Computing canonical images in permutation groups with Graph Backtracking

Christopher Jefferson; Rebecca Waldecker; Wilf A. Wilson

doi:10.1016/j.jaca.2023.100010

Computing canonical images in permutation groups with Graph Backtracking

Christopher Jefferson, Rebecca Waldecker (Lead / Corresponding author), Wilf A. Wilson

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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 [9], which extends Jeffrey Leon's Partition Backtrack framework [14], [15]. Our methods generalise both Nauty [17] and Steve Linton's Minimal image algorithm [16].

Original language	English
Article number	100010
Number of pages	11
Journal	Journal of Computational Algebra
Volume	8
Early online date	4 Oct 2023
DOIs	https://doi.org/10.1016/j.jaca.2023.100010
Publication status	Published - Dec 2023

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10.1016/j.jaca.2023.100010Licence: CC BY

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title = "Computing canonical images in permutation groups with Graph Backtracking",

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 [9], which extends Jeffrey Leon's Partition Backtrack framework [14], [15]. Our methods generalise both Nauty [17] and Steve Linton's Minimal image algorithm [16].",

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AU - Waldecker, Rebecca

AU - Wilson, Wilf A.

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AB - 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 [9], which extends Jeffrey Leon's Partition Backtrack framework [14], [15]. Our methods generalise both Nauty [17] and Steve Linton's Minimal image algorithm [16].

U2 - 10.1016/j.jaca.2023.100010

DO - 10.1016/j.jaca.2023.100010

M3 - Article

VL - 8

JO - Journal of Computational Algebra

JF - Journal of Computational Algebra

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Computing canonical images in permutation groups with Graph Backtracking

Abstract

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