Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spanning Lattice Polytopes and the Uniform Position Principle   A lattice polytope $P$ is called IDP if any lattice point in its $k$th dilate
is a sum of $k$ lattice points in $P$. In 1991 Stanley proved a strong
inequality in Ehrhart theory for IDP lattice polytopes. We show that his
conclusion holds under much milder assumptions, namely if the lattice polytope
$P$ is spanning, i.e., any lattice point of the ambient lattice is an integer
affine combination of lattice points in $P$. As an application, we get a
generalization of Hibi's Lower Bound Theorem. Our proof relies on generalizing
Bertini's theorem to the semistandard situation and Harris' Uniform Position
Principle to certain curves in weighted projective space.

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The categories of this paper are: cs
20
The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con