The boundary volume of a lattice polytope

Details The boundary volume of a lattice polytope The boundary volume of a lattice polytope

2010-02-15

arxiv.org/abs/1002.2815v3

Mathematics

Combinatorics

21 pages; subsumes arXiv:1002.1908 [math.CO]; to appear in the Bulletin of the Australian Mathematical Society

Scientific paper

For a d-dimensional convex lattice polytope P, a formula for the boundary volume is derived in terms of the number of boundary lattice points on the first $\floor{d/2}$ dilations of P. As an application we give a necessary and sufficient condition for a polytope to be reflexive, and derive formulae for the f-vector of a smooth polytope in dimensions 3, 4, and 5. We also give applications to reflexive order polytopes, and to the Birkhoff polytope.

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