Generalized latin squares I

Abstract The classical definition of Latin squares is generalized by allowing multiple occurences of symbols in each row and each column. A perfect k, l >- Latin square is an N X N array in which any row or column contains every distinct symbol and the symbol at position ( i, j ) appears exactly k times in the i th row and l times in the j th column, or vice versa. Existence of such squares and the notion of orthogonality for such squares are studied. Several algorithms for constructing such squares are presented.