A polynomial P in n complex variables is said to have the "half-plane property" (or Hurwitz property) if it is nonvanishing whenever all the variables lie in the open right half-plane. Such polynomials arise in combinatorics, reliability theory, electrical circuit theory and statistical mechanics. A particularly important case is when the polynomial is homogeneous and multiaffine: then it is the (weighted) generating polynomial of an r-uniform set system. We prove that the support (set of nonzero coefficients) of a homogeneous multiaffine polynomial with the half-plane property is necessarily the set of bases of a matroid. Conversely, we ask: For which matroids M does the basis generating polynomial P_{B(M)} have the half-plane property? Not all matroids have the half-plane property, but we find large classes that do: all sixth-root-of-unity matroids, and a subclass of transversal (or cotransversal) matroids that we call "nice". Furthermore, the class of matroids with the half-plane property is closed under minors, duality, direct sums, 2-sums, series and parallel connection, full-rank matroid union, and some special cases of principal truncation, principal extension, principal cotruncation and principal coextension. Our positive results depend on two distinct (and apparently unrelated) methods for constructing polynomials with the half-plane property: a determinant construction (exploiting "energy" arguments), and a permanent construction (exploiting the Heilmann-Lieb theorem on matching polynomials). We conclude with a list of open questions.Comment: LaTeX2e, 111 pages. Submission includes Mathematica programs niceprincipal.m and nicetransversal.m Version 2 corrects a small error at the beginning of Appendix B, and makes a few small improvements elsewhere. To appear in Advances in Applied Mathematic

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In this paper we argue for the utility of status characteristics theory (Berger et al. 1977) in accounting for research concerned with gender differences in interpersonal task situations. We state and defend a basic status argument that differences in stereotypical gender task behaviors are a direct function of status differences or of attempts to cope with status differences. We show support for this argument in several areas of research: the influence, participation and performer evaluations of group members; their relative performance-reactor profiles; the relation of these behavioral profiles to the assignment of personality traits; the correlation of status position with the gender typing of tasks (i.e., male-identified, female-identified, or neutral); the relationship between gender status and salient information about other statuses; the role of expectations for rewards; and the emergence of mechanisms for coping with the implication of a low gender status position. We conclude that status characteristics theory can provide a set of interrelated explanations of the relationship of gender to interpersonal task behaviors.

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Abstract. Univariate polynomials with only real roots, while special, do occur often enough that their properties can lead to interesting conclusions in diverse areas. Due mainly to the recent work of two young mathematicians, Julius Borcea and Petter Brändén, a very successful multivariate generalization of this method has been developed. The first part of this paper surveys some of the main results of this theory of multivariate stable polynomials-the most central of these results is the characterization of linear transformations preserving stability of polynomials. The second part presents various applications of this theory in complex analysis, matrix theory, probability and statistical mechanics, and combinatorics.

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