Distinct Distances with ${\ell }_p$ Spaces

Moaaz AlQady, Riley Chabot, William Dudarov +11

We study Erd\H os's distinct distances problem under ${\ell }_p$ metrics with integer $p$. We improve the current best bound for this problem from $\Omega (n^{4/5})$ to $\Omega (n^{6/7-\epsilon })$, for…