Family 166CombinatoricsNo LeanNot yet digested
The higher-dimensional Erdős distinct-distances conjecture
For every fixed d ≥ 3, any n ≥ 2 distinct points in ℝ determine at least distinct distances, with depending only on dimension. This matches the integer-grid order and resolves the higher-dimensional Erdős distinct-distances conjecture with a constant-factor bound.
Manuscripts in this family · 1
The higher-dimensional Erdős distinct-distances conjecture
Sep 23, 2026·paper.pdf
For every fixed integer d ≥ 3, we prove that every set of n ≥ 2 distinct points in ℝ determines at least distinct distances, where depends only on d. This resolves the higher-dimensional Erdős distinct-distances conjecture positively.