Christopher Jefferson, Rebecca Waldecker, Wilf A. Wilson
{"title":"Computing canonical images in permutation groups with Graph Backtracking","authors":"Christopher Jefferson, Rebecca Waldecker, Wilf A. Wilson","doi":"10.1016/j.jaca.2023.100010","DOIUrl":null,"url":null,"abstract":"<div><p>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 <span>[9]</span>, which extends Jeffrey Leon's Partition Backtrack framework <span>[14]</span>, <span>[15]</span>. Our methods generalise both Nauty <span>[17]</span> and Steve Linton's Minimal image algorithm <span>[16]</span>.</p></div>","PeriodicalId":100767,"journal":{"name":"Journal of Computational Algebra","volume":"8 ","pages":"Article 100010"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Algebra","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2772827723000074","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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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].
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