Symmetric and Hankel-Symmetric Transportation Polytopes

Authors

Lei Cao, Shandong Normal University - China; Nova Southeastern UniversityFollow
Zhi Chen, Nanjing Agricultural University - China
Qiang Li, Nanjing Agricultural University - China
Huilan Li, Shandong Normal University - China

Document Type

Article

Publication Date

4-15-2020

Publication Title

Linear and Multilinear Algebra

Keywords

Transportation polytopes, Doubly stochastic matrices

ISSN

0308-1087

First Page

1

Last Page

19

Abstract

In this paper, we consider the symmetric and Hankel-symmetric transportation polytope U^t&h(R,S), which is the convex set of all symmetric and Hankel-symmetric non-negative matrices with prescribed row sum vector R and prescribed column sum vector S. We characterize all extreme points of U^t&h(R,S). Moreover, we show that the extreme points of Ω^t&h_n, the polytope of symmetric and Hankel-symmetric doubly stochastic matrices, can be obtained from the extreme points of U^t&h(R,S) by specializing to the case that R = S = (1, 1, ..., 1) E Rⁿ.

Comments

©2020 Informa UK Limited, trading as Taylor & Francis Group

Additional Comments

National Natural Science Foundation of China grant #s: 11601233, 11701339; Fundamental Research Funds for the Central Universities grant #: KJQN201718; Natural Science Foundation of Jiangsu Province grant #: BK20160708

NSUWorks Citation

Cao, Lei; Chen, Zhi; Li, Qiang; and Li, Huilan, "Symmetric and Hankel-Symmetric Transportation Polytopes" (2020). Mathematics Faculty Articles. 296.
https://nsuworks.nova.edu/math_facarticles/296

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019

DOI

10.1080/03081087.2020.1750548