Newsgroups: comp.archives
Path: utzoo!utgpu!news-server.csri.toronto.edu!ox.com!msen.com!emv
From: ghot@ms.uky.edu (Allan Adler)
Subject: [sci.math] Re: Magic square questions
Message-ID: <1991Apr16.233944.4604@ox.com>
Followup-To: sci.math
Sender: emv@msen.com (Edward Vielmetti, MSEN)
Reply-To: ghot@ms.uky.edu (Allan Adler)
Organization: University Of Kentucky, Dept. of Math Sciences
References: <11180001@hpsgm2.sgp.hp.com> <1991Apr16.095425.2061@odin.diku.dk> <1991Apr16.181510.28286@ms.uky.edu>
Date: Tue, 16 Apr 1991 23:39:44 GMT
Approved: emv@msen.com (Edward Vielmetti, MSEN)
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Archive-name: math/algebra/monoid/1991-04-16
Archive: f.ms.uky.edu:/pub/math-papers/monoid.tar.Z [128.163.128.6]
Original-posting-by: ghot@ms.uky.edu (Allan Adler)
Original-subject: Re: Magic square questions
Reposted-by: emv@msen.com (Edward Vielmetti, MSEN)


Torben Mogensen mentions a method of multiplying two magic squares to get
another one.

I first published this method in a paper in the Monthly in 1978. I noted
that the operation is associative, left and right cancellative and has an
identity element and also made sense for magic N-cubes. Thus magic N-cubes
form a monoid for every N>1. I also conjectured that the monoid is free.

In my paper, Magic N-Cubes Form A Free Monoid, I proved this conjecture.
The paper is available via anonymous ftp from f.ms.uky.edu in compressed
tar format in the file pub/math-papers/monoid.tar.Z.

As for his question about magic cubes with side less than 7, there is one
displayed in my 1978 Monthly paper, a 3x3x3, constructed using Prouhet
sequences, a method also introduced in the 1978 paper.

A generalization of the results of that method is introduced in my paper
Magic Cubes and the 3-Adic Zeta Function, available via anonymous ftp in
the file pub/math-papers/magic.tar.Z.

Allan Adler
ghot@ms.uky.edu

-- comp.archives file verification
f.ms.uky.edu
-rw-rw-r--  1 686      132         49505 Mar 23 02:06 /pub/math-papers/monoid.tar.Z
found monoid ok
f.ms.uky.edu:/pub/math-papers/monoid.tar.Z
