Odd Order Pandiagonal Latin and Magic Cubes in Three and Four Dimensions
Combinatorics
2007-05-23 v1
Abstract
Explicit algorithms are developed for constructing odd order n pandiagonal latin cubes in 3 and 4 dimensions, and these are used to construct pandiagonal magic cubes and 4 dimensional hypercubes, respectively. It is established that these structures exist in 3 dimensions only for odd orders n not less than 11, and in 4 dimensions only for odd orders n not less than 17. Estimates for the number of such structures as functions of n in 3 and 4 dimensions are also presented.
Keywords
Cite
@article{arxiv.math/0210275,
title = {Odd Order Pandiagonal Latin and Magic Cubes in Three and Four Dimensions},
author = {Solomon Gartenhaus},
journal= {arXiv preprint arXiv:math/0210275},
year = {2007}
}
Comments
30 pages, Latex