Polynomials with the half-plane property and the support theorems
type: Item
instance of: scholarly article
title: Polynomials with the half-plane property and the support theorems
zbMATH Open document ID: 1061.05019
published in: Journal of Combinatorial Theory. Series B
publication date: 2005-05-04T00:00:00Z
review text: A multivariate polynomial has the half-plane property whenever it has no roots when all variables have positive real part. Extending an earlier theorem that the support of every homogeneous multiaffine polynomial forms the set of bases of a matroid, the paper establishes a condition ensuring that the support forms a jump system (a generalization of matroids); this condition is that all terms in the polynomial have the same parity. Connections to the location of the roots of reliability polynomials are explored.
reviewed by: Charles J. Colbourn
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 05A99
zbMATH DE Number: 2165071
zbMATH Keywords: generating polynomial
zbMATH Keywords: half-plane property
zbMATH Keywords: matroid
zbMATH Keywords: jump system
zbMATH Keywords: reliability polynomial
author: Young-Bin Choe
MaRDI profile type: Publication
full work available at URL: j.jctb.2004.12.001
OpenAlex ID: W2009710044
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cites work: Q4301917
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cites work: Q4111952
DOI: 10.1016/J.JCTB.2004.12.001
description: scientific article; zbMATH DE number 2165071