Enumeration of associative magic squares of order 7
Combinatorics
2019-06-19 v1
Abstract
An associative magic square is a magic square such that the sum of any 2 cells at symmetric positions with respect to the center is constant. The total number of associative magic squares of order 7 is enormous, and thus, it is not realistic to obtain the number by simple backtracking. As a recent result, Artem Ripatti reported the number of semi-magic squares of order 6 (the magic squares of 6x6 without diagonal sum conditions) in 2018. In this research, with reference to Ripatti's method of enumerating semi-magic squares, we have calculated the total number of associative magic squares of order 7. There are exactly 1,125,154,039,419,854,784 associative magic squares of order 7, excluding symmetric patterns.
Cite
@article{arxiv.1906.07461,
title = {Enumeration of associative magic squares of order 7},
author = {Go Kato and Shin-ichi Minato},
journal= {arXiv preprint arXiv:1906.07461},
year = {2019}
}
Comments
18 pages, 10 figures