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Belt diameter of $Π$-zonotopes

We prove that any d-dimensional zonotope obtained from permutahedron by deleting zone vectors has belt diameter at most 3. Moreover if d is not greater than 6 then its belt diameter is bounded from above by 2. Also we show that these bounds are sharp. As a consequence we show that diameter of the edge graph of dual polytope for such zonotopes is not greater then 4 and 3 respectively.

preprint2012arXivOpen access
Alexey Garber
math.COmath.MG
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Alexey Garber

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