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Sylvester simplices: Triangulations and Ehrhart-theoretic aspects
The Sylvester simplex $\mathsf{Sylv}_d^k$ is a $d$-dimensional lattice simplex with exactly $k$ interior lattice points. Sylvester simplices are conjectured to be the volume maximizers among all $d$-dimensional lattice polytopes with exactly $k$ interior lattice points for any $k\geq 1$. Even strong
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