Full patterns in truncated transportation polytopes
Darald J. Hartfiel · Linear and Multilinear Algebra · 1991
Let R = (r 1,…,rm ) and S = (s 1,…,s n) be vectors and D = (dij ) an m × n matrix all having positive entries. Let Ω(R,S,D) = {m × n matrices A = (aij ) such that and 0≦aij for all i,j}. For any A∊Ω(R,S,D) let A∗=(a∗ ij be the (0,1)-matrix with a∗ ij=1 if and only if aij>0. Let ω∗(R,S,D)={A∗ where A∊Ω(R,S,D)}. A matrixA∊Ω∗(R,S,D) is called a full pattern matrix if whenever any 0 of A is replaced by a 1, yielding B, then B∊Ω∗(R,S,D). This paper describes the full pattern matrices in Ω∗(R,S,D)