From BRYAN@wvnvm.wvnet.edu Wed Jul 12 10:31:12 1995 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA26378; Wed, 12 Jul 95 10:31:12 EDT Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R2) with BSMTP id 0082; Wed, 12 Jul 95 10:31:11 EDT Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 5371; Wed, 12 Jul 1995 10:31:11 -0400 Message-Id: Date: Wed, 12 Jul 1995 10:31:10 -0400 (EDT) From: "Jerry Bryan" To: "Cube Lovers List" Subject: Re: Partial Results, Edges only (with Face Centers), Qturns In-Reply-To: Message of 07/10/95 at 16:20:29 from BRYAN@wvnvm.wvnet.edu On 07/10/95 at 16:20:29 Jerry Bryan said: >The local maximum unique up to M-conjugacy is the 6-H position >(see Symmetry and Local Maxima). I do not yet have a process >for the 6-H, but I should be able to have one soon. I can now give one way to do it as (UD)(RR)(LL)(UD). It seems too simple once you chase it down. Note that this is *not* the 6-H position when you apply the process to the whole cube; you have to omit the corners for this process to yield the 6-H. Nonetheless, the pattern is a nice one when the process is applied to the whole cube, one that looks familiar, although I cannot place it. It is *almost* what I described as the "interesting" part of three of the 10q local maxima on the whole cube, but the "interesting" part of the 10q local maxima is (U'D')(RR)(LL)(UD) instead. It might be noted that the length of this position is also 8q on an edges-only-without-centers cube (see my note of 8 Dec 1993 22:41:38). I did not actually provide a process for the without-centers case, but the same process works for the 6-H edges-only with or without centers for this position. Such is not always true. I have talked about it before, but many minimal processes for without-center cubes induce an invisible rotation which becomes visible when the Face centers are included. This is probably as good a time as any to correct an old error, pointed out to me by Dan Hoey. The length of a position without centers is the minimum taken over C of the length of the same position with centers -- that is, the minimum of the respective lengths of the same position rotated 24 different ways. For searches without centers I store representatives of the form Y=Repr{m'Xmc}. At one point, I said |Y|=min{|Yc|}. This is certainly not true. Y is just one of the {Yc}, and it is totally arbitrary which one it is. The difficulty is really a notational one. It is the length of Y without centers which is min{|Yc|}, not the length of Y itself (with centers). But I don't have a good way to say "Y without centers" or especially to say "length of Y without centers". But in any case, the most interesting cases to me are the ones where the length without centers matches the length with centers, so that the minimal process for the without centers case does not induce an invisible rotation. The position at hand is such a case. Finally, the position is in the anti-slice group (i.e., (UD)(RL)(RL)(UD)), so the position is a local maximum in the anti-slice edges only group with a length 4a. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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