From BRYAN@wvnvm.wvnet.edu Thu Oct 5 21:01:18 1995 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA12445; Thu, 5 Oct 95 21:01:18 EDT Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R3) with BSMTP id 0286; Wed, 04 Oct 95 10:26:46 EDT Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 0750; Wed, 4 Oct 1995 10:26:43 -0400 Message-Id: Date: Wed, 4 Oct 1995 10:26:41 -0400 (EDT) From: "Jerry Bryan" To: "Cube Lovers List" Subject: Question It is well known that if we define G= for the twelve quarter turns q in Q, we can also generate G as G=, 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 , 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. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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