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A006247 Number of simple pseudoline arrangements with a marked cell. Number of Euclidean pseudo-order types: nondegenerate abstract order types of configurations of n points in the plane.
(Formerly M0917)
7
1, 1, 1, 2, 3, 16, 135, 3315, 158830, 14320182, 2343203071, 691470685682, 366477801792538 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..13.

O. Aichholzer, Order Types for Small Point Sets

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. [Computes a(10)]

S. Felsner and J. E. Goodman, Pseudoline Arrangements. In: Toth, O’Rourke, Goodman (eds.) Handbook of Discrete and Computational Geometry, 3rd edn. CRC Press, 2018.

J. Ferte, V. Pilaud and M. Pocchiola, On the number of simple arrangements of five double pseudolines, arXiv:1009.1575 [cs.CG], 2010; Discrete Comput. Geom. 45 (2011), 279-302.

Lukas Finschi, A Graph Theoretical Approach for Reconstruction and Generation of Oriented Matroids, A dissertation submitted to the Swiss Federal Institute of Technology, Zurich for the degree of Doctor of Mathematics, 2001.

L. Finschi, Homepage of Oriented Matroids

L. Finschi and K. Fukuda, Complete combinatorial generation of small point set configurations and hyperplane arrangements, pp. 97-100 in Abstracts 13th Canadian Conference on Computational Geometry (CCCG '01), Waterloo, Aug. 13-15, 2001.

J. E. Goodman and R. Pollack, Semispaces of configurations, cell complexes of arrangements, J. Combin. Theory, A 37 (1984), 257-293.

D. E. Knuth, Axioms and hulls, Lect. Notes Comp. Sci., Vol. 606.

Alexander Pilz and Emo Welzl, Order on order types, Discrete & Computational Geometry, 59 (No. 4, 2015), 886-922.

Manfred Scheucher, Hendrik Schrezenmaier, Raphael Steiner, A Note On Universal Point Sets for Planar Graphs, arXiv:1811.06482 [math.CO], 2018.

FORMULA

Asymptotics: a(n) = 2^(Theta(n^2)). 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^2} <= a(n) <= 2^{d n^2} is fulfilled. For more information see e.g. the Handbook of Discrete and Computational Geometry. - Manfred Scheucher, Sep 12 2019

CROSSREFS

Cf. A006248, A014540, A063852, A063666, A325595, A325628

Sequence in context: A139802 A292207 A063666 * A052318 A141309 A179442

Adjacent sequences:  A006244 A006245 A006246 * A006248 A006249 A006250

KEYWORD

nonn,nice,hard,more,changed

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

a(12) from Manfred Scheucher and Günter Rote, Aug 31 2019

a(13) from Manfred Scheucher and Günter Rote, Sep 12 2019

STATUS

approved

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Last modified September 15 04:09 EDT 2019. Contains 327062 sequences. (Running on oeis4.)