David G. Wagner
Multivariate stable polynomials: theory and applications.
Thu, 11/19/2009 - 16:01 — SomNambulAuthors: David G. Wagner
Subjects: Complex Variables
AbstractUnivariate 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 Br\"and\'en, 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 lattice of integer flows of a regular matroid.
Fri, 08/28/2009 - 23:56 — SomNambulAuthors: Yi Su, David G. Wagner
Subjects: Combinatorics
AbstractFor a finite multigraph G, let \Lambda(G) denote the lattice of integer flows
of G -- this is a finitely generated free abelian group with an integer-valued
positive definite bilinear form. Bacher, de la Harpe, and Nagnibeda show that
if G and H are 2-isomorphic graphs then \Lambda(G) and \Lambda(H) are
isometric, and remark that they were unable to find a pair of nonisomorphic
3-connected graphs for which the corresponding lattices are isometric. We
explain this by examining the lattice \Lambda(M) of integer flows of any
regular matroid M.
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