Balanced bipartite weighing designs

Balanced bipartite 4-cycle designs

Some Balanced Bipartite Row-column Designs

A series of balanced bipartite row-column designs (BBPRC-designs) into sets of treatments with v1=4t+3 (test treatments) v2=2t+2 (control treatments) with varying replication has been obtained by supplementing a set of v2=2t+2 treatments in blank positions of non-orthogonal RC design of Agrawal (1966). Such designs find applications in agricultural and industrial experimentation where the inves...

Applying Balanced Generalized Weighing Matrices to Construct Block Designs

Balanced generalized weighing matrices are applied for constructing a family of symmetric designs with parameters (1 + qr(rm+1 − 1)/(r − 1), rm, rm−1(r − 1)/q), where m is any positive integer and q and r = (qd − 1)/(q − 1) are prime powers, and a family of non-embeddable quasi-residual 2−((r+1)(rm+1−1)/(r−1), rm(r+ 1)/2, rm(r− 1)/2) designs, where m is any positive integer and r = 2d− 1, 3 · 2...

On the existence of balanced bipartite designs, II

A block, considered as a set of elements together with its adjacency matrix M, is called a B-block if M is the adjacency matrix of a complete bipartite graph Kk,, k, . A balanced bipartite design with parameters b, u, r, k, h, kl, k2 (briefly BBD(u, k, A; kl)) is an arrangement of u elements into b B-blocks such that every B-block contains k = kl + ki elements, every element occurs in exactly r...

Bipartite Designs

We investigate the solution set of the following matrix equation: A T B = J + diag(d); where A and B are n n f0; 1g matrices, J is the matrix with all entries equal one and d is a full support vector. We prove that in some special cases (such as: both Ad ?1 and Bd ?1 have full supports, where d ?1 = (d ?1 1 ; : : : ; d ?1 n) T ; both A and B have constant column sums; d ?1 1 6 = ?1; and A has c...