Generalized latin square

Abstract

LetX be a n-set and letA = [aij] be an xn matrix for whichaij ⊆X, for 1 ≤i, j ≤n. A is called a generalized Latin square onX, if the following conditions is satisfied:\( \cup _{i = 1}^n a_{ij} = X = \cup _{j = 1}^n a_{ij} \). In this paper, we prove that every generalized Latin square has an orthogonal mate and introduce a Hv -structure on a set of generalized Latin squares. Finally, we prove that every generalized Latin square of ordern, has a transversal set.