A note on palindromic δ-vectors for certain rational polytopes
Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart δ-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an el...
| Main Authors: | , |
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| Format: | Article |
| Published: |
2008
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| Online Access: | https://eprints.nottingham.ac.uk/30719/ |
| _version_ | 1848794043612397568 |
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| author | Fiset, Matthew Kasprzyk, Alexander M. |
| author_facet | Fiset, Matthew Kasprzyk, Alexander M. |
| author_sort | Fiset, Matthew |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart δ-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an elementary lattice-point proof of this fact. |
| first_indexed | 2025-11-14T19:09:55Z |
| format | Article |
| id | nottingham-30719 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:09:55Z |
| publishDate | 2008 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-307192020-05-04T16:27:42Z https://eprints.nottingham.ac.uk/30719/ A note on palindromic δ-vectors for certain rational polytopes Fiset, Matthew Kasprzyk, Alexander M. Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart δ-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an elementary lattice-point proof of this fact. 2008-06-06 Article PeerReviewed Fiset, Matthew and Kasprzyk, Alexander M. (2008) A note on palindromic δ-vectors for certain rational polytopes. Electronic Journal of Combinatorics, 15 . N18/1-N18/4. ISSN 1077-8926 http://www.combinatorics.org/Volume_15/Abstracts/v15i1n18.html |
| spellingShingle | Fiset, Matthew Kasprzyk, Alexander M. A note on palindromic δ-vectors for certain rational polytopes |
| title | A note on palindromic δ-vectors for certain rational polytopes |
| title_full | A note on palindromic δ-vectors for certain rational polytopes |
| title_fullStr | A note on palindromic δ-vectors for certain rational polytopes |
| title_full_unstemmed | A note on palindromic δ-vectors for certain rational polytopes |
| title_short | A note on palindromic δ-vectors for certain rational polytopes |
| title_sort | note on palindromic δ-vectors for certain rational polytopes |
| url | https://eprints.nottingham.ac.uk/30719/ https://eprints.nottingham.ac.uk/30719/ |