2021/12/09 by Christopher Jefferson, Jefferson, Christopher, Rebecca Waldecker +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #20-08 (Primary) 20B05 (Secondary) #DNA and Nucleic Acid Chemistry #Drug Transport and Resistance Mechanisms #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2112.05065
openalex publication_date 2021/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Backtrack search is a fundamental technique for computing with finite permutation groups, which has been formulated in terms of points, ordered partitions, and graphs. We provide a framework for discussing the most common forms of backtrack search in a generic way. We introduce the concept of perfect refiners to better understand and compare the pruning power available in these different settings. We also present a new formulation of backtrack search, which allows the use of graphs with additional vertices, and which is implemented in the software package Vole. For each setting, we classify the groups and cosets for which there exist perfect refiners. Moreover, we describe perfect refiners for many naturally-occurring examples of stabilisers and transporter sets, including applications to normaliser and subgroup conjugacy problems for 2-closed groups.