The number of "magic" squares and hypercubes

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We define a magic square to be a square matrix whose entries are nonnegative integers and whose rows, columns, and main diagonals sum up to the same number. We prove structural results for the number of such squares as a function of the size of the matrix and the line sum. We give examples for small sizes and show similar results for symmetric, pandiagonal magic squares, and magic hypercubes.
11 pages, 2 figures

Keywords

Combinatorics, Number Theory, 05A15, 52C07; 11H06, 11P21

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/63029

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0201013
 http://arxiv.org/abs/math/0201013
 American Mathematical Monthly 110, no. 8 (2003), 707-717

Collections

arXiv