A063542 - OEIS

%I #20 Aug 18 2018 17:45:44

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

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

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

%H O. Aichholzer and H. Krasser, <a href="http://www.ist.tugraz.at/publications/oaich/psfiles/ak-psotd-01.ps.gz">The point set order type data base: a collection of applications and results</a>, pp. 17-20 in Abstracts 13th Canadian Conference on Computational Geometry (CCCG '01), Waterloo, Aug. 13-15, 2001.

%H O. Aichholzer, R. Fabila-Monroy, T. Hackl, C. Huemer, A. Pilz, and B. Vogtenhuber. <a href="http://www.ist.tugraz.at/files/publications/geometry/afhhpv-lbnsc-13-cgta.pdf">Lower bounds for the number of small convex k-holes</a>. Computational Geometry: Theory and Applications, 47(5):605-613, 2014.

%H O. Aichholzer, R. Fabila-Monroy, T. Hackl, C. Huemer, A. Pilz, B. Vogtenhuber, <a href="http://www.eurogiga-compose.eu/posezo/n12_c1_min_crossing_number_153/n12_c1_min_crossing_number_153.php">A set of 12 points minimizing the numbers of convex 3-, 4-, and 5-holes.</a>

%H O. Aichholzer, T. Hackl, and M. Scheucher, <a href="http://www.eurogiga-compose.eu/posezo/n12_c1_min_convex_3_4_5_holes/n12_c1_min_convex_3_4_5_holes.php">A set of 13 points minimizing the numbers of convex 3-, 4-, and 5-holes.</a>

%H M. Scheucher, <a href="http://www.ist.tugraz.at/staff/scheucher/publ/bachelors_thesis_2013.pdf">Counting Convex 5-Holes</a>, Bachelor's thesis, Graz University of Technology, Austria, 2013, in German.

%Y 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.

%K nonn,more

%O 4,3

%A _N. J. A. Sloane_, Aug 14 2001

%E a(11)-a(13) from _Manfred Scheucher_, Aug 17 2018