简单正交多阵SOMA(4,n)的存在性  

Existence of Simple Orthogonal Multi-array SOMA(4, n)

作　　者：张燕艳 李韵 王素[1] ZHANG Yanyan;LI Yun;WANG Su(School of Sciences,Nantong University,Nantong 226019,China;Basic Teaching Institute,Nantong Institute of Technology,Nantong 226002,China;Nantong University Xinglin College,Nantong 226007,China)

机构地区：[1]南通大学理学院,江苏南通226019 [2]南通理工学院基础教学学院,江苏南通226002 [3]南通大学杏林学院,江苏南通226007

出　　处：《南通大学学报（自然科学版）》2018年第2期50-54,共5页Journal of Nantong University(Natural Science Edition)　

基　　金：国家自然科学基金项目(11371207)

摘　　要：设整数k>0,n≥2,简单正交多阵SOMA(k,n)是一个n×n的方阵A,它的每一个单元格包含kn-元集S的一个k-元子集且满足:1)S的每个元素在A的每一行和每一列恰好出现一次;2)S的每个2-元子集至多出现在A的一个单元格中.总结了SOMA(k,n)存在的最新结果,并且阐述了它和相互正交拉丁方之间的关系,同时通过直接构造的方法证明了n≥5,SOMA(4,n)的存在性,并且提出了进一步研究的问题.Let k 0 and n ≥ 2 be integers. A simple orthogonal multi-array SOMA（k, n） is an n × n array A each of whose entries is a k-subset of a kn-set S of symbols, such that every symbol of S occurs exactly once in each row and exactly once in each column of A, and every 2-subset of S is contained in at most one entry of A. In this note, it is summarized that the latest results of the existence of a SOMA（k, n） and explain the relationship between it and mutually orthogonal Latin squares, and by direct construction show that there exists a SOMA（4, n） for n ≥ 5.And further research questions are also put forward.

关 键 词：正交阵 简单正交多阵 拉丁方 正交性 存在性 

分 类 号：O157.2[理学—数学] O157.3[理学—基础数学]