ghot@ms.uky.edu (Allan Adler) (04/17/91)
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