## Mathematics Faculty Articles

#### Title

The extreme points of centrosymmetric transportation polytopes

#### Document Type

Article

#### Publication Date

1-1-2021

#### Publication Title

Linear Algebra and Its Applications

#### Keywords

Centrosymmetric matrices, Doubly stochastic matrices, Transportation polytopes

#### ISSN

00243795

#### Volume

608

#### First Page

214

#### Last Page

235

#### Abstract

Denote by Uπ(R,S) the convex set of nonnegative centrosymmetric matrices with given row sum vector R and column sum vector S, and denote by U≤π(R,S) the convex set of nonnegative centrosymmetric matrices with the row sum vector componentwisely dominated by R and the column sum vector componentwisely dominated by S respectively. We characterize all extreme points of Uπ(R,S) and U≤π(R,S). In addition, we show that the extreme points of Ωnπ, the polytope of all n×n centrosymmetric doubly stochastic matrices, and the extreme points of ωnπ, the polytope of all n×n centrosymmetric doubly substochastic matrices, can be obtained by letting R=S=(1,1,…,1) in Uπ(R,S) and U≤π(R,S) respectively.

#### NSUWorks Citation

Chen, Zhi; Cao, Lei; and Koyuncu, Selcuk, "The extreme points of centrosymmetric transportation polytopes" (2021). *Mathematics Faculty Articles*. 324.

https://nsuworks.nova.edu/math_facarticles/324

#### ORCID ID

0000-0001-7613-7191

#### ResearcherID

G-7341-2019

#### DOI

10.1016/j.laa.2020.08.029

COinS