[GAP Forum] Checking if permutation action has self-paired orbitals

[Robert Bailey]

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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