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On the half-plane property and the {T}utte group of a matroid
Department of Mathematics, Stockholm University.ORCID iD: 0000-0003-1055-1474
Department of Mathematics, University of Miami, Coral Gables.
2010 (English)In: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902, Vol. 100, no 5, 485-492 p.Article in journal (Refereed) Published
Abstract [en]

A multivariate polynomial is stable if it is non-vanishing whenever all variables have positive imaginary parts. A matroid has the weak half-plane property (WHPP) if there exists a stable polynomial with support equal to the set of bases of the matroid. If the polynomial can be chosen with all of its non-zero coefficients equal to one then the matroid has the half-plane property (HPP). We describe a systematic method that allows us to reduce the WHPP to the HPP for large families of matroids. This method makes use of the Tutte group of a matroid. We prove that no projective geometry has the WHPP and that a binary matroid has the WHPP if and only if it is regular. We also prove that T(8) and R(9) fail to have the WHPP.

Place, publisher, year, edition, pages
2010. Vol. 100, no 5, 485-492 p.
Keyword [en]
Matroid, Tutte group, Stable polynomial, Half-plane property
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-78734DOI: 10.1016/j.jctb.2010.04.001ISI: 000277395000006OAI: oai:DiVA.org:kth-78734DiVA: diva2:492826
Note
QC 20120221Available from: 2012-02-08 Created: 2012-02-08 Last updated: 2017-12-08Bibliographically approved

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Brändén, Petter

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