Symmetric and Hankel-Symmetric Transportation Polytopes

Lei Cao; Zhi Chen; Qiang Li; Huilan Li

doi:10.1080/03081087.2020.1750548

Symmetric and Hankel-Symmetric Transportation Polytopes

Lei Cao
, Zhi Chen
, Qiang Li
, Huilan Li

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Pages (from-to)	955-973
Number of pages	19
Journal	Linear and Multilinear Algebra
Volume	70
Issue number	5
DOIs	https://doi.org/10.1080/03081087.2020.1750548
State	Published - Apr 15 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2020 Informa UK Limited, trading as Taylor & Francis Group.

Funding

Z. Chen is supported by the National Natural Science Foundation of China [No. 11601233]; the Fundamental Research Funds for the Central Universities [No. KJQN201718]; the Natural Science Foundation of Jiangsu Province [BK20160708]. H. Li is supported by the National Natural Science Foundation of China [No. 11701339]. We are grateful to the anonymous referees for their valuable comments on our paper.

Funders	Funder number
National Natural Science Foundation of China	11601233
National Natural Science Foundation of China
Natural Science Foundation of Jiangsu Province	11701339, BK20160708
Natural Science Foundation of Jiangsu Province
Fundamental Research Funds for the Central Universities	KJQN201718
Fundamental Research Funds for the Central Universities

ASJC Scopus Subject Areas

Algebra and Number Theory

Keywords

Doubly stochastic matrices
Transportation polytopes
15B51
52B05
doubly stochastic matrices
05A18

Disciplines

Mathematics

Access to Document

10.1080/03081087.2020.1750548

Cite this

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title = "Symmetric and Hankel-Symmetric Transportation Polytopes",

abstract = "In this paper, we consider the symmetric and Hankel-symmetric transportation polytope Ut\&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 Ut\&h(R,S). Moreover, we show that the extreme points of Ωt\&hn, the polytope of symmetric and Hankel-symmetric doubly stochastic matrices, can be obtained from the extreme points of Ut\&h(R,S) by specializing to the case that R = S =(1, 1, ..., 1) E Rn.",

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doi = "10.1080/03081087.2020.1750548",

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AU - Cao, Lei

AU - Chen, Zhi

AU - Li, Qiang

AU - Li, Huilan

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Y1 - 2020/4/15

N2 - In this paper, we consider the symmetric and Hankel-symmetric transportation polytope Ut&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 Ut&h(R,S). Moreover, we show that the extreme points of Ωt&hn, the polytope of symmetric and Hankel-symmetric doubly stochastic matrices, can be obtained from the extreme points of Ut&h(R,S) by specializing to the case that R = S =(1, 1, ..., 1) E Rn.

AB - In this paper, we consider the symmetric and Hankel-symmetric transportation polytope Ut&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 Ut&h(R,S). Moreover, we show that the extreme points of Ωt&hn, the polytope of symmetric and Hankel-symmetric doubly stochastic matrices, can be obtained from the extreme points of Ut&h(R,S) by specializing to the case that R = S =(1, 1, ..., 1) E Rn.

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KW - 52B05

KW - doubly stochastic matrices

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JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

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Symmetric and Hankel-Symmetric Transportation Polytopes

Abstract

Bibliographical note

Funding

ASJC Scopus Subject Areas

Keywords

Disciplines

Access to Document

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