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arXiv · 1004.1661

On the number of points in a lattice polytope

Arseniy Akopyan·Makoto Tagami
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Abstract

In this article we will show that for every natural $d$ and $n>1$ there exists a natural number $t$ such that for every $d$-dimensional simplicial complex $\mathcal{T}$ with vertices in $\mathbb{Z}^d$, the number of lattice points in the $t^{\mathrm{th}}$ dilate of $\mathcal{T}$ is exactly $χ(\mathcal{T})$ modulo $n$, where $χ(\mathcal{T})$ is the Euler characteristic of $\mathcal{T}$.

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Arseniy Akopyan, Makoto Tagami. 2017-09-14. On the number of points in a lattice polytope. https://doi.org/10.1515/integ.2011.046

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