The boundary volume of a lattice polytope
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...
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| Format: | Article |
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Australian Mathematical Society
2011
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| Online Access: | https://eprints.nottingham.ac.uk/30720/ |
| _version_ | 1848794043902853120 |
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| author | Hegedüs, Gábor Kasprzyk, Alexander M. |
| author_facet | Hegedüs, Gábor Kasprzyk, Alexander M. |
| author_sort | Hegedüs, Gábor |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:09:55Z |
| format | Article |
| id | nottingham-30720 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:09:55Z |
| publishDate | 2011 |
| publisher | Australian Mathematical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-307202020-05-04T16:31:11Z https://eprints.nottingham.ac.uk/30720/ The boundary volume of a lattice polytope Hegedüs, Gábor Kasprzyk, Alexander M. 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. Australian Mathematical Society 2011-09-26 Article PeerReviewed 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 Lattice polytope Boundary volume Reflexive polytope Order polytope Birkhoff polytope http://dx.doi.org/10.1017/S0004972711002577 doi:10.1017/S0004972711002577 doi:10.1017/S0004972711002577 |
| spellingShingle | Lattice polytope Boundary volume Reflexive polytope Order polytope Birkhoff polytope Hegedüs, Gábor Kasprzyk, Alexander M. The boundary volume of a lattice polytope |
| title | The boundary volume of a lattice polytope |
| title_full | The boundary volume of a lattice polytope |
| title_fullStr | The boundary volume of a lattice polytope |
| title_full_unstemmed | The boundary volume of a lattice polytope |
| title_short | The boundary volume of a lattice polytope |
| title_sort | boundary volume of a lattice polytope |
| topic | Lattice polytope Boundary volume Reflexive polytope Order polytope Birkhoff polytope |
| url | https://eprints.nottingham.ac.uk/30720/ https://eprints.nottingham.ac.uk/30720/ https://eprints.nottingham.ac.uk/30720/ |