[next] [prev] [up] Date: Sat, 02 Aug 80 12:26:00 -0700 (PDT)
[next] [prev] [up] From: Bill McKeeman <McKeeman@PARC-MAXC >
~~~ [prev] [up] Subject: Re: a metric for the cube group.

Alan, I enjoyed your presentation. I am convinced that counting the RLFBUD
manipulations will not give a metric. I do not, however, see an easy way to
compute twists T(M). I think one gets a metric only if one takes the minimum
over some set of manipulations. That is, take a set, AM, of atomic moves
including their inverses, let AM* be the strings of AM, and |M| be the length
of M in AM*. Then
D(a, b) = min |M| such that a = bM
defines a metric. D(a,b) would sometimes be undefined if AM did not generate
the whole group. The recent discussion on shortest solutions is in fact about the
maximum of such a T(M) for all M in some AM*.


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