From BRYAN@wvnvm.wvnet.edu Wed Jun 28 12:52:18 1995 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA20782; Wed, 28 Jun 95 12:52:18 EDT Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R2) with BSMTP id 4454; Wed, 28 Jun 95 10:09:51 EDT Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 0089; Wed, 28 Jun 1995 10:09:52 -0400 Message-Id: Date: Wed, 28 Jun 1995 10:09:51 -0400 (EDT) From: "Jerry Bryan" To: "Cube Lovers List" Subject: Re: Re: A Third Way to Calculate the Real Size of Cube Space? In-Reply-To: Message of 06/20/95 at 14:39:00 from , Martin.Schoenert@Math.RWTH-Aachen.DE I guess I am going to have to break down and get a copy of GAP. It is truly impressive how much GAP can do so easily. My interpretation of Martin's GAP program is that it implements the general outline of the algorithm I described, except that GAP was able to calculate the number of K-symmetric permutations in a very simple and direct way, whereas I was going to have to puzzle each one out by hand. The heart of Martin's program appears to be the following, and I have a couple of questions. > # compute how many elements have at least this symmetry group > number := Size( Centralizer( G, rep ) ); The first question is: how does the Size function work? As a simpler example than the one above, what if you simply say Size(G)? I am naively assuming that G is specified to GAP in terms of generators only, and that it makes no attempt to actually represent each element of G (too big!). And I have seen snippets of GAP libraries for G posted by Mark Longridge, and they look like generators. I have been in several group theory books lately, and I don't recall seeing a general algorithm presented for determining the size of a finite group based on its generators. The second question is like unto the first: how does the Centralizer function work? In this particular case, we don't really need the Centralizer, we only need the Size of the Centralizer, but the question remains in either case. Surely, GAP does not literally try each element of G and each element of rep to see which elements commute (too big again). So what is the general algorithm? = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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