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ISSN 1088-6850(e) ISSN 0002-9947(p)

Inequalities and Ehrhart $\delta$ -vectors

Author(s): A. Stapledon
Journal: Trans. Amer. Math. Soc. 361 (2009), 5615-5626.
MSC (2000): Primary 52B20
Posted: May 13, 2009
MathSciNet review: 2515826
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Abstract: For any lattice polytope , we consider an associated polynomial $\bar{\delta}_{P}(t)$ and describe its decomposition into a sum of two polynomials satisfying certain symmetry conditions. As a consequence, we improve upon known inequalities satisfied by the coefficients of the Ehrhart $\delta$ -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.

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