Dear Frédéric, You may also be able to approach your problem by thinking of it in terms of coherent configurations and/or association schemes (an area which is unfortunately a terminological minefield), for which there are some useful GAP functions available. The first is the "Elementary functions for association schemes on GAP" of Hanaki: see http://math.shinshu-u.ac.jp/~hanaki/as/gap/association_scheme.gap
Also, Peter Cameron has some relevant GAP functions on his webpage, which work especially well for CCs obtained from permutation groups: see http://www.maths.qmul.ac.uk/~pjc/gapprogs.html For instance, Peter's programs include a function for testing if a group is generously transitive, i.e. every orbital is self-paired. I hope this is of some use to you! Regards, Robert. ----- Original Message ----- From: Frederic Vanhove <fvanh...@cage.ugent.be> Date: Friday, September 20, 2013 6:02 am Subject: [GAP Forum] Checking if permutation action has self-paired orbitals To: "fo...@gap-system.org" <fo...@gap-system.org> > Dear forum, > > suppose you have a group acting on a set. The orbitals are the orbits > > on ordered pairs of elements of that set, and their number > can be computed in GAP using > RankAction(groupname,setname); > > But I would like to know if these orbitals are self-paired, i.e. that > > (x1,x2) and (x2,x1) are always in the same orbit. > What is the easiest way to check this? > > More generally, I would like to check if the permutation character is > at > least multiplicity-free. > > Many thanks, > Kind regards, > Frédéric > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
