The Magic of Permutation Matrices: Categorizing, Counting and Eigenspectra of Magic Squares
History and Overview
2010-07-20 v1
Abstract
Permutation matrices play an important role in understand the structure of magic squares. In this work, we use a class of symmetric permutation matrices than can be used to categorize magic squares. Many magic squares with a high degree of symmetry are studied, including classes that are generalizations of those categorized by Dudeney in 1917. We show that two classes of such magic squares are singular and the eigenspectra of such magic squares are highly structured. Lastly, we prove that natural magic squares of singly-even order of these classes do note exist.
Cite
@article{arxiv.1007.3239,
title = {The Magic of Permutation Matrices: Categorizing, Counting and Eigenspectra of Magic Squares},
author = {Peter Staab and Charles Fisher and Mark Maggio and Michael Andrade and Erin Farrell and Haley Schilling},
journal= {arXiv preprint arXiv:1007.3239},
year = {2010}
}
Comments
26 pages