Counting packings of generic subsets in finite groups

Abstract : 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.
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Contributor : Roland Bacher <>
Submitted on : Wednesday, October 3, 2012 - 11:26:12 AM
Last modification on : Friday, March 29, 2019 - 11:28:05 AM
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  • HAL Id : hal-00531684, version 3
  • ARXIV : 1011.0975

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

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