The boundary volume of a lattice polytope

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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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Official URL: http://dx.doi.org/10.1017/S0004972711002577

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

RIS ID:

https://nottingham-repository.worktribe.com/output/708218

Additional Information:

Keywords:

Lattice polytope, Boundary volume, Reflexive polytope, Order polytope, Birkhoff polytope

Schools/Departments:

University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences

Identification Number:

https://doi.org/10.1017/S0004972711002577

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