On Joint Realization of (0,1) -matrices

Let R=(r_1,…,r_m),S=(s_1,…,s_n),R’=(r_1',…,r_m') and S'=(S_1',…,S_m')be non-negative integral vectors.Denote by (R,S)the class of(0,1)-matrices withrow sum vector R and column sum vector S. The three classes (R,S), (R’,S’)and (R R’,S S’)are called jointly realizable if there exist a matrix A in (R,S)and a matrix B in (R’,S’)such that A B∈ (R R’,S S’). In 1980,R.A.Brualdi and R.P.Anstee posed the following conjecture inde-pendently(see 1]).