Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Best possible lower bounds on the coefficients of Ehrhart polynomials   For an integral convex polytope $\mathcal{P} \subset \mathbb{R}^d$, we recall
$L_\mathcal{P}(n)=|n\mathcal{P} \cap \mathbb{Z}^d|$ the Ehrhart polynomial of
$\mathcal{P}$. Let $g_r(\mathcal{P})$ be the $r$th coefficients of
$L_\mathcal{P}(n)$ for $r=0,\ldots,d$. Martin Henk and Makoto Tagami gave lower
bounds on the coefficients $g_r(\mathcal{P})$ in terms of the volume of
$\mathcal{P}$. They proved that these bounds are best possible for $r \in
\{1,2,d-2\}$. We show that these bounds are also optimal for $r=3$ and $d-r$
even and we give a new best possible bound for $r=d-3$.

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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs