The boundary volume of a lattice polytope

Hegedüs, Gábor and Kasprzyk, Alexander M. (2011) The boundary volume of a lattice polytope. Bulletin of the Australian Mathematical Society, 85 (1). pp. 84-104. ISSN 1755-1633

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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.

Item Type: Article
Additional Information: Copyright Australian Mathematical Society 2011
Keywords: Lattice polytope, Boundary volume, Reflexive polytope, Order polytope, Birkhoff polytope
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1017/S0004972711002577
Related URLs:
URLURL Type
http://www.austms.org.au/Publ/Bulletin/Publisher
Depositing User: Kasprzyk, Dr Alexander
Date Deposited: 12 Nov 2015 13:46
Last Modified: 14 Sep 2016 03:29
URI: http://eprints.nottingham.ac.uk/id/eprint/30720

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