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Article
An Update on a Few Permanent Conjectures
Special Matrices
  • Fuzhen Zhang, Nova Southeastern University
Document Type
Article
Publication Date
8-1-2016
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
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
DOI
10.1515/spma-2016-0030
Citation Information
Fuzhen Zhang. "An Update on a Few Permanent Conjectures" Special Matrices Vol. 4 Iss. 1 (2016) p. 305 - 316 ISSN: 2300-7451
Available at: http://0-works.bepress.com.library.simmons.edu/fuzhen-zhang/165/