Discrete Concavity and Zeros of Polynomials

https://doi.org/10.1016/j.endm.2009.07.088Get rights and content

Abstract

Murota et al. have recently developed a theory of discrete convex analysis as a framework to solve combinatorial optimization problems using ideas from continuous optimization. This theory concerns M-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. We also provide a short proof of Speyer's “hive theorem” which he used to give a new proof of Horn's conjecture on eigenvalues of sums of Hermitian matrices. Due to limited space a more coherent treatment and proofs will appear elsewhere.

References (11)

There are more references available in the full text version of this article.

Cited by (0)

1

Supported by the Göran Gustafsson Foundation. The author is also at the Department of Mathematics, Stockholm University, SE-106 91, Stockholm, Sweden.

View full text