Mathematics Faculty Articles

Title

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

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 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 sn - 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.

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019

DOI

10.1016/j.laa.2018.06.031

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