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On the half-plane property and the Tutte group of a matroid
Stockholm University, Faculty of Science, Department of Mathematics.
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:su:diva-49233DOI: 10.1016/j.jctb.2010.04.001ISI: 000277395000006OAI: oai:DiVA.org:su-49233DiVA: diva2:376765
Note
authorCount :2Available from: 2010-12-13 Created: 2010-12-13 Last updated: 2017-12-11Bibliographically approved

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