Efficient finite permutation groups and homomesy computation in common lisp

Robert Smith, Brendan Pawlowski

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The study of permutations is of central importance to mathematics. Computation with permutation groups has typically been limited to systems such as GAP and Magma. In this paper we describe cl-permutation, a system for doing computations with permutation groups in ANSI Common Lisp. Homomesies, a recent concept introduced by Propp and Roby, are elaborated upon from a group-theoretic and linear-algebraic perspective. As a result, algorithms for manipulating them and better understanding their structure are presented. Finally, these algorithms are realized using cl-permutation.

Original languageEnglish (US)
Title of host publicationProceedings of ILC 2014 - 8th International Lisp Conference
PublisherAssociation for Computing Machinery
Number of pages9
ISBN (Print)9781450329316
StatePublished - 2014
Event8th International Lisp Conference, ILC 2014 - Montreal, QC, Canada
Duration: Aug 14 2014Aug 17 2014

Publication series

NameACM International Conference Proceeding Series


Other8th International Lisp Conference, ILC 2014
CityMontreal, QC


  • Common Lisp
  • computer algebra
  • group theory
  • homomesy
  • permutation
  • permutation group


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