The boundary volume of a lattice polytope

Heged�s, G�bor; Kasprzyk, Alexander M.

Abstract

For a d-dimensional convex lattice polytope P, a formula for the boundary volume vol(δP) is derived in terms of the number of boundary lattice points on the first [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.

Citation

Hegedüs, G., & Kasprzyk, A. M. (2011). The boundary volume of a lattice polytope. Bulletin of the Australian Mathematical Society, 85(1), https://doi.org/10.1017/S0004972711002577

• Journal Article Type: Article
• Publication Date: Sep 26, 2011
• Deposit Date: Nov 12, 2015
• Publicly Available Date: Nov 12, 2015
• Journal: Bulletin of the Australian Mathematical Society
• Print ISSN: 0004-9727
• Electronic ISSN: 1755-1633
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 85
• Issue: 1
• DOI: https://doi.org/10.1017/S0004972711002577
• Keywords: Lattice polytope, Boundary volume, Reflexive polytope, Order polytope, Birkhoff polytope
• Public URL: https://nottingham-repository.worktribe.com/output/708218
• Publisher URL: http://dx.doi.org/10.1017/S0004972711002577
• Related Public URLs: http://www.austms.org.au/Publ/Bulletin/
• Additional Information: Copyright Australian Mathematical Society 2011