Partitions of the Polytope of Doubly Substochastic Matrices

Authors

Lei Cao, Shandong Normal University - China; Georgian Court UniversityFollow
Zhi Chen, Nanjing Agricultural University - China

Document Type

Article

Publication Date

2-15-2019

Publication Title

Linear Algebra and its Applications

Keywords

Set partitions, Doubly substochastic matrices, Transportation polytopes

ISSN

0024-3795

Volume

563

First Page

98

Last Page

122

Abstract

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.

Comments

©2019 Elsevier Inc. All rights reserved.

Additional Comments

National Natural Science Foundation of China grant #: 11601233; Fundamental Research Funds for the Central Universities grant #: KJQN201718; Natural Science Foundation of Jiangu Province grant #: BK20160708

NSUWorks Citation

Cao, Lei and Chen, Zhi, "Partitions of the Polytope of Doubly Substochastic Matrices" (2019). Mathematics Faculty Articles. 278.
https://nsuworks.nova.edu/math_facarticles/278

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019

DOI

10.1016/j.laa.2018.10.024