Permanents of Doubly Substochastic Matrices

Lei Cao; Zhi Chen; Selcuk Koyuncu; Huilan Li

doi:10.1080/03081087.2018.1513448

Permanents of Doubly Substochastic Matrices

Lei Cao
, Zhi Chen
, Selcuk Koyuncu
, Huilan Li

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

5 Scopus citations

Abstract

Let ω _n,k denote the convex polytope of doubly substochastic matrices with sub-defect k. Let h(A) and I(A) denote the maximum and minimum diagonals of A ∈ ω _n,k respectively. In this paper, we study the relation between the permanent function and the maximum (minimum) diagonals, which are defined below. More specifically, we give the upper bound of the permanent function on ω _n,k in terms of the h-function. We also study the upper bound of the permanent function on both the product and direct product of matrices in ω _n,k.

Original language	American English
Pages (from-to)	594-605
Number of pages	12
Journal	Linear and Multilinear Algebra
Volume	68
Issue number	3
DOIs	https://doi.org/10.1080/03081087.2018.1513448
State	Published - Aug 30 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

Funding

The second author is supported by the National Natural Science Foundation of China (No. 11601233); the Fundamental Research Funds for the Central Universities (No. KYZ201650); the Natural Science Foundation of Jiangsu Province (BK20160708). The forth author is supported by the National Natural Science Foundation of China (No. 11701339). We are grateful to the anonymous referee for his/her very valuable comments on our paper.

Funders	Funder number
National Natural Science Foundation of China	11601233
Natural Science Foundation of Jiangsu Province	11701339, BK20160708
Fundamental Research Funds for the Central Universities	KYZ201650

ASJC Scopus Subject Areas

Algebra and Number Theory

Keywords

Doubly stochastic matrices
Doubly substochastic matrices
Sub-defect
Permanent
doubly substochastic matrices
15A15
15A69
sub-defect

Disciplines

Mathematics

Access to Document

10.1080/03081087.2018.1513448

Cite this

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title = "Permanents of Doubly Substochastic Matrices",

abstract = "Let ω n,k denote the convex polytope of doubly substochastic matrices with sub-defect k. Let h(A) and I(A) denote the maximum and minimum diagonals of A ∈ ω n,k respectively. In this paper, we study the relation between the permanent function and the maximum (minimum) diagonals, which are defined below. More specifically, we give the upper bound of the permanent function on ω n,k in terms of the h-function. We also study the upper bound of the permanent function on both the product and direct product of matrices in ω n,k.",

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author = "Lei Cao and Zhi Chen and Selcuk Koyuncu and Huilan Li",

note = "Publisher Copyright: {\textcopyright} 2018, {\textcopyright} 2018 Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2018",

month = aug,

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doi = "10.1080/03081087.2018.1513448",

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TY - JOUR

T1 - Permanents of Doubly Substochastic Matrices

AU - Cao, Lei

AU - Chen, Zhi

AU - Koyuncu, Selcuk

AU - Li, Huilan

PY - 2018/8/30

Y1 - 2018/8/30

N2 - Let ω n,k denote the convex polytope of doubly substochastic matrices with sub-defect k. Let h(A) and I(A) denote the maximum and minimum diagonals of A ∈ ω n,k respectively. In this paper, we study the relation between the permanent function and the maximum (minimum) diagonals, which are defined below. More specifically, we give the upper bound of the permanent function on ω n,k in terms of the h-function. We also study the upper bound of the permanent function on both the product and direct product of matrices in ω n,k.

AB - Let ω n,k denote the convex polytope of doubly substochastic matrices with sub-defect k. Let h(A) and I(A) denote the maximum and minimum diagonals of A ∈ ω n,k respectively. In this paper, we study the relation between the permanent function and the maximum (minimum) diagonals, which are defined below. More specifically, we give the upper bound of the permanent function on ω n,k in terms of the h-function. We also study the upper bound of the permanent function on both the product and direct product of matrices in ω n,k.

KW - Doubly stochastic matrices

KW - Doubly substochastic matrices

KW - Sub-defect

KW - Permanent

KW - doubly substochastic matrices

KW - 15A15

KW - 15A69

KW - sub-defect

UR - https://nsuworks.nova.edu/math_facarticles/272

UR - https://www.scopus.com/pages/publications/85053235808

UR - https://www.scopus.com/pages/publications/85053235808#tab=citedBy

U2 - 10.1080/03081087.2018.1513448

DO - 10.1080/03081087.2018.1513448

M3 - Article

SN - 0308-1087

VL - 68

SP - 594

EP - 605

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 3

ER -

Permanents of Doubly Substochastic Matrices

Abstract

Bibliographical note

Funding

ASJC Scopus Subject Areas

Keywords

Disciplines

Access to Document

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