Abstract
To classify the lattice polytopes with a given δ-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 δ-polynomials are of the form 1+tk+⋯+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 δ-polynomials will be performed, when v is either p2 or pq, where p and q are prime integers with p≠q. Moreover, we consider the number of Gorenstein simplices, up to unimodular equivalence, with the expected δ-polynomial.
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