From cube-lovers-errors@mc.lcs.mit.edu Tue Oct 7 17:04:52 1997 Return-Path: Received: from sun30.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id RAA06610; Tue, 7 Oct 1997 17:04:51 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From jbryan@pstcc.cc.tn.us Tue Oct 7 16:59:58 1997 Date: Tue, 07 Oct 1997 16:59:25 -0400 (Eastern Daylight Time) From: Jerry Bryan Subject: Maximality Analysis Through 11q To: cube-lovers@ai.mit.edu Message-Id: Not too long ago, I reported that my Shamir program had completed searching through 11q from Start, that the results did confirm my previous results using tape spinning programs, that no local maxima were found 11q from Start, and that otherwise nothing new was found. I have come to realize that there is a small bit of new information. I really should post the maximality analysis in its entirety, because the whole row 11q from Start is new. The row 11q from Start does include the failure to find any new local maxima. As always, the local maxima are in the right-most column, where all 12 moves go closer to Start. Maximalility Analysis In Terms of Patterns (M-conjugacy classes) Number of Moves which go Closer to Start 1 1 1 0 1 2 3 4 5 6 7 8 9 0 1 2 |x| 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 2 0 2 3 0 0 0 0 0 0 0 0 0 0 3 0 20 4 1 0 0 0 0 0 0 0 0 0 4 0 182 34 2 1 0 0 0 0 0 0 0 0 5 0 1677 280 20 1 0 0 0 0 0 0 0 0 6 0 15642 2561 184 8 0 0 0 0 0 0 0 0 7 0 145974 23773 1721 61 0 0 0 0 0 0 0 0 8 0 1362579 222235 16241 663 1 3 0 3 0 0 0 0 9 0 12719643 2077549 153026 5954 74 15 2 3 0 0 0 0 10 0 118711701 19418503 1438825 58862 925 318 11 37 0 8 0 4 11 0 1107594690 181433604 13517370 576891 11843 3442 251 321 10 21 2 0 Maximalility Analysis In Terms of Positions Number of Moves which go Closer to Start 0 1 2 3 4 5 6 7 |x| 0 1 0 0 0 0 0 0 0 1 0 12 0 0 0 0 0 0 2 0 96 18 0 0 0 0 0 3 0 912 144 12 0 0 0 0 4 0 8544 1368 96 3 0 0 0 5 0 80088 12816 912 24 0 0 0 6 0 749376 120612 8640 252 0 0 0 7 0 7001712 1135104 82152 2664 0 0 0 8 0 65391504 10645824 777936 28200 48 56 0 9 0 610499652 99666528 7338720 280800 3048 624 96 10 0 5698027296 931905180 69049264 2796978 43800 12336 528 11 0 53164171632 8708296416 648777868 27618360 563880 159024 11904 1 1 1 8 9 0 1 2 |x| 0 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 0 5 0 0 0 0 0 6 0 0 0 0 0 7 0 0 0 0 0 8 27 0 0 0 0 9 108 0 0 0 0 10 1296 0 138 0 42 11 14856 408 828 72 0 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us Pellissippi State (423) 539-7198 10915 Hardin Valley Road (423) 694-6435 (fax) P.O. Box 22990 Knoxville, TN 37933-0990