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arXiv · 1705.05268

Gorenstein simplices with a given $\delta$-polynomial

Takayuki Hibi·Akiyoshi Tsuchiya·Koutarou Yoshida
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Abstract

To classify the lattice polytopes with a given $\delta$-polynomial is an important open problem in Ehrhart theory. A complete classification of the Gorenstein simplices whose normalized volumes are prime integers is known. In particular, their $\delta$-polynomials are of the form $1+t^k+\cdots+t^{(v-1)k}$, where $k$ and $v$ are positive integers. In the present paper, a complete classification of the Gorenstein simplices with the above $\delta$-polynomials will be performed, when $v$ is either $p^2$ or $pq$, where $p$ and $q$ are prime integers with $p \neq q$. Moreover, we consider the number of Gorenstein simplices, up to unimodular equivalence, with the expected $\delta$-polynomial.

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Takayuki Hibi, Akiyoshi Tsuchiya, Koutarou Yoshida. 2017-05-15. Gorenstein simplices with a given $\delta$-polynomial. https://doi.org/10.1016/j.disc.2019.111619

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