SL($n$) covariant vector valuations on polytopes
SL($n$) covariant vector valuations on polytopes
All $\mathrm {SL}(n)$ covariant vector valuations on convex polytopes in $\mathbb {R}^n$ are completely classified without any continuity assumptions. The moment vector turns out to be the only such valuation if $n\ge 3$, while two new functionals show up in dimension two.