Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Solutions to two problems on permanents
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-1055-1474
2012 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 436, no 1, 53-58 p.Article in journal (Refereed) Published
Abstract [en]

In this note we settle two open problems in the theory of permanents by using recent results from other areas of mathematics. Both problems were recently discussed in Bapat's survey [2]. Bapat conjectured that certain quotients of permanents, which generalize symmetric function means, are concave. We prove this conjecture by using concavity properties of hyperbolic polynomials. Motivated by problems on random point processes, Shirai and Takahashi raised the problem: Determine all real numbers a for which the alpha-permanent (or alpha-determinant) is nonnegative for all positive semidefinite matrices. We give a complete solution to this problem by using recent results of Scott and Sokal on completely monotone functions. It turns out that the conjectured answer to the problem is false.

Place, publisher, year, edition, pages
2012. Vol. 436, no 1, 53-58 p.
Keyword [en]
Permanent, alpha-Permanent, alpha-Determinant, Positivity, Hyperbolic polynomial, Complete monotonicity, Symmetric function mean
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-53388DOI: 10.1016/j.laa.2011.06.022ISI: 000297431200005Scopus ID: 2-s2.0-80055063559OAI: oai:DiVA.org:kth-53388DiVA: diva2:470325
Note
QC 20111228Available from: 2011-12-28 Created: 2011-12-28 Last updated: 2017-12-08Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Authority records BETA

Brändén, Petter

Search in DiVA

By author/editor
Brändén, Petter
By organisation
Mathematics (Div.)
In the same journal
Linear Algebra and its Applications
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 69 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf