Erdős Unit Distance: Lower Bound
How many unit distances can a planar n-point set be forced to realize? The best constructions still sit only slightly above linear, far from the O(n^{4/3}) upper bound.
- Impact
- 57 /100
- Funded
- $0
- Donors
- 0
- Of goal
- 0%
Fund this problem
Buy compute. Push the frontier.
Your donation goes entirely to AI compute on this problem. When the purse runs dry, the attempt pauses until the next donor arrives.
Secure checkout · Receipt by email · 100% to compute
- Validated increment
Best constructions remain near-linear with slow-growing factors
The public best lower bounds are of the form Ω(n^{1 + c / log log n}) from lattice-based and number-theoretic constructions. Closing more of the gap toward n^{4/3} is the constructive half of Erdős's problem.
Previous best
Ω(n^{1 + c / log log n}) class constructions
New certified
Same class: no certified asymptotic jump yet
Public literature baseline
Also open