Abstract
AbstractWe 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.
Subject
Computational Theory and Mathematics,General Mathematics
Reference9 articles.
1. Fast recognition of doubly transitive groups
2. ‘Finding blocks of imprimitivity in small-base groups in nearly linear time‘;Schönert;Proceedings 1994 ACM-SIGSAM International Symposium on Symbolic and Algebraic Computation,1994