[GAP Forum] Checking if permutation action has self-paired orbitals
Robert Bailey
robert.bailey at ryerson.ca
Fri Sep 20 12:17:09 BST 2013
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 <fvanhove at cage.UGent.be>
Date: Friday, September 20, 2013 6:02 am
Subject: [GAP Forum] Checking if permutation action has self-paired orbitals
To: "forum at gap-system.org" <forum at 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
>
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