Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Log-Concavity of Hilbert Series of Veronese Subrings and Ehrhart
  Series   For every positive integer $n$, consider the linear operator $\U_{n}$ on
polynomials of degree at most $d$ with integer coefficients defined as follows:
if we write $\frac{h(t)}{(1 - t)^{d + 1}} = \sum_{m \geq 0} g(m) t^{m}$, for
some polynomial $g(m)$ with rational coefficients, then $\frac{\U_{n}h(t)}{(1-
t)^{d + 1}} = \sum_{m \geq 0} g(nm) t^{m}$. We show that there exists a
positive integer $n_{d}$, depending only on $d$, such that if $h(t)$ is a
polynomial of degree at most $d$ with nonnegative integer coefficients and
$h(0) \geq 1$, then for $n \geq n_{d}$, $\U_{n}h(t)$ has simple, real, strictly
negative roots and positive, strictly log concave and strictly unimodal
coefficients. Applications are given to Ehrhart $\delta$-polynomials and
unimodular triangulations of dilations of lattice polytopes, as well as Hilbert
series of Veronese subrings of Cohen--MacCauley graded rings.

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The categories of this paper are: math-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: stat