From mreid@ptc.com Mon May 22 17:31:26 1995 Return-Path: Received: from ptc.com (poster.ptc.com) by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA03820; Mon, 22 May 95 17:31:26 EDT Received: from ducie by ptc.com (5.0/SMI-SVR4-NN) id AA04356; Mon, 22 May 95 17:29:23 EDT Received: by ducie (1.38.193.4/sendmail.28-May-87) id AA21637; Mon, 22 May 1995 17:48:42 -0400 Date: Mon, 22 May 1995 17:48:42 -0400 From: mreid@ptc.com (michael reid) Message-Id: <9505222148.AA21637@ducie> To: cube-lovers@ai.mit.edu Subject: AntiSlice Under M-conjugacy (and a problem with slice) Content-Length: 1713 jerry writes (about the antislice group) > The level 5 local maximum is (U'D')(FB)(FB)(UD)(L'R'). [ ... ] > I have not verified if the length of the local maximum is 10q in G, > nor if it is a local maximum in G. this is exactly what i tried to explain in my recent posts: the latter statement follows from the former. and yes, its length is indeed 10q. it's pretty easy to find maneuvers which end in each quarter turn: (F'B') (UUDD) (FB) (RL) = (U'D') (FFBB) (UD) (R'L') = (R'L') (U'D') (FFBB) (UD) = (R'L') (UD) (FFBB) (U'D') = (RL) (F'B') (UUDD) (FB) = (RL) (FB) (UUDD) (F'B'). > We have the following M-conjugacy results for 4q moves. Strong > and weak local maxima are defined according to my preference. it seems like jerry's terminology is more reasonable, so i'll stop using mine. jerry's figures > Level Positions Strong Weak Total > Local Max Local Max Local Max > > 0 1 0 0 0 > 1 2 0 0 0 > 2 5 0 0 0 > 3 25 0 1 1 > 4 75 0 2 2 > 5 152 0 19 19 > 6 184 1 35 36 > 7 108 0 46 46 > 8 16 0 16 16 > ---- > 568 beg the obvious question: what is that strong local maximum, which is unique up to symmetry? mike