Date: Mon, 25 Sep 95 00:44:40 +0100
From: Michiel Boland <boland@sci.kun.nl >
Subject: Re: Order problems

Jerry wrote:
>I would be curious to hear how you are doing your search. It is
>trivial to see how to calculate the order of a particular
>position. However, it is not obvious to me how to find a
>position of a particular order. I hope it is not the case that
>it is in the archives and I just haven't seen it.

I use a simple brute-force method, that is, I compute the order
of each transform and the number of quarter turns. If there is
already a transform with that order & number of qt, I forget all
about it and go to the next transform.

I have the C source available for anyone who wants to peek at it.

have to twist two adjacent faces in order to get something with
order other than 1, 2 or 4. That saves a bit of time.

On my PC, i finished all transforms of length 6 (quarter- and
half turns), and did some of length 7. Fortunately, as I
mentioned earlier, I managed to get it to work on a somewhat
faster machine, and am now waiting for the results of that. I am
searching all transforms of 10 quarter turns or less.

A process with order 110 must have an even number of quarter
turns, since the permutation on the edges has to be even (the
only possibility is to have an 11-cycle on the edges, which is
an even permutation).
Therefore, since there are no processes with order 110 with 6 or
less quarter turns, this proves that the one of length 8 is
indeed the shortest possible.

Cheers,

--
Michiel Boland <boland@sci.kun.nl>
University of Nijmegen
The Netherlands