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arXiv · 1608.03166

Ehrhart Theory of Spanning Lattice Polytopes

Johannes Hofscheier·Lukas Katthän·Benjamin Nill
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Abstract

A lattice polytope is called spanning if its lattice points affinely span the ambient lattice. We show as a corollary to a general result in the Ehrhart theory of lattice polytopes that the $h^*$-vector of a spanning lattice polytope has no gaps, i. e., $h^*_i =0$ implies $h^*_{i+1}=0$. This generalizes a recent result by Blekherman, Smith, and Velasco, and implies a polyhedral consequence of the Eisenbud-Goto conjecture. We also discuss how this relates to unimodality questions of lattice polytopes and previously achieved decomposition results on lattice polytopes of given degree.

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BibTeXRIS

Johannes Hofscheier, Lukas Katthän, Benjamin Nill. 2017-12-04. Ehrhart Theory of Spanning Lattice Polytopes. https://doi.org/10.1093/imrn%2Frnx065

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