素数阶均衡完美幻方若干问题初探  

Preliminary study of balanced perfect magic square of prime order

作　　者：陈剑南[1] 

机构地区：[1]国防科技大学计算机学院,长沙410073

出　　处：《计算机工程与应用》2009年第21期179-182,共4页Computer Engineering and Applications

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。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 ortbogonal 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.

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 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]