The boundary volume of a lattice polytope

Authors

  • Alexander Mieczyslaw Kasprzyk
  • Gabor Hegedus

Keywords:

Lattice polytope, boundary volume, reflexive polytope, order polytope, Birkhoff polytope

Abstract

For a $d$-dimensional convex lattice polytope $P$, a formula for the boundary volume $\vol{\partial P}$ 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. DOI: 10.1017/S0004972711002577

Published

2011-12-09

Issue

Vol. 85 No. 1 (2012)

Section

Articles
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