Preliminary study of balanced perfect magic square of prime order

doi:10.3778/j.issn.1002-8331.2009.21.053

Computer Engineering and Applications ›› 2009, Vol. 45 ›› Issue (21): 179-182.DOI: 10.3778/j.issn.1002-8331.2009.21.053

• 理论科学研究 • Previous Articles Next Articles

Preliminary study of balanced perfect magic square of prime order

CHEN Jian-nan

Computer Institute，National Uniersity of Defense Technology，Changsha 410073，China

Received:2009-05-05 Revised:2009-06-09 Online:2009-07-21 Published:2009-07-21
Contact: CHEN Jian-nan

素数阶均衡完美幻方若干问题初探

陈剑南

国防科技大学计算机学院，长沙 410073

通讯作者: 陈剑南

Abstract

Abstract: Magic square and latin square are all problems of Combinatorial Mathematics.They are closely related.The paper defines balanced perfect magic square based on the relation between magic square and latin square.It demonstrates the relation between balanced perfect magic square and orthogonal perfect latin squares.It proves that some kinds of latin squares can determine a regular group.It also demonstrates the NP-completeness of the problem that how we complete the unfinished balanced perfect magic square of prime order.

Key words: balanced perfect magic square, perfect latin squares, permutation, regular group, completing partial problem, Non-deterministic Polynomial（NP）-completeness

摘要： 幻方与拉丁方都是属于组合数学范畴的问题，两者关系十分密切。为进一步研究拉丁方与幻方之间的关系，在完美幻方的基础上，提出均衡完美幻方的概念，证明了均衡完美幻方与正交完美拉丁方对是一一对应的，同时发现了基于Zn的n阶完美拉丁方与正则群的联系。还从完美拉丁方的缺陷填充问题出发成功规约到均衡完美幻方的缺陷填充问题上，证明了素数阶均衡完美幻方的缺陷填充判定问题是NP完全的。

关键词: 均衡完美幻方, 完美拉丁方, 置换, 正则群, 缺陷填充问题, NP完全性

CHEN Jian-nan. Preliminary study of balanced perfect magic square of prime order[J]. Computer Engineering and Applications, 2009, 45(21): 179-182.

陈剑南. 素数阶均衡完美幻方若干问题初探
[J]. 计算机工程与应用, 2009, 45(21): 179-182.

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Preliminary study of balanced perfect magic square of prime order

素数阶均衡完美幻方若干问题初探

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