A063851
Triangle T(n,k) (n >= 3, k = 1..n-2) read by rows giving number of nonisomorphic nondegenerate oriented matroids with n points in n-k dimensions.
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 11, 11, 1, 1, 1, 135, 2628, 135, 1, 1, 1, 4382, 9276601, 9276601, 4382, 1, 1, 1, 312356
Offset: 3
Triangle begins:
1
1,1,
1,1,1,
1,1,1,4,
1,1,1,11,11,
1,1,1,135,2628,135,
1,1,1,4382,9276601,9276601,4382,
1,1,1,312356,...
- Lukas Finschi, Homepage of Oriented Matroids [Gives T(9, 5) = T(9, 6) = 9276595.]
- 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.
- 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.
- Komei Fukuda, Hiroyuki Miyata and Sonoko Moriyama, 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 [Beware typos in Table 1.]
A063800
Number of nonisomorphic oriented matroids with n points in 2 dimensions.
Original entry on oeis.org
1, 2, 4, 17, 143, 4890, 461053, 95052532
Offset: 3
- 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.
- 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
- 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.
- Lukas 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.
- Fukuda, Komei; Miyata, Hiroyuki; Moriyama, Sonoko. 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
A063803
Number of nonisomorphic oriented matroids with n points in 5 dimensions.
Original entry on oeis.org
1, 5, 50, 508321
Offset: 6
- 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
A063805
Number of nonisomorphic oriented matroids with n points in dimensions 2 through n-1.
Original entry on oeis.org
1, 3, 8, 34, 380, 192448
Offset: 3
A246988
Number of isomorphism classes of oriented matroids of dimension n and cardinality n+3.
Original entry on oeis.org
1, 4, 12, 25, 50, 91, 164
Offset: 1
A246989
Number of isomorphism classes of oriented matroids of dimension n and cardinality n+4.
Original entry on oeis.org
1, 17, 206, 6029, 508321
Offset: 1
A063801
Number of nonisomorphic oriented matroids with n points in 3 dimensions.
Original entry on oeis.org
1, 3, 12, 206, 181472
Offset: 4
- 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
A063802
Number of nonisomorphic oriented matroids with n points in 4 dimensions.
Original entry on oeis.org
- 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
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