Counting packings of generic subsets in finite groups
The electronic journal of combinatorics, Tome 19 (2012) no. 3
A packing of subsets $\mathcal S_1,\dots,\mathcal S_n$ in a group $G$ is an element $(g_1,\dots,g_n)$ of $G^n$ 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.
DOI :
10.37236/2522
Classification :
05A15, 05C30, 11B73, 11B30, 11P99
Mots-clés : enumerative combinatorics, packings in groups, additive combinatorics, additive number theory, Stirling number
Mots-clés : enumerative combinatorics, packings in groups, additive combinatorics, additive number theory, Stirling number
Affiliations des auteurs :
Roland Bacher 1
@article{10_37236_2522,
author = {Roland Bacher},
title = {Counting packings of generic subsets in finite groups},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {3},
doi = {10.37236/2522},
zbl = {1253.05013},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2522/}
}
Roland Bacher. Counting packings of generic subsets in finite groups. The electronic journal of combinatorics, Tome 19 (2012) no. 3. doi: 10.37236/2522
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