cp's OEIS Frontend

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

%I A006248 M3428 #99 Jun 02 2025 19:27:09
%S A006248 1,1,1,1,1,4,11,135,4382,312356,41848591,10320613331
%N A006248 Number of projective pseudo order types: simple arrangements of pseudo-lines in the projective plane.
%D A006248 J. Bokowski, personal communication.
%D A006248 J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 102.
%D A006248 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006248 J. Bokowski & N. J. A. Sloane, <a href="/A006248/a006248.pdf">Emails, June 1994</a>
%H A006248 F. Cortés Kühnast, J. Dallant, S. Felsner, and M. Scheucher, <a href="https://arxiv.org/abs/2402.13107">An Improved Lower Bound on the Number of Pseudoline Arrangements</a>
%H A006248 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 A006248 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 A006248 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 A006248 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 A006248 L. Finschi, <a href="https://finschi.com/math/om/">Homepage of Oriented Matroids</a>
%H A006248 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 A006248 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 A006248 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 A006248 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 A006248 <a href="/index/So#sorting">Index entries for sequences related to sorting</a>
%F A006248 Asymptotics: 2^{Cn^2} <= a(n) <= 2^{Dn^2} for every n >= N, where N,C,D are constants with 0.1887<C<D<0.6571; see An Improved Lower Bound on the Number of Pseudoline Arrangements by Fernando Cortés Kühnast, Justin Dallant, Stefan Felsner, Manfred Scheucher. [Corrected by _Manfred Scheucher_, Apr 10 2025 on personal communication with Günter Rote.]
%Y A006248 Cf. A006245, A006246, A018242, A063666. A diagonal of A063851.
%K A006248 nonn,nice,hard
%O A006248 1,6
%A A006248 _N. J. A. Sloane_
%E A006248 a(11) from Franz Aurenhammer (auren(AT)igi.tu-graz.ac.at), Feb 05 2002
%E A006248 a(12) from _Manfred Scheucher_ and _Günter Rote_, Sep 07 2019
%E A006248 Definition corrected by _Günter Rote_, Dec 01 2021