Just to extend on Leonard's comments, The paper New refiners for permutation group search [Christopher Jefferson, Markus Pfeiffer, Rebecca Waldecker] gives a brief overview of partitions, while extending it. "Permutation group algorithms based on directed graphs" gives a new, more general framework, which uses directed graphs.
If you are happy looking at code, https://www.github.com/gap-packages/ferret gives a (reasonably) clean reimplementation in C++, while https://github.com/peal/backtrackkit gives a simple, very low-performance implementation (it aims to produce the "right partitions", but does so in a very simple but inefficient way). I also recently gave a brief overview on the topic at the Newtown Institute: https://www.newton.ac.uk/seminar/20200131113012201 , which you may (or may not) find helpful. I'm also happy to answer any questions, particularly about Leon's paper which myself and my co-authors are fairly sure we understand. Chris -----Original Message----- From: Leonard Soicher <l.h.soic...@qmul.ac.uk> Sent: Thursday, September 17, 2020 1:20 PM To: Bill Allombert <bill.allomb...@math.u-bordeaux.fr>; GAP Forum <forum@gap-system.org> Subject: Re: [GAP Forum] introduction to backtrack algorithm with ordered partitions Dear Bill, Dear Forum, You might like to look at Chapter 9 (Backtrack Methods) in A. Seress, "Permutation Group Algorithms", Cambridge University Press, 2003. For recent research in this area, see: C. Jefferson, M. Pfeiffer, R. Waldecker, W.A. Wilson, Permutation group algorithms based on directed graphs, arXiv:1911.04783 [math.GR], 2019. Best, Leonard ________________________________________ From: Bill Allombert <bill.allomb...@math.u-bordeaux.fr> Sent: 14 September 2020 11:49 To: GAP Forum Subject: [GAP Forum] introduction to backtrack algorithm with ordered partitions Dear Forum, I am interested in an introduction to the concept of backtrack algorithm with ordered partitions. (which is mentionned in the last section of the GAP manual) So far I have found Leon paper Permutation Group Algorithms Based on Partitions, I: Theory and Algorithms Is there something else I missed ? Cheers, Bill _______________________________________________ Forum mailing list Forum@gap-system.org https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fmail.gap-system.org%2Fmailman%2Flistinfo%2Fforum&data=02%7C01%7C%7Cc6707e89319e4124be1208d8589bfc30%7C569df091b01340e386eebd9cb9e25814%7C0%7C1%7C637356774264126640&sdata=e8LKw5CfuD5%2Bf6RKvIaCl1tf29januOsvfbXq8MjEMs%3D&reserved=0 _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
