Abstract
Many problems in Combinatorics and related fields reduce to the problem of computing orbits of groups acting on finite sets. One of the techniques is known under the name Snakes and Ladders. We offer the alternate name poset classification algorithm. We will describe this technique and compare the performance on example problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Al-Azemi, A., Betten, A., Chowdhury, S.R.: A rainbow clique search algorithm for BLT-sets. In: Davenport, J.H., Kauers, M., Labahn, G., Urban, J. (eds.) ICMS 2018. LNCS, vol. 10931, pp. 71–79. Springer, Cham (2018)
Bamberg, J., Betten, A., Cara, Ph., De Beule, J., Lavrauw, M., Neunhöffer, M.: Finite Incidence Geometry. FinInG - a GAP package, version 1.4 (2017)
Betten, A.: Classifying discrete objects with orbiter. ACM Commun. Comput. Algebra 47(3/4), 183–186 (2014). https://doi.org/10.1145/2576802.2576832
Betten, A.: Orbiter - a program to classify discrete objects (2016–2018). https://github.com/abetten/orbiter
Betten, A., Braun, M., Fripertinger, H., Kerber, A., Kohnert, A., Wassermann, A.: Error-Correcting Linear Codes, Classification by Isometry and Applications. Algorithms and Computation in Mathematics, vol. 18. Springer, Heidelberg (2006). https://doi.org/10.1007/3-540-31703-1
Betten, A.: Rainbow cliques and the classification of small BLT-sets. In: Kauers, M. (ed.) ISSAC 2013, 26–29 June 2013, Boston, Massachusetts, pp. 53–60 (2013)
Betten, A., Hirschfeld, J.W.P., Karaoglu, F.: Classification of cubic surfaces with twenty-seven lines over the finite field of order thirteen. Eur. J. Math. 4(1), 37–50 (2018)
Betten, A., Karaoglu, F.: Cubic surfaces over small finite fields. Submitted to Designs, Codes and Cryptography
Betten, A.: Classifying cubic surfaces over finite fields using orbiter. In: Davenport, J.H., Kauers, M., Labahn, G., Urban, J. (eds.) ICMS 2018. LNCS, vol. 10931, pp. 55–61. Springer, Cham (2018)
Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symbolic Comput. 24, 235–265 (1997)
Braun, M.: Some new designs over finite fields. Bayreuth. Math. Schr. 74, 58–68 (2005)
The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.8.10 (2018). https://www.gap-system.org
Kaski, P., Östergård, P.: Classification Algorithms for Codes and Designs. Algorithms and Computation in Mathematics, vol. 15. Springer, Heidelberg (2006). https://doi.org/10.1007/3-540-28991-7
Koch, M.: Neue Strategien zur Lösung von Isomorphieproblemen. (German) [New strategies for the solution of isomorphism problems] Ph.D. thesis. University of Bayreuth (2015)
Leon, J.S.: Partitions, refinements, and permutation group computation. In: Groups and Computation, II (New Brunswick, NJ, 1995), vol. 28. DIMACS Series Discrete Mathematics Theoretical Computer Science, pp. 123–158. American Mathematical Society, Providence (1997)
McKay, B.D.: Isomorph-free exhaustive generation. J. Algorithms 26(2), 306–324 (1998)
McKay, B.D., Piperno, A.: Practical graph isomorphism II. J. Symbolic Comput. 60, 94–112 (2014). https://doi.org/10.1016/j.jsc.2013.09.003
Schmalz, B.: Verwendung von Untergruppenleitern zur Bestimmung von Doppelnebenklassen. (German) [Use of subgroup ladders for the determination of double cosets]. Bayreuth. Math. Schr. 31, 109–143 (1990)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Betten, A. (2018). How Fast Can We Compute Orbits of Groups?. In: Davenport, J., Kauers, M., Labahn, G., Urban, J. (eds) Mathematical Software – ICMS 2018. ICMS 2018. Lecture Notes in Computer Science(), vol 10931. Springer, Cham. https://doi.org/10.1007/978-3-319-96418-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-96418-8_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-96417-1
Online ISBN: 978-3-319-96418-8
eBook Packages: Computer ScienceComputer Science (R0)