Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Log-concavity of characteristic polynomials and the Bergman fan of
  matroids   In a recent paper, the first author proved the log-concavity of the
coefficients of the characteristic polynomial of a matroid realizable over a
field of characteristic 0, answering a long-standing conjecture of Read in
graph theory. We extend the proof to all realizable matroids, making progress
towards a more general conjecture of Rota-Heron-Welsh. Our proof follows from
an identification of the coefficients of the reduced characteristic polynomial
as answers to particular intersection problems on a toric variety. The
log-concavity then follows from an inequality of Hodge type.

13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph