Existence of Weakly Pandiagonal Orthogonal Latin Squares  

作　　者：Yong ZHANG Wen LI Jian Guo LEI 

机构地区：[1]College of Mathematics and Information Science, Hebei Normal University

出　　处：《Acta Mathematica Sinica,English Series》2013年第6期1089-1094,共6页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.61071221,10831002,11071207 and 11201407);Natural Science Foundation of Jiangsu Higher Education Institutions of China(Grant No.12KJD110007);Natural Science Foundation of Jiangsu Province(Grant No.BK2012245)

摘　　要：A weakly pandiagonal Latin square of order n over the number set {0, 1, . . . , n-1} is a Latin square having the property that the sum of the n numbers in each of 2n diagonals is the same. In this paper, we shall prove that a pair of orthogonal weakly pandiagonal Latin squares of order n exists if and only if n ≡ 0, 1, 3 （mod 4） and n≠3.A weakly pandiagonal Latin square of order n over the number set {0, 1, . . . , n-1} is a Latin square having the property that the sum of the n numbers in each of 2n diagonals is the same. In this paper, we shall prove that a pair of orthogonal weakly pandiagonal Latin squares of order n exists if and only if n ≡ 0, 1, 3 （mod 4） and n≠3.

关 键 词：Latin square weakly pandiagonal Knut Vik design 

分 类 号：O151.21[理学—数学]