Latin Matrix and Its Construction

Shanqi Pang 1 and Yingshan Zhang 2
1 Department of Mathematics, Henan Normal University, Xinxiang 453007, P. R. China
2 Department of Statistics, East China Normal University, Shanghai 200062, P. R. China


Abstract     Full Text  PDF

In this paper, the definitions of Latin matrix and orthogonal Latin matrices are introduced. By using the property of orthogonal array, a checking method for orthogonal Latin matrices is presented. Through the generalized Kronecker product and permutation matrix, we study the construction methods for orthogonal Latin matrices such as addition, multiplication and permutation matrix method. Some applications to Combinatorics and Statistics are given.