Vol. 9, No. 1, 2019

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An algorithm for enumerating difference sets

Dylan Peifer

Vol. 9 (2019), 35–41
Abstract

The DifSets package for GAP implements an algorithm for enumerating all difference sets in a group up to equivalence and provides access to a library of results. The algorithm functions by finding difference sums, which are potential images of difference sets in quotient groups of the original group, and searching their preimages. In this way, the search space can be dramatically decreased, and searches of groups of relatively large order (such as order 64 or order 96) can be completed.

Keywords
difference sets, exhaustive search, GAP
Mathematical Subject Classification 2010
Primary: 05B10
Supplementary material

An algorithm for enumerating all difference sets in a group

Milestones
Received: 5 July 2018
Revised: 4 September 2018
Accepted: 26 February 2019
Published: 18 May 2019
Authors
Dylan Peifer
Department of Mathematics
Cornell University
Ithaca, NY
United States