How many sorted projections determine n points in k dimensions?

Christopher Gorham Lester, Raymond Hau Sørensen

Let $d_1,\dots ,d_m$ be directions in ${\mathbb{R}}^k$, where $k\ge 2$. A multiset $X$ of $n$ points of ${\mathbb{R}}^k$ projects to the $m$ multisets of numbers $\{\{x\cdot d_j : x\in…