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

4,3

References

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

Links

Table of n, a(n) for n=4..13.

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.

Sequence in context: A373962 A342211 A262927 * A294413 A122554 A111734

Adjacent sequences: A063539 A063540 A063541 * A063543 A063544 A063545

Keyword

nonn,more

Author

N. J. A. Sloane, Aug 14 2001

Extensions

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

Status

approved