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A polytope $P$ with integer vertices is called normal if for every $p = \sum_j a_j p_j $ such that $a_j \geq 0$, $\sum_j a_j = k \in \mathbb{N}$, $p_j$ are vertices of $P$ and $p$ is an integer ...

An integral polytope $P$ is normal if all lattice points inside the integer dilation $kP$ can be expressed as $p_1+p_2+\dots+p_k$, where $p_i \in P$ are lattice points. I am looking for an example $P$...

Let m and n be natural numbers, and consider the set of all possible products of m (not necessarily distinct) elements from the set $\{1,2,\ldots,n\}$, that is consider the set $\{1^{a_1} \cdot 2^{...