## Mathematics Faculty Articles

# 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

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