Efficient Finite Permutation Groups and Homomesy Computation in Common Lisp

Abstract

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.