Monotone path polytopes arise as a special case of the construction of fiberpolytopes, introduced by Billera and Sturmfels. A simple example is provided bythe permutahedron, which is a monotone path polytope of the standard unit cube.The permutahedron is the zonotope polar to the braid arrangement. We show howthe zonotopes polar to the cones of certain deformations of the braidarrangement can be realized as monotone path polytopes. The construction is anextension of that of the permutahedron and yields interesting connectionsbetween enumerative combinatorics of hyperplane arrangements and geometry ofmonotone path polytopes.
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