Polynomials with the half-plane property and matroid theory

By Petter Brand'en. 2006

146 citations recorded by the source corpus.

A polynomial f is said to have the half-plane property if there is an open half-plane H subset of C, whose boundary contains the origin, such that f is non-zero whenever all the variables are in H. ...

Subfields: Computational Theory and Mathematics, Computer Graphics and Computer-Aided Design, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/2bce52d160752feb206ea4ee575c4db209dfb79a

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In Computational Theory and Mathematics

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Citations in the corpus

Multivariate Pólya–Schur classification problems in the Weyl algebra (2006, methodology): “The second author is grateful to The Mittag-Leffler Institute forits hospitality in Spring 2005 when this and related projects [9, 10, 12, 15 ] were started.”
The Lee-Yang and Pólya-Schur programs. I. Linear operators preserving stability (2008, methodology): “Multi-affine Polynomials and the Lieb-Sokal Lemma 9 2.2.”
Negative Dependence in Sampling (2012, unknown): “A reason for the robustness of the strong Rayleigh property is the following alternative definition due to Brändén (2007).”
Multivariate stable polynomials: theory and applications (2009, background): “6 of [8] and Theorem 3 of [16]).”
Unimodality, log-concavity, real-rootedness and beyond (2015, background): “ence that graphic matroids are HPP follows from Theorem 9.4 and Proposition 9.1. A similar reasoning proves that all regular matroids are HPP, and that all matroids representable over C are WHPP, see [17,33]. On the other hand, the Vamos cube V8 is not representable over any eld, and still V8 is HPP”