Matrices of zeros and ones with given line sums and a zero block

We study the existence of (0,1)-matrices with given line sums and a fixed zero block. An algorithm is given to construct such a matrix which is based on three applications of the well-known Gale–Ryser algorithm for constructing (0,1)-matrices with given line sums. A characterization in terms of a certain “structure matrix” is proved. Further properties of this structure matrix are also established, and its rank is determined and interpreted combinatorially.