[next] [prev] [up] Date: Wed, 04 Oct 95 10:26:41 -0400
[next] [prev] [up] From: Jerry Bryan <BRYAN@wvnvm.wvnet.edu >
~~~ ~~~ [up] Subject: <F,U,L,R,D> Question

It is well known that if we define G=<Q> for the twelve quarter turns
q in Q, we can also generate G as G=<F,U,L,R,D>, leaving out B and B'.
Leaving out any other quarter turn would do as well, but I
am going to stick to leaving out B for illustrative purposes.

However, when one of the quarter turns is left out, the length of most
positions will change. In particular, we will no longer have |B|=1.
My reading of the archives indicates that we do not know what the
length of B would be in this situation, nor what a minimal process
for B would be.

I am going to take a crack at this problem via exhaustive search.
But I like to use representative elements of conjugacy classes in
my searches, and I don't think I can do so in this situation.

For full-blown searches of G, I use M-conjugacy classes. For subsets
and/or restrictions of G, I use appropriate subsets and/or restrictions
of M. But I don't think I can use conjugacy classes at all for this
problem. The group is still G, even though lengths have changed, so
no subset and/or restriction of M is appropriate. But when G is
generated as <F,U,L,R,D>, we do not necessarily have |X|=|m'Xm|
for all m in M.

Am I missing something obvious? I don't think so, but in the
meantime I am going to have to start the search without conjugacy
classes. Bummer.

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Robert G. Bryan (Jerry Bryan)                        (304) 293-5192
Associate Director, WVNET                            (304) 293-5540 fax
837 Chestnut Ridge Road                              BRYAN@WVNVM
Morgantown, WV 26505                                 BRYAN@WVNVM.WVNET.EDU

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