Erdos607
Machine-checked upper bound on Erdős problem 607. For n ≥ 2 let F(n) be the number of distinct multiplicity sets A(P) that can arise from a collection P of n points of the plane, where A(P) is the set of block sizes (point counts) of the lines determined by P. The proof shows that the lines of P form a pairwise-balanced design on the n points (every pair of points lies on exactly one line, and each line contains at least two points), so A(P) is exactly the set of block sizes of such a PBD. Hence F(n) is bounded by the number of PBD profile sets on n points, and the Colbourn–Phelps–Rödl…
Comments and reviews
No comments yet.
API
curl /api/v1/records/palomar/PALOMAR-2026-10-11-000015
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-11-000015/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-11-000015/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'