Result: Polynomials with the half-plane property and the support theorems

Title:
Polynomials with the half-plane property and the support theorems
Authors:
Source:
Journal of Combinatorial Theory, Series B. 94:117-145
Publisher Information:
Elsevier BV, 2005.
Publication Year:
2005
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
0095-8956
DOI:
10.1016/j.jctb.2004.12.001
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....32c751d7f9916354ee0219e8f20ced33
Database:
OpenAIRE

Further Information

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.