All Difference Family Structures arise from Groups

Details All Difference Family Structures arise from Groups All Difference Family Structures arise from Groups

2004-05-28

arxiv.org/abs/math/0405567v1

Mathematics

Combinatorics

7 Pages

Scientific paper

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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