A222315
Second-from-right diagonal of A063851.
Original entry on oeis.org
1, 1, 1, 11, 2628, 9276601
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.
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
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
A063852
Number of nonisomorphic nondegenerate oriented matroids with n points in dimensions 2 through n-1.
Original entry on oeis.org
1, 2, 3, 7, 25, 2901
Offset: 3
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).)
Showing 1-5 of 5 results.