An update on a few permanent conjectures

Fuzhen Zhang

Special Matrices (2016)

  • Volume: 4, Issue: 1, page 305-316
  • ISSN: 2300-7451

Abstract

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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.)

How to cite

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Fuzhen Zhang. "An update on a few permanent conjectures." Special Matrices 4.1 (2016): 305-316. <http://eudml.org/doc/286762>.

@article{FuzhenZhang2016,
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.)},
author = {Fuzhen Zhang},
journal = {Special Matrices},
keywords = {Bapat-Sunder conjecture; Chollet conjecture; Drury conjecture; Foregger conjecture; Liang-So- Zhang conjecture; Lie conjecture; Marcus conjecture; Marcus-Minc conjecture; permanent; permanent dominance conjecture; permanent-on-top conjecture; Schur power matrix; Liang-So-Zhang conjecture; permanent dominance conjecture},
language = {eng},
number = {1},
pages = {305-316},
title = {An update on a few permanent conjectures},
url = {http://eudml.org/doc/286762},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Fuzhen Zhang
TI - An update on a few permanent conjectures
JO - Special Matrices
PY - 2016
VL - 4
IS - 1
SP - 305
EP - 316
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.)
LA - eng
KW - Bapat-Sunder conjecture; Chollet conjecture; Drury conjecture; Foregger conjecture; Liang-So- Zhang conjecture; Lie conjecture; Marcus conjecture; Marcus-Minc conjecture; permanent; permanent dominance conjecture; permanent-on-top conjecture; Schur power matrix; Liang-So-Zhang conjecture; permanent dominance conjecture
UR - http://eudml.org/doc/286762
ER -

References

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