کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9516176 1343767 2005 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Polynomials with the half-plane property and the support theorems
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Polynomials with the half-plane property and the support theorems
چکیده انگلیسی
A polynomial P(x) in n complex variables is said to have the half-plane property if P(x)≠0 whenever all the variables have positive real parts. The generating polynomial for the set of all spanning trees of a graph G is one example. Motivated by the fact that the edge set of each spanning tree of G is a basis of the graphic matroid induced by G, it is shown by Choe et al. (Adv. Appl. Math. 32 (2004) 88-187) that the support of any homogeneous multiaffine polynomial with the half-plane property constitutes the set of all bases of a matroid. In this paper we show, when all the terms of a polynomial with the half-plane property have degrees of same parity, the support constitutes a jump system which is a generalization of matroids. Open problems and a few directions for further research will also be discussed.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series B - Volume 94, Issue 1, May 2005, Pages 117-145
نویسندگان
,