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A006248 Number of projective pseudo order types: simple arrangements of pseudo-lines in the projective plane.
(Formerly M3428)
15

%I M3428 #94 Nov 15 2023 06:00:40

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

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

%D J. Bokowski, personal communication.

%D J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 102.

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

%H J. Bokowski & N. J. A. Sloane, <a href="/A006248/a006248.pdf">Emails, June 1994</a>

%H Stefan Felsner and Jacob E. Goodman, <a href="https://www.csun.edu/~ctoth/Handbook/chap5.pdf">Pseudoline Arrangements</a>, 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

%H S. Felsner and J. E. Goodman, <a href="https://doi.org/10.1201/9781315119601">Pseudoline Arrangements</a>. In: Toth, O'Rourke, Goodman (eds.) Handbook of Discrete and Computational Geometry, 3rd edn. CRC Press, 2018.

%H J. Ferté, V. Pilaud and M. Pocchiola, <a href="http://arxiv.org/abs/1009.1575">On the number of simple arrangements of five double pseudolines</a>, arXiv:1009.1575 [cs.CG], 2010; Discrete Comput. Geom. 45 (2011), 279-302.

%H Lukas Finschi, <a href="http://dx.doi.org/10.3929/ethz-a-004255224">A Graph Theoretical Approach for Reconstruction and Generation of Oriented Matroids</a>, A dissertation submitted to the Swiss Federal Institute of Technology, Zurich for the degree of Doctor of Mathematics, 2001.

%H L. Finschi, <a href="https://finschi.com/math/om/">Homepage of Oriented Matroids</a>

%H L. Finschi and K. Fukuda, <a href="http://www.cccg.ca/proceedings/2001/finschi-1053.ps.gz">Complete combinatorial generation of small point set configurations and hyperplane arrangements</a>, pp. 97-100 in Abstracts 13th Canadian Conference on Computational Geometry (CCCG '01), Waterloo, Aug. 13-15, 2001.

%H Komei Fukuda, Hiroyuki Miyata, and Sonoko Moriyama, <a href="http://arxiv.org/abs/1204.0645">Complete Enumeration of Small Realizable Oriented Matroids</a>, arXiv:1204.0645 [math.CO], 2012; Discrete Comput. Geom. 49 (2013), no. 2, 359--381. MR3017917. - From _N. J. A. Sloane_, Feb 16 2013

%H Jacob E. Goodman, Joseph O'Rourke, and Csaba D. Tóth, editors, <a href="https://www.csun.edu/~ctoth/Handbook/HDCG3.html">Handbook of Discrete and Computational Geometry</a>, CRC Press, 2017, see Table 5.6.1. [General reference for 2017 edition of the Handbook] - _N. J. A. Sloane_, Nov 14 2023

%H D. E. Knuth, <a href="https://doi.org/10.1007/3-540-55611-7">Axioms and Hulls</a>, Lect. Notes Comp. Sci., Vol. 606, Springer-Verlag, Berlin, Heidelberg, 1992, p.35, entry E_n.

%H <a href="/index/So#sorting">Index entries for sequences related to sorting</a>

%F Asymptotics: 2^{Cn^2} <= a(n) <= 2^{Dn^2} for every n >= N, where N,C,D are constants with 1<C<D . For more information see e.g. Felsner and Goodman. - _Manfred Scheucher_, Sep 12 2019 [reformulated by _Günter Rote_, Dec 01 2021]

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

%K nonn,nice,hard

%O 1,6

%A _N. J. A. Sloane_

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

%E a(12) from _Manfred Scheucher_ and _Günter Rote_, Sep 07 2019

%E Definition corrected by _Günter Rote_, Dec 01 2021

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)