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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Inequalities and Ehrhart $ \delta$-vectors


Author: A. Stapledon
Journal: Trans. Amer. Math. Soc. 361 (2009), 5615-5626
MSC (2000): Primary 52B20
Published electronically: May 13, 2009
MathSciNet review: 2515826
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Abstract: For any lattice polytope $ P$, 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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Additional Information

A. Stapledon
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: astapldn@umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04776-X
PII: S 0002-9947(09)04776-X
Received by editor(s): January 9, 2008
Received by editor(s) in revised form: February 22, 2008
Published electronically: May 13, 2009
Additional Notes: The author was supported by Mircea Mustaţǎ’s Packard Fellowship and by an Eleanor Sophia Wood travelling scholarship from the University of Sydney
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.