A006248 Number of projective pseudo order types: simple arrangements of pseudo-lines in the projective plane.

1, 1, 1, 1, 1, 4, 11, 135, 4382, 312356, 41848591, 10320613331

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• hard

References

• J. Bokowski, personal communication.
• J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 102.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• J. Bokowski & N. J. A. Sloane, Emails, June 1994
• F. Cortés Kühnast, J. Dallant, S. Felsner, and M. Scheucher, An Improved Lower Bound on the Number of Pseudoline Arrangements
• 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
• 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. Ferté, 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.
• Komei Fukuda, Hiroyuki Miyata, and Sonoko Moriyama, Complete Enumeration of Small Realizable Oriented Matroids, arXiv:1204.0645 [math.CO], 2012; Discrete Comput. Geom. 49 (2013), no. 2, 359--381. MR3017917. - From _N. J. A. Sloane_, Feb 16 2013
• 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
• D. E. Knuth, Axioms and Hulls, Lect. Notes Comp. Sci., Vol. 606, Springer-Verlag, Berlin, Heidelberg, 1992, p.35, entry E_n.
• Index entries for sequences related to sorting

Crossrefs

Cf. A006245, A006246, A018242, A063666. A diagonal of A063851.

Formula

Asymptotics: 2^{Cn^2} <= a(n) <= 2^{Dn^2} for every n >= N, where N,C,D are constants with 0.1887Manfred Scheucher, Apr 10 2025 on personal communication with Günter Rote.]

Extensions

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

a(12) from Manfred Scheucher and Günter Rote, Sep 07 2019

Definition corrected by Günter Rote, Dec 01 2021