Permanents of Doubly Substochastic Matrices

Authors

Lei Cao, Shandong Normal University - China; Georgian Court UniversityFollow
Zhi Chen, Nanjing Agricultural University - China
Selcuk Koyuncu, University of North Georgia
Huilan Li, Shandong Normal University - China

Document Type

Article

Publication Date

8-30-2018

Publication Title

Linear and Multilinear Algebra

Keywords

Permanent, Doubly substochastic matrices, Sub-defect

ISSN

0308-1087

First Page

1

Last Page

12

Abstract

Let ω_n,k denote the convex polytope of doubly substochastic matrices with sub-defect k. Let h(A) and l(A) denote the maximum and minimum diagonals of A ϵ 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.

Comments

©2018 Informa UK Limited, trading as Taylor & Francis Group

Additional Comments

National Natural Science Foundation of China grant #s: 11601233, 11701339; Fundamental Research Funds for the Central Universities grant #: KYZ201650; Natural Science Foundation of Jiangsu Province grant #: BK20160708

NSUWorks Citation

Cao, Lei; Chen, Zhi; Koyuncu, Selcuk; and Li, Huilan, "Permanents of Doubly Substochastic Matrices" (2018). Mathematics Faculty Articles. 272.
https://nsuworks.nova.edu/math_facarticles/272

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019

DOI

10.1080/03081087.2018.1513448