From BRYAN@wvnvm.wvnet.edu Thu May 18 10:17:25 1995 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA24497; Thu, 18 May 95 10:17:25 EDT Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R2) with BSMTP id 8692; Thu, 18 May 95 09:29:25 EDT Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 5434; Thu, 18 May 1995 09:29:25 -0400 Message-Id: Date: Thu, 18 May 1995 09:29:24 -0400 (EDT) From: "Jerry Bryan" To: , "Cube Lovers List" Subject: Re: more on the slice group In-Reply-To: Message of 05/11/95 at 17:57:14 from mreid@ptc.com On 05/11/95 at 17:57:14 mreid@ptc.com said: >jerry asks about P-symmetric positions. coincidentally, i happened >to investigate these a few weeks back, and here's what i found: >(i calculated by hand, so i'd be grateful for any confirmation.) >there are 128 P-symmetric positions, 4 of which are M-symmetric. I can confirm your count. These positions are called X class positions in Dan's taxonomy. That is, there are 124 positions Y unique up to M-conjugancy for which Symm(Y)=X1 or Symm(Y)=X2 or Symm(Y)=X3, where X1, X2, and X3 are the three conjugate subgroups of M in Dan's taxonomy of subgroups which contain sixteen elements. Hence, we describe the 124 positions as being class X positions. The 4 M-symmetric positions are also X-symmetric, but we don't count them as class X. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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