A186926 Maximal number of isosceles right triangles in a set of n points in the plane.

1, 4, 8, 11, 15, 20, 28, 35, 43, 52, 64, 74, 85, 97, 112, 124, 139, 156, 176, 192, 210, 229, 252, 271, 291, 314, 338, 363, 389, 417, 448, 473, 501, 531, 564, 594, 626, 659, 696, 728, 763, 799, 836, 874, 914, 955, 1000, 1038

Offset: 3

Author

Jonathan Vos Post, Mar 01 2011

Keywords

• nonn
• hard

Comments

The values for n >= 15 are only conjectural.

Links

• Bernardo M. Abrego, Silvia Fernandez-Merchant and David B. Roberts, On the maximum number of isosceles right triangles in a finite point set, arXiv:1102.5347 [math.CO], 2011. Also in Involve, 4:1 (2011), 27-42.
• P. Erdős and G. Purdy, Some extremal problems in geometry, Journal of Combinatorial Theory 10 (1971), 246-252.
• P. Erdős and G. Purdy, Some extremal problems in geometry III, Proc. 6th Southeastern Conference in Combinatorics, Graph Theory and Comp. (Florida Atlantic Univ., Boca Raton, Fla., 1975), pp. 291-308. Congressus Numerantium, No. XIV, Utilitas Math., Winnipeg, Man., 1975.
• P. Erdős and G. Purdy, Some extremal problems in geometry IV., Proc. 7th Southeastern Conference in Combinatorics, Graph Theory and Comp. (Louisiana State Univ., Baton Rouge, La., 1976), pp. 3.
• Sascha Kurz, Plane point sets with many squares or isosceles right triangles, arXiv:2112.12716 [math.CO], 2021.

Crossrefs

Cf. A051602, A186705.

Extensions

Edited by N. J. A. Sloane, Mar 04 2011

More terms from Sascha Kurz, Jan 14 2022