A018242 Number of projective order types.

1, 1, 1, 1, 1, 1, 4, 11, 135, 4381, 312114, 41693377

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more

Comments

Table 5.6.1 in the Felsner-Goodman survey contains this sequence in the second row, but the line is incorrectly labeled. The origin of these data is the paper of Aichholzer and Krasser. - Günter Rote, Apr 16 2025

Links

• Oswin Aichholzer, Hannes Krasser: Abstract order type extension and new results on the rectilinear crossing number. Comput. Geom. 36(1), 2-15 (2007), Table 1
• Stefan Felsner and Jacob E. Goodman, Pseudoline Arrangements, Chapter 5 of Handbook of Discrete and Computational Geometry, 3rd edition, Jacob E. Goodman, Joseph O'Rourke, and Csaba D. Tóth, editors, CRC Press, 2017, see Table 5.6.1. [alternative link][alternative link] [Specific reference for this sequence] - N. J. A. Sloane, Nov 14 2023
• Komei Fukuda, Hiroyuki Miyata, Sonoko Moriyama, Complete Enumeration of Small Realizable Oriented Matroids. Discrete Comput. Geom. 49 (2013), no. 2, 359-381, see Table 2. MR3017917. Also arXiv:1204.0645 [math.CO], 2012. - From _N. J. A. Sloane_, Feb 16 2013

Crossrefs

Cf. A006247, A006248, A063666. A diagonal of A222317.

Formula

Asymptotics: a(n) = 2^(Theta(n log n)). This is Bachmann-Landau notation, that is, there are constants n_0, c, and d, such that for every n >= n_0 the inequality 2^(c n log n) <= a(n) <= 2^(d n log n) is satisfied. For more information see e.g. the Handbook of Discrete and Computational Geometry. - Manfred Scheucher, Sep 12 2019

Extensions

a(11) from Franz Aurenhammer (auren(AT)igi.tu-graz.ac.at), Feb 05 2002