5. Misc
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Conjecture 5.1.
Let $P$ be a convex body with baricenter at 0. Suppose that $P$ contains no integer points in its interior besides 0. The volume of $P$ is at most $\frac{(n+1)^n}{n!}$.
Cite this as: AimPL: The geometry of polynomials in combinatorics and sampling, available at http://aimpl.org/geompolysampling.