From BRYAN@wvnvm.wvnet.edu Fri Oct 6 16:39:08 1995 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA01095; Fri, 6 Oct 95 16:39:08 EDT Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R3) with BSMTP id 8544; Fri, 06 Oct 95 09:25:11 EDT Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 2139; Fri, 6 Oct 1995 09:25:12 -0400 Message-Id: Date: Fri, 6 Oct 1995 09:25:11 -0400 (EDT) From: "Jerry Bryan" To: "Cube Lovers List" Subject: Preliminary Search Results for The first step in finding |B| in is to build a little Start-rooted data base using only the ten generators F, F', U, U', etc. I was able to search eight levels deep with a "quick and dirty" search. To search deeper would take a good bit longer. I hope that eight levels will be enough to calculate |B|. By constructing a companion B-rooted data base, I should be able to test up to 15 levels deep. (B is odd, so eight levels deep for each half-depth search only gets you 15 levels total instead of 16.) I haven't started the search for B yet, but I thought the results so far might be of minor interest in their own right. As I indicated before, these are actual cube positions. I haven't figured out any way to apply conjugacy classes to this problem. I find it a little puzzling that the branching factor is not monotonically decreasing (c.f., level 3 to level 4). Level Number of Local Branching Positions Max Factor 0 1 0 1 10 0 10.000 2 77 0 7.700 3 584 0 7.584 4 4,434 0 7.592 5 33,664 0 7.592 6 255,320 0 7.584 7 1,933,936 7.575 8 14,635,503 7.568 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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