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The boundary volume of a lattice polytope

Hegedüs, Gábor; Kasprzyk, Alexander M.

Authors

Gábor Hegedüs

Alexander M. Kasprzyk



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.

Journal Article Type Article
Publication Date Sep 26, 2011
Journal Bulletin of the Australian Mathematical Society
Print ISSN 0004-9727
Electronic ISSN 1755-1633
Publisher Cambridge University Press (CUP)
Peer Reviewed Peer Reviewed
Volume 85
Issue 1
Institution Citation Hegedüs, G., & Kasprzyk, A. M. (2011). The boundary volume of a lattice polytope. Bulletin of the Australian Mathematical Society, 85(1), doi:10.1017/S0004972711002577
DOI https://doi.org/10.1017/S0004972711002577
Keywords Lattice polytope, Boundary volume, Reflexive polytope, Order polytope, Birkhoff polytope
Publisher URL http://dx.doi.org/10.1017/S0004972711002577
Related Public URLs http://www.austms.org.au/Publ/Bulletin/
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information Copyright Australian Mathematical Society 2011

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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