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.
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)
