From @mitvma.mit.edu,@WVNVM.WVNET.EDU:BRYAN@WVNVM.WVNET.EDU Sat Dec 25 22:48:40 1993 Return-Path: <@mitvma.mit.edu,@WVNVM.WVNET.EDU:BRYAN@WVNVM.WVNET.EDU> Received: from mitvma.mit.edu by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA20316; Sat, 25 Dec 93 22:48:40 EST Message-Id: <9312260348.AA20316@life.ai.mit.edu> Received: from MITVMA.MIT.EDU by mitvma.mit.edu (IBM VM SMTP V2R2) with BSMTP id 2435; Sat, 25 Dec 93 22:48:38 EST Received: from WVNVM.WVNET.EDU (NJE origin MAILER@WVNVM) by MITVMA.MIT.EDU (LMail V1.1d/1.7f) with BSMTP id 7378; Sat, 25 Dec 1993 22:48:38 -0500 Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.1d/1.7f) with BSMTP id 3493; Sat, 25 Dec 1993 22:46:06 -0500 X-Acknowledge-To: Date: Sat, 25 Dec 1993 22:46:06 EST From: "Jerry Bryan" To: "Cube Lovers List" Subject: Withdrawal of Proposal I wish to withdraw, for the time being, my proposed answer to Dan Hoey's question about how large is the cube group when symmetries are taken into account. Notwithstanding two rounds of "correction", I believe my proposal is fundamentally incorrect, and it will take some time to come up with something better. I believe that my proposed approximation is incorrect by a factor of 24. That is, my proposed approximation would be correct for corners plus edges (without centers), but would need to be multiplied by 24 in order to be correct for corners plus edges (with centers). My proposed approximation was 4.3 * 10^19 / (24*24*2). I now believe it should be 4.3 * 10^19 / (24 * 2), with the former figure correct only if centers are omitted. Secondly, I believe that my proposed procedure to calculate an exact value from the known sizes of corner and edge groups is incorrect. My procedure would be correct if all equivalence classes had exactly 1152 elements. But they don't. It is not presently clear to me whether the size of the equivalence classes when corners and edges are combined can be calculated from the known sizes of equivalence classes for corners and edges separately, or whether a computer search will have to be performed for the case where corners and edges are combined. I will get back to this in a week or two. In the meantime, my apologies if I have wasted your time, and I look forward to any words of wisdom that any of you all might have. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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 If you don't have time to do it right today, what makes you think you are going to have time to do it over again tomorrow?