From hoey@aic.nrl.navy.mil  Tue May  9 12:11:08 1995
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Date: Tue, 9 May 95 12:11:02 EDT
From: hoey@aic.nrl.navy.mil (Dan Hoey)
Message-Id: <9505091611.AA26374@Sun0.AIC.NRL.Navy.Mil>
To: "Jerry Bryan" <BRYAN@wvnvm.wvnet.edu>
Cc: "Cube Lovers List" <cube-lovers@ai.mit.edu>
Subject: Re: more on the slice group

Jerry Bryan writes:

> I don't yet understand why Mike's position is a local maximum in the
> full cube group.  But assuming it is, it is not only the shortest
> local maximum, it is the first local maximum which is not
> Q-transitive (i.e, we have |{m'Xm}|=24, hence we have |Symm(X)|=2,
> and the size of the symmetry groups for Q-transitive positions
> must be divisible by 12.).

No, the 4-spot pattern is also a local maximum at 12 qtw, although its
symmetry group is of order 16.  Jim Saxe and I reported this on 22
March 1981, in "No short relations and a new local maximum".

Dan
Hoey@AIC.NRL.Navy.Mil