Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete concavity and the half-plane property   Murota et al. have recently developed a theory of discrete convex analysis
which concerns M-convex functions on jump systems. We introduce here a family
of M-concave functions arising naturally from polynomials (over a field of
generalized Puiseux series) with prescribed non-vanishing properties. This
family contains several of the most studied M-concave functions in the
literature. In the language of tropical geometry we study the tropicalization
of the space of polynomials with the half-plane property, and show that it is
strictly contained in the space of M-concave functions. 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.

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The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin