From BRYAN@wvnvm.wvnet.edu Fri May 19 10:35:47 1995 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA25707; Fri, 19 May 95 10:35:47 EDT Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R2) with BSMTP id 7520; Fri, 19 May 95 09:01:34 EDT Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 8484; Fri, 19 May 1995 09:00:53 -0400 Message-Id: Date: Fri, 19 May 1995 09:00:52 -0400 (EDT) From: "Jerry Bryan" To: "Cube Lovers List" Subject: AntiSlice Under M-conjugacy Mark Longridge's antislice results are as follows: > arrangements arrangements >Moves Deep (2q or anti-slice moves) (4q or double anti-slice moves) > > 0 1 1 > 1 6 9 > 2 27 51 > 3 120 265 > 4 423 864 > 5 1,098 1,785 > 6 1,770 2,017 > 7 1,650 1,008 > 8 851 144 > 9 198 > ----- ----- > 6,144 6,144 We now have the following M-conjugacy results (2q moves only, still working on 4q moves). Level Positions Local Maxima 0 1 0 1 1 0 2 3 0 3 10 0 4 37 0 5 93 1 6 166 2 7 147 7 8 89 12 9 21 21 ---- 568 The level 5 local maximum is (U'D')(FB)(FB)(UD)(L'R'). The position is not its own inverse, but we can use as an inverse (U'D')(FB)(FB)(UD)(LR). Hence, (U'D')(FB)(FB)(UD) forms a nice "middle" of the sequence. In fact, the (U'D')(FB)(FB)(UD) position in some ways seems more interesting than the local maximum itself. Does it already have a name? I have not verified if the length of the local maximum is 10q in G, nor if it is a local maximum in G. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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