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Algorithmic Recognition of Actions of 2-Homogeneous Groups on Pairs

Published online by Cambridge University Press:  01 February 2010

Graham R. Sharp

Abstract

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We give an algorithm that takes as input a transitive permutation group (G, Ω) of degree n={m\choose 2}, and decides whether or not Ω is G-isomorphic to the action of G on the set of unordered pairs of some set Γ on which G acts 2-homogeneously. The algorithm is constructive: if a suitable action exists, then one such will be found, together with a suitable isomorphism. We give a deterministic O(sn logcn) implemention of the algorithm that assumes advance knowledge of the suborbits of (G, Ω). This leads to deterministic O(sn2) and Monte-Carlo O(sn logcn) implementations that do not make this assumption.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 1 , 1998 , pp. 109 - 147
Copyright
Copyright © London Mathematical Society 1998

References

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Supplementary material: File

JCM 1 Sharp Appendix C

Sharp Appendix C

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