Vol. 9, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Volume 14, Issue 1
Volume 13, Issue 1
Volume 12, Issue 1
Volume 11, Issue 1
Volume 10, Issue 1
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 1
Volume 7, Issue 1
Volume 6, Issue 1
Volume 5, Issue 1
Volume 4, Issue 1
Volume 3, Issue 1
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1948-7916
Author Index
To Appear
Other MSP Journals
An algorithm for enumerating difference sets

Dylan Peifer

Vol. 9 (2019), 35–41

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.

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

An algorithm for enumerating all difference sets in a group

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