Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetric Alcoved Polytopes   Generalized alcoved polytopes are polytopes whose facet normals are roots in
a given root system. We call a set of points in an alcoved polytope a
generating set if there does not exist a strictly smaller alcoved polytope
containing it. The type $A$ alcoved polytopes are precisely the tropical
polytopes that are also convex in the usual sense. In this case the tropical
generators form a generating set. We show that for any root system other than
$F_4$, every alcoved polytope invariant under the natural Weyl group action has
a generating set of cardinality equal to the Coxeter number of the root system.

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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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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: econ
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: stat