A063666 Euclidean order types: number of realizable order types of n points in the plane.

1, 2, 3, 16, 135, 3315, 158817, 14309547, 2334512907

Offset: 3

Author

Hannes Krasser (hkrasser(AT)igi.tu-graz.ac.at), Aug 22 2001

Keywords

• hard
• more
• nice
• nonn

Comments

Also the number of nonisomorphic nondegenerate acyclic rank 3 oriented matroids on n elements that are representable over the reals. - Manfred Scheucher, May 09 2022

References

• O. Aichholzer, F. Aurenhammer and H. Krasser. Enumerating order types for small point sets with applications. In Proc. 17th Ann. ACM Symp. Computational Geometry, pages 11-18, Medford, Massachusetts, USA, 2001.

Links

• O. Aichholzer, F. Aurenhammer and H. Krasser, Enumerating order types for small point sets with applications
• O. Aichholzer, F. Aurenhammer and H. Krasser, Enumerating order types for small point sets with applications, Order 19(3):265-281, September 2002.
• Stefan Felsner and Jacob E. Goodman, Pseudoline Arrangements, Chapter 5 of Handbook of Discrete and Computational Geometry, CRC Press, 2017, see Table 5.6.1. [Specific reference for this sequence] - _N. J. A. Sloane_, Nov 14 2023
• Stefan Felsner and J. E. Goodman, Pseudoline Arrangements. In: Toth, O'Rourke, Goodman (eds.) Handbook of Discrete and Computational Geometry, 3rd edn. CRC Press, 2018.
• Jacob E. Goodman, Joseph O'Rourke, and Csaba D. Tóth, editors, Handbook of Discrete and Computational Geometry, CRC Press, 2017, see Table 5.6.1. [General reference for 2017 edition of the Handbook] - _N. J. A. Sloane_, Nov 14 2023

Crossrefs

Cf. A006247.

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