3 problems

Let $d,k\in\mathbb{N}$. For $P\subseteq\mathbb{R}^d$ and an $\ell^1$-distance $\lambda>0$, say that $\lambda$ occurs in an axis-parallel direction if there are $x\in P$ and…

Let $d,k\in\mathbb{N}$, let $P\subseteq\mathbb{R}^d$ be a set determining at most $k$ distinct $\ell^1$-distances, and let $\Lambda_d(k)$ be the corresponding extremal construction…

Erdős–Mordell open problem. In taxicab geometry, the inequality