Resolvable balanced bipartite designs

A block B denotes a set of k = k"1 + k"2 elements which are divided into two subsets, B^1 and B^2, where |B^i| = k"i, i = 1 or 2. Two elements are said to be linked in B if and only if they belong to different subsets of B. A balanced bipartite design, BBD(v, k"1, k"2, @l), is an arrangement of v elements into b blocks, each containing k elements such that each element occurs in exactly r blocks and any two distinct elements are linked in exactly @l blocks. A resolvable balanced bipartite design, RBBD(v, k"1, k"2, @l), is a BBD(v, k"1, k"2, @l), the b blocks of which can be divided into r sets which are called complete replications, such that each complete replication contains all the v elements of the design. Necessary conditions for the existence of RBBD(v, 1, k"2, @l) and RBBD(v, n, n, @l) are obtained and it is shown that some of the conditions are also sufficient. In particular, necessary and sufficient conditions for the existence of RBBD(v, 1, k"2, @l), where k"2 is odd or equal to two, and of RBBD(v, n, n, @l), where n is even and 2n - 1 is a prime power, are given.