Record number :

1527555

Title of article :

Polynomials with the half-plane property and the support theorems

Author/Authors :

Choe، نويسنده , , YoungBin، نويسنده ,

Issue Information :

روزنامه با شماره پیاپی سال 2005

Pages :

29

From page :

117

To page :

145

Abstract :

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.

Keywords :

Generating polynomial , Half-plane property , Definite-parity , Matroid , Basis , jump system , Support

Journal title :

Journal of Combinatorial Theory Series B

Journal title :

Journal of Combinatorial Theory Series B

Serial Year :

2005

Link To Document :