Classification of Ehrhart polynomials of integral simplices

Higashitani, Akihiro

Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

Résumé

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.

Détail

DOI : 10.46298/dmtcs.3065