Inequalities for Permanents and Permanental Minors of Row Substochastic Matrices

Zhi Chen; Jiawei Li; Lizhen Yang; Zelin Zhu; Lei Cao

doi:10.13001/1081-3810.4084

Inequalities for Permanents and Permanental Minors of Row Substochastic Matrices

Zhi Chen
, Jiawei Li
, Lizhen Yang
, Zelin Zhu
, Lei Cao

Department of Mathematics

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

Abstract

In this paper, some inequalities for permanents and permanental minors of row substochastic matrices are proved. The convexity of the permanent function on the interval between the identity matrix and an arbitrary row substochastic matrix is also proved. In addition, a conjecture about the permanent and permanental minors of square row substochastic matrices with fixed row and column sums is formulated.

Original language	American English
Article number	46
Pages (from-to)	633-643
Number of pages	11
Journal	Electronic Journal of Linear Algebra
Volume	35
Issue number	1
DOIs	https://doi.org/10.13001/1081-3810.4084
State	Published - Dec 1 2019

Bibliographical note

Publisher Copyright:
© 2019, International Linear Algebra Society. All rights reserved.

Funding

∗Received by the editors on July 16, 2019. Accepted for publication on November 15, 2019. Handling Editor: Raphael Loewy. Corresponding Author: Zhi Chen. †Department of Mathematics, Nanjing Agricultural University, Jiangsu 210095, China ([email protected]). Supported by the National Natural Science Foundation of China (no. 11601233), the Fundamental Research Funds for the Central Universities (no. KJQN201718), and the Natural Science Foundation of Jiangsu Province (no. BK20160708). ‡Department of Mathematics, Nanjing Agricultural University, Jiangsu 210095, China. Lizhen Yang, Zelin Zhu, and Jiawei Li were supported by the Student Research Training Program (no. 1923A09). §Department of Mathematics, Halmos College, Nova Southeastern University, FL, 33314, USA.

Funders	Funder number
National Natural Science Foundation of China	11601233
Natural Science Foundation of Jiangsu Province	BK20160708, 1923A09
Fundamental Research Funds for the Central Universities	KJQN201718

ASJC Scopus Subject Areas

Algebra and Number Theory

Keywords

Doubly stochastic matrices
Doubly substochastic matrices
Permanents
Row substochastic matrices
Transportation polytopes

Disciplines

Mathematics

Access to Document

10.13001/1081-3810.4084

Inequalities for Permanents and Permanental Minors of Row SubstocFinal published version, 368 KBLicense: Unspecified

Cite this

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keywords = "Doubly stochastic matrices, Doubly substochastic matrices, Permanents, Row substochastic matrices, Transportation polytopes",

author = "Zhi Chen and Jiawei Li and Lizhen Yang and Zelin Zhu and Lei Cao",

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AU - Zhu, Zelin

AU - Cao, Lei

PY - 2019/12/1

Y1 - 2019/12/1

N2 - In this paper, some inequalities for permanents and permanental minors of row substochastic matrices are proved. The convexity of the permanent function on the interval between the identity matrix and an arbitrary row substochastic matrix is also proved. In addition, a conjecture about the permanent and permanental minors of square row substochastic matrices with fixed row and column sums is formulated.

AB - In this paper, some inequalities for permanents and permanental minors of row substochastic matrices are proved. The convexity of the permanent function on the interval between the identity matrix and an arbitrary row substochastic matrix is also proved. In addition, a conjecture about the permanent and permanental minors of square row substochastic matrices with fixed row and column sums is formulated.

KW - Doubly stochastic matrices

KW - Doubly substochastic matrices

KW - Permanents

KW - Row substochastic matrices

KW - Transportation polytopes

UR - https://nsuworks.nova.edu/math_facarticles/290

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DO - 10.13001/1081-3810.4084

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JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

IS - 1

M1 - 46

ER -

Inequalities for Permanents and Permanental Minors of Row Substochastic Matrices

Abstract

Bibliographical note

Funding

ASJC Scopus Subject Areas

Keywords

Disciplines

Access to Document

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