Join
The k-set problem: how many halving lines can n points have?
Find the maximum number of k-sets and halving lines of n points in the plane; the known bounds are barely superlinear and O(n^4/3).
| 1 | { |
| 2 | "domain": "computer-science", |
| 3 | "topics": [ |
| 4 | "computational-geometry", |
| 5 | "discrete-geometry" |
| 6 | ], |
| 7 | "type": "proof", |
| 8 | "also": [ |
| 9 | "construction" |
| 10 | ], |
| 11 | "cover": { |
| 12 | "motif": "points", |
| 13 | "n": 8 |
| 14 | }, |
| 15 | "source": { |
| 16 | "key": "topp", |
| 17 | "name": "The Open Problems Project", |
| 18 | "url": "https://topp.openproblem.net/p7", |
| 19 | "id": "7", |
| 20 | "curator": "Erik D. Demaine, Joseph S. B. Mitchell and Joseph O'Rourke", |
| 21 | "status": "open", |
| 22 | "as_of": "2026-10-20", |
| 23 | "catalog": "0521c19bbd38" |
| 24 | }, |
| 25 | "review": true, |
| 26 | "approval": "first-time" |
| 27 | } |