All Difference Family Structures arise from Groups

2004/05/28 by Tim Boykett, Boykett, Tim
Computer Science · Engineering · Mathematics · #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #graph theory and CDMA systems #math.CO #math.GR #msc:05B05

paper · pdf · doi:10.48550/arxiv.math/0405567

7 Pages

arxiv created 2004/05/28 · arxiv updated 2009/12/01

Abstract

Difference families are traditionally built using groups as their basis. This paper looks at what sort of generalised difference family constructions could be made, using the standard basis of translation and difference. The main result is that minimal requirements on the structure force nothing that groups cannot give, at least in the finite case. Thus all difference families arise from groups.

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