Date: 2 Aug 1980 12:26 PDT From: McKeeman at PARC-MAXC Subject: Re: a metric for the cube group. In-reply-to: ALAN's message of 2 August 1980 01:55-EDT (yawn) To: Alan Bawden cc: CUBE-HACKERS at MIT-MC 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*. Bill