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Geometry |
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Authors: Theophilus Agama
Using the method of compression, we show that volume $Vol(K)$ of a ball $K$ in $\mathbb{R}^n$ with a single lattice point in it's interior as center of mass satisfies the lower bound \begin{align} Vol(K)\gg \frac{n^n}{\sqrt{n}}\nonumber \end{align}thereby disproving the Ehrhart volume conjecture, which claims that the upper bound must hold \begin{align} Vol(K) \leq \frac{(n+1)^n}{n!}\nonumber \end{align}for all convex bodies with the required property.
Comments: 7 Pages.
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[v1] 2022-05-09 20:26:35
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