Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Piles of Cubes, Monotone Path Polytopes and Hyperplane Arrangements   Monotone path polytopes arise as a special case of the construction of fiber
polytopes, introduced by Billera and Sturmfels. A simple example is provided by
the permutahedron, which is a monotone path polytope of the standard unit cube.
The permutahedron is the zonotope polar to the braid arrangement. We show how
the zonotopes polar to the cones of certain deformations of the braid
arrangement can be realized as monotone path polytopes. The construction is an
extension of that of the permutahedron and yields interesting connections
between enumerative combinatorics of hyperplane arrangements and geometry of
monotone path polytopes.

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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: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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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: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin