Belt diameter of zonotopes obtained from permutahedron by deleting zone vectors

Details Belt diameter of zonotopes obtained from permutahedron by deleting zone vectors Belt diameter of zonotopes obtained from permutahedron by deleting zone vectors

2011-11-12

arxiv.org/abs/1111.2932v2

Mathematics

Combinatorics

13 pages, 10 figures, version 2 with several misprints corrected

Scientific paper

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.

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