Hiroshima Mathematical Journal

Sharp inequalities for the permanental dominance conjecture

Ryo Tabata

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Abstract

For the normalized generalized matrix function $\overline d_{\chi}^{G} (A)$ for $3 \times 3$ positive semi-definite Hermitian matrices $A$, the permanental dominance conjecture $\per A \geq \overline d_{\chi}^{G} (A)$ is known to hold. In this paper, we show that this inequality is not sharp, and give a sharper bound.

Article information

Source
Hiroshima Math. J. Volume 40, Number 2 (2010), 205-213.

Dates
First available in Project Euclid: 2 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1280754421

Mathematical Reviews number (MathSciNet)
MR2680656

Zentralblatt MATH identifier
1215.15008

Subjects
Primary: 15A15: Determinants, permanents, other special matrix functions [See also 19B10, 19B14] 20A30

Keywords
symmetric group permanent generalized matrix function

Citation

Tabata, Ryo. Sharp inequalities for the permanental dominance conjecture. Hiroshima Math. J. 40 (2010), no. 2, 205--213. https://projecteuclid.org/euclid.hmj/1280754421.


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