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25 April 2024

» arxiv » 1704.5532

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Smooth polytopes with negative Ehrhart coefficients
Federico Castillo ; Fu Liu ; Benjamin Nill ;
Date:	18 Apr 2017
Abstract:	In this note, we present examples of smooth lattice polytopes whose Ehrhart polynomials have some negative coefficients. This answers negatively a question by Bruns. Using Berline-Vergne valuations, we show that the dimension of this specific class of examples must be at least 7. We also discuss a stronger positivity property and state several open questions.
Source:	arXiv, 1704.5532
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