I have a finite set of vectors $\mathcal{S} \subset \mathbb{R}^n$ with mixed-integer components (let's say $n_c$ and $n_i$, with $n = n_c + n_i$). I was wondering whether $\mathcal{S}$ is always partially ordered, e.g., under lexicographic order, or I do need something more.
Any reference on the topic would be greatly appreciated.