Minimal and canonical images
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We describe a family of new algorithms for finding the canonical image of a set of points under the action of a permutation group. This family of algorithms makes use of the orbit structure of the group, and a chain of subgroups of the group, to efficiently reduce the amount of search that must be performed to find a canonical image. We present a formal proof of correctness of our algorithms and describe experiments on different permutation groups that compare our algorithms with the previous state of the art.
Jefferson , C , Jonauskyte , E , Pfeiffer , M & Waldecker , R 2019 , ' Minimal and canonical images ' , Journal of Algebra , vol. 521 , pp. 481-506 . https://doi.org/10.1016/j.jalgebra.2018.11.009
Journal of Algebra
© 2018 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/ ).
DescriptionAll authors thank the DFG (Wa 3089/6-1) and the EPSRC CCP CoDiMa (EP/M022641/1) for supporting this work. The first author would like to thank the Royal Society, and the EPSRC (EP/M003728/1). The third author would like to acknowledge support from the OpenDreamKit Horizon 2020 European Research Infrastructures Project (#676541). The first and third author thank the Algebra group at the Martin-Luther Universität Halle-Wittenberg for the hospitality and the inspiring environment. The fourth author wishes to thank the Computer Science Department of the University of St Andrews for its hospitality during numerous visits.
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