A006248
Number of projective pseudo order types: simple arrangements of pseudo-lines in the projective plane.
Original entry on oeis.org
1, 1, 1, 1, 1, 4, 11, 135, 4382, 312356, 41848591, 10320613331
Offset: 1
- 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).
- 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
a(11) from Franz Aurenhammer (auren(AT)igi.tu-graz.ac.at), Feb 05 2002
A048872
Number of non-isomorphic arrangements of n lines in the real projective plane such that the lines do not all pass through a common point.
Original entry on oeis.org
1, 2, 4, 17, 143, 4890, 460779
Offset: 3
- J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 102.
- B. Grünbaum, Arrangements and Spreads. American Mathematical Society, Providence, RI, 1972, p. 4.
- 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
- 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, Illustration of a(3) - a(6) [based on Fig. 2.1 of Grünbaum, 1972]
See
A132346 for the sequence when we include the arrangement where the lines do pass through a common point, which is 1 greater than this.
a(7)-a(9) from Handbook of Discrete and Computational Geometry, 2017, by
Andrey Zabolotskiy, Oct 09 2017
A172144
Number of chirotopes resulting from realizable uniform oriented matroids of rank 3 over a ground set of n elements modulo permutations.
Original entry on oeis.org
1, 3, 4, 41, 706, 28287
Offset: 3
Johannes Brunnemann (jbrunnem(AT)math.upb.de) and David Rideout, Nov 19 2010
- J. Brunnemann and D. Rideout, "Oriented matroids—combinatorial structures underlying loop quantum gravity", Class.Quant.Grav. 27, 205008 (2010).
- J. Richter-Gebert, "On the Realizability Problem of Combinatorial Geometries - Decision Methods", Ph.D. thesis, TH-Darmstadt 1992, 144 pages.
A222317
Triangle read by rows: T(n,k) (n>=3, 1<=k<=n-2) = number of uniform realizable oriented matroids with n elements and rank n-k+1.
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 11, 11, 1, 1, 1, 135, 2604, 135, 1, 1, 1, 4381
Offset: 3
Triangle begins
1
1 1
1 1 1
1 1 1 4
1 1 1 11 11
1 1 1 135 2604 135
1 1 1 4381 unknown unknown unknown
...
- Fukuda, Komei; Miyata, Hiroyuki; Moriyama, Sonoko. Complete Enumeration of Small Realizable Oriented Matroids. Discrete Comput. Geom. 49 (2013), no. 2, 359--381. MR3017917. (The (4) in the r=4 row of Table 2 should probably be (1).)
A339177
a(n) is the number of arrangements on n pseudocircles which are NonKrupp-packed.
Original entry on oeis.org
1, 3, 46, 3453, 784504
Offset: 3
- S. Felsner and M. Scheucher, Arrangements of Pseudocircles: On Circularizability, Discrete & Computational Geometry, Ricky Pollack Memorial Issue, 64(3), 2020, pages 776-813.
- S. Felsner and M. Scheucher, Homepage of Pseudocircles.
- C. Medina, J. Ramírez-Alfonsín, and G. Salazar, The unavoidable arrangements of pseudocircles, Proc. Amer. Math. Soc. 147, 2019, pages 3165-3175.
- M. Scheucher, Points, Lines, and Circles: Some Contributions to Combinatorial Geometry, PhD thesis, Technische Universität Berlin, 2020.
Cf.
A296406 (number of arrangements on pairwise intersecting pseudocircles).
Cf.
A006248 (number of arrangements on pseudocircles which are Krupp-packed, i.e., arrangements on pseudo-greatcircles).
Cf.
A018242 (number of arrangements on circles which are Krupp-packed, i.e., arrangements on greatcircles).
Showing 1-5 of 5 results.
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