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

Authors

Zhi Chen, Nanjing Agricultural University - China
Lei Cao, Georgian Court UniversityFollow

Document Type

Article

Publication Date

10-15-2018

Publication Title

Linear Algebra and its Applications

Keywords

Permanent, Doubly substochastic matrices, Sub-defect

ISSN

0024-3795

Volume

555

First Page

412

Last Page

431

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

Comments

©2018 Elsevier Inc. All rights reserved.

NSUWorks Citation

Chen, Zhi and Cao, Lei, "On the Maximum of the Permanent of (I − A)" (2018). Mathematics Faculty Articles. 275.
https://nsuworks.nova.edu/math_facarticles/275

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019

DOI

10.1016/j.laa.2018.06.031