On Joint Realization of (0,1) -matrices

Let R=（r1,…,rm）,S=（s1,…,sn）,R’=（r1’,…,rm’） and S’=（S1’,…,Sm’）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]）.