Partitions of the Polytope of Doubly Substochastic Matrices
Linear Algebra and its Applications
Set partitions, Doubly substochastic matrices, Transportation polytopes
In this paper, we provide three different ways to partition the polytope of doubly substochastic matrices into subpolytopes via the prescribed row and column sums, the sum of all elements and the sub-defect respectively. Then we characterize the extreme points of each type of convex subpolytopes. The relations of the extreme points of the subpolytopes in the three partitions are also given.
Cao, Lei and Chen, Zhi, "Partitions of the Polytope of Doubly Substochastic Matrices" (2019). Mathematics Faculty Articles. 278.