On the Maximum of the Permanent of (I − A)

Zhi Chen; Lei Cao

doi:10.1016/j.laa.2018.06.031

On the Maximum of the Permanent of (I − A)

Zhi Chen
, Lei Cao

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

2 Scopus citations

Abstract

Let ω⁸_n and ^~ω⁸_n denote the convex sets of doubly substochastic matrices and row substochastic matrices with the sum of all entries equal to s, respectively. In this paper, we give the upper bound of the permanent of I - A for A ϵ ^~ω⁸_n. We also give the upper bound of the permanent of I - A for A ϵ ^~ω⁸_n, where either n is even, or n is odd and s ≤ n - 1. For the case when n is odd and n - 1 < s ≤ n, we give some discussion and conjectures.

Ω

ϵ

ω

Original language	American English
Pages (from-to)	412-431
Number of pages	20
Journal	Linear Algebra and its Applications
Volume	555
DOIs	https://doi.org/10.1016/j.laa.2018.06.031
State	Published - Oct 15 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018

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).

Funders	Funder number
National Natural Science Foundation of China	11601233
Natural Science Foundation of Jiangsu Province	BK20160708

ASJC Scopus Subject Areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Keywords

Doubly substochastic matrices
Permanent
Sub-defect

Disciplines

Mathematics

Access to Document

10.1016/j.laa.2018.06.031

Cite this

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title = "On the Maximum of the Permanent of (I − A)",

abstract = "Let ω8n and \textasciitilde{}ω8n denote the convex sets of doubly substochastic matrices and row substochastic matrices with the sum of all entries equal to s, respectively. In this paper, we give the upper bound of the permanent of I - A for A ϵ \textasciitilde{}ω8n. We also give the upper bound of the permanent of I - A for A ϵ \textasciitilde{}ω8n, where either n is even, or n is odd and s ≤ n - 1. For the case when n is odd and n - 1 < s ≤ n, we give some discussion and conjectures. Ω ϵ ω",

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author = "Zhi Chen and Lei Cao",

note = "Publisher Copyright: {\textcopyright} 2018",

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doi = "10.1016/j.laa.2018.06.031",

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T1 - On the Maximum of the Permanent of (I − A)

AU - Chen, Zhi

AU - Cao, Lei

PY - 2018/10/15

Y1 - 2018/10/15

N2 - Let ω8n and ~ω8n denote the convex sets of doubly substochastic matrices and row substochastic matrices with the sum of all entries equal to s, respectively. In this paper, we give the upper bound of the permanent of I - A for A ϵ ~ω8n. We also give the upper bound of the permanent of I - A for A ϵ ~ω8n, where either n is even, or n is odd and s ≤ n - 1. For the case when n is odd and n - 1 < s ≤ n, we give some discussion and conjectures. Ω ϵ ω

AB - Let ω8n and ~ω8n denote the convex sets of doubly substochastic matrices and row substochastic matrices with the sum of all entries equal to s, respectively. In this paper, we give the upper bound of the permanent of I - A for A ϵ ~ω8n. We also give the upper bound of the permanent of I - A for A ϵ ~ω8n, where either n is even, or n is odd and s ≤ n - 1. For the case when n is odd and n - 1 < s ≤ n, we give some discussion and conjectures. Ω ϵ ω

KW - Doubly substochastic matrices

KW - Permanent

KW - Sub-defect

UR - https://nsuworks.nova.edu/math_facarticles/275

UR - https://www.scopus.com/pages/publications/85049323336

UR - https://www.scopus.com/pages/publications/85049323336#tab=citedBy

U2 - 10.1016/j.laa.2018.06.031

DO - 10.1016/j.laa.2018.06.031

M3 - Article

SN - 0024-3795

VL - 555

SP - 412

EP - 431

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

On the Maximum of the Permanent of (I − A)

Abstract

Bibliographical note

Funding

ASJC Scopus Subject Areas

Keywords

Disciplines

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Cite this

On the Maximum of the Permanent of (I − A)

Abstract

Bibliographical note

Funding

ASJC Scopus Subject Areas

Keywords

Disciplines

Access to Document

Other files and links

Fingerprint

Cite this

On the Maximum of the Permanent of (I − A)