On all of whose members are indecomposable

Let m and n be positive integers, and let R=(r1,r2,…,rm) and S=(s1,s2,…,sn) be non-negative integral vectors with r1+ +rm=s1+ +sn. In this paper, we present some sufficient conditions for any (0,1)-matrix with row sum vector R and column sum vector S to be indecomposable.