David Ruelle
Grace-like polynomials
(38K, plain tex)

ABSTRACT.  Results of somewhat mysterious nature are known on the location of 
zeros of certain polynomials associated with statistical mechanics 
(Lee-Yang circle theorem) and also with graph counting. In an attempt 
at clarifying the situation we introduce and discuss here a natural 
class of polynomials. Let $P(z_1,\ldots,z_m,w_1,\ldots,w_n)$ be 
separately of degree 1 in each of its $m+n$ arguments. We say that 
$P$ is a Grace-like polynomial if $P(z_1,\ldots,w_n)\ne0$ whenever 
there is a circle in ${\bf C}$ separating $z_1,\ldots,z_m$ from 
$w_1,\ldots,w_n$. A number of properties and characterizations of 
these polynomials are obtained.