English

The number of "magic" squares and hypercubes

Combinatorics 2007-05-23 v3 Number Theory

Abstract

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.

Keywords

Cite

@article{arxiv.math/0201013,
  title  = {The number of "magic" squares and hypercubes},
  author = {Matthias Beck and Moshe Cohen and Jessica Cuomo and Paul Gribelyuk},
  journal= {arXiv preprint arXiv:math/0201013},
  year   = {2007}
}

Comments

11 pages, 2 figures