An Update on a Few Permanent Conjectures

Authors

Fuzhen Zhang, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

8-2016

Publication Title

Special Matrices

Keywords

Bapat-Sunder conjecture, Chollet conjecture, Drury conjecture, Foregger conjecture, Liang-SoZhang conjecture, Lie conjecture, Marcus conjecture, Marcus-Minc conjecture, Permanent, Permanent dominance conjecture, Permanent-on-top conjecture, Schur power matrix

ISSN

2300-7451

Volume

4

Issue/No.

1

First Page

305

Last Page

316

Abstract

We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture†, Lieb permanent dominance conjecture, Bapat and Sunder conjecture† on Hadamard product and diagonal entries, Chollet conjecture on Hadamard product, Marcus conjecture on permanent of permanents, and several other conjectures. Some of these conjectures are recently settled; some are still open.We also raise a few new questions for future study. (†conjectures have been recently settled negatively.)

Comments

©2016 Fuzhen Zhang, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.

Additional Comments

National Natural Science Foundation of China grant #: 11571220

NSUWorks Citation

Zhang, Fuzhen, "An Update on a Few Permanent Conjectures" (2016). Mathematics Faculty Articles. 211.
https://nsuworks.nova.edu/math_facarticles/211

DOI

10.1515/spma-2016-0030