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%I M0917 #118 Dec 22 2023 14:25:22
%S 1,1,1,2,3,16,135,3315,158830,14320182,2343203071,691470685682,
%T 366477801792538
%N Number of simple arrangements of n pseudolines in the projective plane with a marked cell. Number of Euclidean pseudo-order types: nondegenerate abstract order types of configurations of n points in the plane.
%C Also the number of nonisomorphic nondegenerate acyclic rank 3 oriented matroids on n elements. - _Manfred Scheucher_, May 09 2022
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H O. Aichholzer, <a href="http://www.ist.tugraz.at/staff/aichholzer/research/rp/triangulations/ordertypes/">Order Types for Small Point Sets</a>
%H O. Aichholzer, F. Aurenhammer and H. Krasser, <a href="http://dx.doi.org/10.1023/A:1021231927255">Enumerating order types for small point sets with applications</a>, In Proc. 17th Ann. ACM Symp. Computational Geometry, pages 11-18, Medford, Massachusetts, USA, 2001. [Computes a(10)]
%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 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 Lukas 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 Henry Förster, Philipp Kindermann, Tillmann Miltzow, Irene Parada, Soeren Terziadis, and Birgit Vogtenhuber, <a href="https://arxiv.org/abs/2312.05010">Geometric Thickness of Multigraphs is (exists in reals)-complete</a>, arXiv:2312.05010 [cs.CG], 2023.
%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> [<a href="https://doi.org/10.1201/9781315119601">alternative link</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 J. E. Goodman and R. Pollack, <a href="http://dx.doi.org/10.1016/0097-3165(84)90050-5">Semispaces of configurations, cell complexes of arrangements</a>, J. Combin. Theory, A 37 (1984), 257-293.
%H D. E. Knuth, <a href="http://www-cs-faculty.stanford.edu/~uno/aah.html">Axioms and hulls</a>, Lect. Notes Comp. Sci., Vol. 606.
%H Alexander Pilz and Emo Welzl, <a href="http://drops.dagstuhl.de/opus/volltexte/2015/5119/">Order on order types</a>, Discrete & Computational Geometry, 59 (No. 4, 2015), 886-922.
%H Manfred Scheucher, Hendrik Schrezenmaier, and Raphael Steiner, <a href="https://arxiv.org/abs/1811.06482">A Note On Universal Point Sets for Planar Graphs</a>, arXiv:1811.06482 [math.CO], 2018.
%F 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 satisfied. For more information see e.g. the Handbook of Discrete and Computational Geometry. - _Manfred Scheucher_, Sep 12 2019
%Y Cf. A006248, A014540, A063852, A063666, A325595, A325628, A006245
%K nonn,nice,hard,more
%O 1,4
%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_, Aug 31 2019
%E a(13) from _Manfred Scheucher_ and _Günter Rote_, Sep 12 2019
%E Definition clarified by _Manfred Scheucher_, Jun 22 2023
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