Mathematics – Combinatorics
Scientific paper
2009-06-05
J. Combin. Theory Ser. B 100 (2010), no. 5, 485-492
Mathematics
Combinatorics
8 pages. To appear in J. Combin. Theory Ser. B
Scientific paper
10.1016/j.jctb.2010.04.001
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 nonzero 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.
Brändén Petter
González D'León Rafael S.
No associations
LandOfFree
On the half-plane property and the Tutte group of a matroid does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the half-plane property and the Tutte group of a matroid, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the half-plane property and the Tutte group of a matroid will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-522261