# Questions tagged [lattice-polytopes]

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### Infinite dimensional lattice for integers and the Riemann hypothesis?

It is known that for each finite set of primes $p$ we have: $\log(p)$ are linear independent over the rational numbers. We have $\log(ab) = \log(a)+\log(b)$ and $\log(n) = \sum_{p |n}v_p(n) \log(p)$. ...
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### Denominators of rational polytopes in terms of hyperplane coefficients

Let $\mathcal{P}$ be a convex polytope in $\mathbb{R}^n$ given in the form $\mathcal{P} = \{ x \in \mathbb{R}^n\colon A x\leq b \}$. Suppose that the entries of $A$ and $b$ are integers. Then it is ...
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### Counting Voronoi cells generated by lattice points

I am working on a problem in dynamical systems where I need to count Voronoi cells arising from nearest neighbours to a subset of the lattice. (See the picture below for an example: the shaded region ...
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### Minimum weight triangulation of lattice points in a circle

Let $r$ be a natural number, and consider the $\mathbb{Z}^2$ lattice points $S$ inside or on the circle $C$ of radius $r$ centered on the origin. Let $P$ be the convex hull of $S$; so $P$ is inscribed ...
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I made the following observation and I am wondering if it is always true. Let $x_1$, $x_2$, $x_3$ and $x_4$ be four positive integer points in the plane ($x_i\in\mathbb{Z^2_{\geq 0}}$) forming a ...