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Akihiro Higashitani - Classification of Ehrhart polynomials of integral simplices

dmtcs:3065 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3065
Classification of Ehrhart polynomials of integral simplicesConference paper

Authors: Akihiro Higashitani 1

  • 1 Department of Pure and Applied Mathematics

Let δ (\mathcal{P} )=(δ _0,δ _1,\ldots,δ _d) be the δ -vector of an integral convex polytope \mathcal{P} of dimension d. First, by using two well-known inequalities on δ -vectors, we classify the possible δ -vectors with \sum_{i=0}^d δ _i ≤3. Moreover, by means of Hermite normal forms of square matrices, we also classify the possible δ -vectors with \sum_{i=0}^d δ _i = 4. In addition, for \sum_{i=0}^d δ _i ≥5, we characterize the δ -vectors of integral simplices when \sum_{i=0}^d δ _i is prime.


Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: Ehrhart polynomial, δ -vector, integral convex polytope, integral simplex.,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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