Article

# Ehrhart polynomials of integral simplices with prime volumes

07/2011;
Source: arXiv

ABSTRACT For an integral convex polytope $\Pc \subset \RR^N$ of dimension $d$, we call
$\delta(\Pc)=(\delta_0, \delta_1,..., \delta_d)$ the $\delta$-vector of $\Pc$
and $\vol(\Pc)=\sum_{i=0}^d\delta_i$ its normalized volume. In this paper, we
will establish the new equalities and inequalities on $\delta$-vectors for
integral simplices whose normalized volumes are prime. Moreover, by using
those, we will classify all the possible $\delta$-vectors of integral simplices
with normalized volume 5 and 7.

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##### Article: Inequalities and Ehrhart -vectors
[hide abstract]
ABSTRACT: -vector of a lattice polytope. We also provide combinatorial proofs of two results of Stanley that were previously established using techniques from commutative algebra. Finally, we give a necessary numerical criterion for the existence of a regular unimodular lattice triangulation of the boundary of a lattice polytope.
• Decompositions of rational convex polytopes. R P Stanley . 333-342.