A063542 Least number of empty convex quadrilaterals (4-gons) determined by n points in the plane.

0, 1, 3, 6, 10, 15, 23, 32, 42, 51

Offset: 4

Author

N. J. A. Sloane, Aug 14 2001

Keywords

• nonn
• more

References

• K. Dehnhardt. Leere konvexe Vielecke in ebenen Punktmengen. PhD thesis, TU Braunschweig, Germany, 1987.

Links

• O. Aichholzer and H. Krasser, The point set order type data base: a collection of applications and results, pp. 17-20 in Abstracts 13th Canadian Conference on Computational Geometry (CCCG '01), Waterloo, Aug. 13-15, 2001.
• O. Aichholzer, R. Fabila-Monroy, T. Hackl, C. Huemer, A. Pilz, and B. Vogtenhuber. Lower bounds for the number of small convex k-holes. Computational Geometry: Theory and Applications, 47(5):605-613, 2014.
• O. Aichholzer, R. Fabila-Monroy, T. Hackl, C. Huemer, A. Pilz, B. Vogtenhuber, A set of 12 points minimizing the numbers of convex 3-, 4-, and 5-holes.
• O. Aichholzer, T. Hackl, and M. Scheucher, A set of 13 points minimizing the numbers of convex 3-, 4-, and 5-holes.
• M. Scheucher, Counting Convex 5-Holes, Bachelor's thesis, Graz University of Technology, Austria, 2013, in German.

Crossrefs

Cf. A063541 and A276096 for empty convex 3- and 5-gons (a.k.a. k-holes), respectively. The rectilinear crossing number A014540 is the number of (not necessarily empty) convex quadrilaterals.

Extensions

a(11)-a(13) from Manfred Scheucher, Aug 17 2018