Akihiro Higashitani
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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)
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https://doi.org/10.46298/dmtcs.3065
Classification of Ehrhart polynomials of integral simplicesConference paper
Authors: Akihiro Higashitani 1
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Akihiro Higashitani
1 Department of Pure and Applied Mathematics
Let δ(P)=(δ0,δ1,…,δd) be the δ -vector of an integral convex polytope P of dimension d. First, by using two well-known inequalities on δ -vectors, we classify the possible δ -vectors with ∑di=0δi≤3. Moreover, by means of Hermite normal forms of square matrices, we also classify the possible δ -vectors with ∑di=0δi=4. In addition, for ∑di=0δi≥5, we characterize the δ -vectors of integral simplices when ∑di=0δi 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]
Bibliographic References
1 Document citing this article
José Antonio Arciniega-Nevárez;Marko Berghoff;Eric Rubiel Dolores-Cuenca, 2022, An algebra over the operad of posets and structural binomial identities, arXiv (Cornell University), 29, 1, 10.1007/s40590-022-00478-9, http://arxiv.org/abs/2105.06633.