A063804
Triangle T(n,k) (n >= 3, k = 1..n-2) read by rows, giving number of nonisomorphic oriented matroids with n points in n-k dimensions.
Original entry on oeis.org
1, 1, 2, 1, 3, 4, 1, 4, 12, 17, 1, 5, 25, 206, 143, 1, 6, 50, 6029, 181472, 4890, 1, 7, 91, 508321
Offset: 3
Triangle begins:
1
1 2
1 3 4
1 4 12 17
1 5 25 206 143
1 6 50 6029 181472 4890
1 7 91 508321 unknown unknown 461053
...
- 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.
- Fukuda, Komei; Miyata, Hiroyuki; Moriyama, Sonoko. Complete Enumeration of Small Realizable Oriented Matroids. Discrete Comput. Geom. 49 (2013), no. 2, 359--381. MR3017917. - From N. J. A. Sloane, Feb 16 2013
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
A180501
Triangle read by row. T(n,m) gives the number of isomorphism classes of arrangements of n pseudolines and m double pseudolines in the projective plane.
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 1, 3, 9, 46, 2, 16, 265, 6998, 153528
Offset: 0
- J. Ferté, V. Pilaud and M. Pocchiola, On the number of arrangements of five double pseudolines, Abstracts 18th Fall Workshop on Comput. Geom. (FWCG08), Troy, NY, October 2008.
See
A180500 for isomorphism classes of simple arrangements of n pseudolines and m double pseudolines in the projective plane.
See
A180502 for isomorphism classes of arrangements of n pseudolines and m double pseudolines in the Moebius strip.
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