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arXiv · 1810.01065

Lattice points in vector-dilated quadratic irrational polytopes

Yashaswika Gaur·Tian An Wong
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Abstract

We study the Ehrhart theory of quadratic irrational polytopes that undergo vector dilations. That is, for a given polytope with vertices in $\mathbb{Q}(\sqrt{D})$, and a different dilation factor for each facet, we show that the leading term of the lattice-point count behaves similar to an Ehrhart polynomial, generalizing previous work of Borda on scalar dilations of quadratic irrational polytopes. As a result, a form of the Ehrhart-Macdonald reciprocity law is obtained for the leading term.

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Yashaswika Gaur, Tian An Wong. 2018-10-02. Lattice points in vector-dilated quadratic irrational polytopes. https://arxiv.org/abs/1810.01065

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