Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gale duality bounds for roots of polynomials with nonnegative
  coefficients   We bound the location of roots of polynomials that have nonnegative
coefficients with respect to a fixed but arbitrary basis of the vector space of
polynomials of degree at most $d$. For this, we interpret the basis polynomials
as vector fields in the real plane, and at each point in the plane analyze the
combinatorics of the Gale dual vector configuration. This approach permits us
to incorporate arbitrary linear equations and inequalities among the
coefficients in a unified manner to obtain more precise bounds on the location
of roots. We apply our technique to bound the location of roots of Ehrhart and
chromatic polynomials. Finally, we give an explanation for the clustering seen
in plots of roots of random polynomials.

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The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn