arXiv math/02102752002-10-17math.CO

Odd Order Pandiagonal Latin and Magic Cubes in Three and Four Dimensions

Solomon Gartenhaus

备注：: 30 pages, Latex

英文摘要：

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.

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