An Update on a Few Permanent Conjectures

Fuzhen Zhang

doi:10.1515/spma-2016-0030

An Update on a Few Permanent Conjectures

Fuzhen Zhang

Department of Mathematics

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

22 Scopus citations

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.)

Original language	American English
Pages (from-to)	305-316
Number of pages	12
Journal	Special Matrices
Volume	4
Issue number	1
DOIs	https://doi.org/10.1515/spma-2016-0030
State	Published - Aug 26 2016

Bibliographical note

Publisher Copyright:
© 2016 Fuzhen Zhang, published by De Gruyter Open.

Funding

I am grateful to R. Bapat, R. Brualdi, G.-S. Cheon, S. Drury, and V. Shchesnovich for valuable comments. I am especially indebted to Prof. Drury for his help with the counterexamples. The project was partially supported by National Natural Science Foundation of China (No. 11571220) through Shanghai University.

Funders	Funder number
National Natural Science Foundation of China	11571220
Shanghai University

ASJC Scopus Subject Areas

Algebra and Number Theory
Geometry and Topology

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
Liang-So-Zhang conjecture

Disciplines

Discrete Mathematics and Combinatorics
Mathematics
Physical Sciences and Mathematics

Access to Document

10.1515/spma-2016-0030

An Update on a Few Permanent ConjecturesFinal published version, 487 KBLicense: Unspecified

Cite this

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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.)",

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month = aug,

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doi = "10.1515/spma-2016-0030",

language = "American English",

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N2 - 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.)

AB - 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.)

KW - Bapat-Sunder conjecture

KW - Chollet conjecture

KW - Drury conjecture

KW - Foregger conjecture

KW - Liang-SoZhang conjecture

KW - Lie conjecture

KW - Marcus conjecture

KW - Marcus-Minc conjecture

KW - Permanent

KW - Permanent dominance conjecture

KW - Permanent-on-top conjecture

KW - Schur power matrix

KW - Liang-So-Zhang conjecture

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DO - 10.1515/spma-2016-0030

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VL - 4

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ER -

An Update on a Few Permanent Conjectures

Abstract

Bibliographical note

Funding

ASJC Scopus Subject Areas

Keywords

Disciplines

Access to Document

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