Computing canonical images in permutation groups with Graph Backtracking

2022/09/06 by Jefferson, Christopher, Waldecker, Rebecca, Wilson, Wilf A.
#20-08 #20B05 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2209.02534

Abstract

We describe a new algorithm for finding a canonical image of an object under the action of a finite permutation group. This algorithm builds on previous work using Graph Backtracking, which extends Jeffrey Leon's Partition Backtrack framework. Our methods generalise both Nauty and Steve Linton's Minimal image algorithm.

Related

• Minimal and Canonical Images
• Permutation group algorithms based on directed graphs (extended version)
• Permutation group algorithms based on directed graphs
• A method for building permutation representations of finitely presented\n groups
• Generating tuples of integers modulo the action of a permutation group and applications