math.NT]; Théorie des groupes [math.GR]

Roland Bacher. Counting packings of generic subsets in finite groups. The Electronic Journal of Combinatorics, 2012, 19 (3), pp.#P7. ⟨hal-00531684v3⟩