From BRYAN@wvnvm.wvnet.edu Fri Apr 14 23:33:20 1995 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA02160; Fri, 14 Apr 95 23:33:20 EDT Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R2) with BSMTP id 4917; Fri, 14 Apr 95 21:12:54 EDT Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 4876; Fri, 14 Apr 1995 21:12:54 -0400 Message-Id: Date: Fri, 14 Apr 1995 21:12:53 -0400 (EDT) From: "Jerry Bryan" To: "Cube Lovers List" Subject: Re: Repetitive Application of Elements of Q* In-Reply-To: Message of 04/14/95 at 17:06:48 from BRYAN@wvnvm.wvnet.edu The astute reader will have noticed that there *has* to be an error in the table as it was originally posted. It is impossible for there to be two distinct sequences of length 2, because there is only one position unique up to M-conjugancy which is only one qturn from Start. All of the lengths in the original table except for one were short by one. I had two programs -- one to generate the sequences to a file, and a second to analyze the sequences. The first program did not write Start to the file, resulting in all the sequences except one being one short. Here follows the correction. (Incorrect) (Correct) > Operation Length Length > of of > Sequence Sequence > F* 11 12 > U* 10 11 > L* 7 8 > R* 3 4 > D* 9 10 > B* 2 2 !! > F'* 7 8 > U'* 10 11 > L'* 4 5 > R'* 6 7 > D'* 7 8 > B'* 2 3 >To take a little more interesting case, I tried i(F*D'*) ^ n. In this >case, there were 63 unique elements in the sequence, and then the >8-th through the 63-rd elements repeated. Hence, the final cycle had >56 elements rather than the 2 elements of the simpler cases. Similarly, here there were 64 unique elements in the sequence, with the 9-th through the 64-th elements repeated. The final cycle still (correctly) had 56 elements. The length of the final cycle has to be even, of course, since qturns are odd. > = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = >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 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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