Corrigendum to “A criterion for the half-plane property” [Discrete Math. 309 (2008) 1385–1390]

A criterion for the half-plane property

We establish a convenient necessary and sufficient condition for a multiaffine real polynomial to be stable, and use it to verify that the half-plane property holds for seven small matroids that resisted the efforts of Choe, Oxley, Sokal, and Wagner [5]. In recent years, matroid theory has found connections with certain analytic properties of real multivariate polynomials. These properties are ...

Discrete Concavity and the Half-Plane Property

Murota et al. have recently developed a theory of discrete convex analysis which concerns M -convex and L-convex functions on jump systems. We introduce here a family of M -concave functions arising naturally from polynomials (over the field of Puiseux series) with prescribed non-vanishing properties. This family contains several of the most studied M -concave functions in the literature. We al...

Math 239 : Discrete Mathematics for the Life Sciences Spring 2008

Math 149, Fall 2008 Discrete Geometry Lecture Notes

Introduction to Discrete Math

are non-zero. Solution: First suppose the above some has no non-zero entries on its diagonal. Since A(G)i,j is the number of walks of length k from i to j, if the sum above has non-zero diagonal entries, then for any pair of vertices i, j there is a walk of some length from i to j. This implies there is a path from i to j. Since i, j are arbitrary, we conclude that G is connected. Now assume G ...