A001200
Number of linear geometries on n (unlabeled) points.
Original entry on oeis.org
1, 1, 1, 2, 3, 5, 10, 24, 69, 384, 5250, 232929, 28872973
Offset: 0
- L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 303, #42.
- CRC Handbook of Combinatorial Designs, 1996, pp. 216, 697.
- J. Doyen, Sur le nombre d'espaces linéaires non isomorphes de n points. Bull. Soc. Math. Belg. 19 1967 421-437.
- P. Robillard, On the weighted finite linear spaces. Bull. Soc. Math. Belg. 22 (1970), 227-241.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- Mohamed Barakat, Reimer Behrends, Christopher Jefferson, Lukas Kühne, Martin Leuner, On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture, arXiv:1907.01073 [math.CO], 2019.
- A. Betten and D. Betten, Linear spaces with at most 12 points, J. Combinatorial Designs, Volume 7, 1999, pp. 119 - 145.
- J. E. Blackburn, H. H. Crapo, and D. A. Higgs, A catalogue of combinatorial geometries, Math. Comp 27 1973 155-166.
- J. Doyen, Sur le nombre d'espaces linéaires non isomorphes de n points [Annotated and scanned copy]
- D. G. Glynn, Rings of geometries II, J. Combin. Theory, A 49 (1988), 26-66.
- D. G. Glynn, A geometrical isomorphism algorithm, Bull. ICA 7 (1993), 36-38.
- Robert Haas, Cographs, arXiv:1905.12627 [math.GM], 2019.
- G. Heathcote, Linear spaces on 16 points, J. Combin. Designs, Vol. 1, No. 5 (1993), 359-378.
- Nathan Kaplan, Susie Kimport, Rachel Lawrence, Luke Peilen and Max Weinreich, Counting arcs in projective planes via Glynn's algorithm, J. Geom. 108, No. 3, 1013-1029 (2017).
- Ch. Pietsch, On the classification of linear spaces of order 11, J. Comb. Designs, Vol. 3, No. 3 (1995), 185-193.
A056642
Number of linear spaces on n (labeled) points.
Original entry on oeis.org
1, 1, 2, 6, 32, 353, 8390, 433039, 50166354, 13480967630
Offset: 1
W. M. B. Dukes (dukes(AT)stp.dias.ie), Aug 28 2000
- L. M. Batten and A. Beutelspacher: The theory of finite linear spaces, Cambridge Univ. Press, 1993 (see the Appendix).
- L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 303, #42.
- J. Doyen, Sur le nombre d'espaces linéaires non isomorphes de n points, Bull. Soc. Math. Belg. 19 (1967), 421-437.
- J. A. Thas, Sur le nombre d'espaces linéaires non isomorphes de n points, Bull. Soc. Math. Belg. 21 (1969), 57-66.
- W. M. B. Dukes, Tables of matroids.
- W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000.
- W. M. Dukes, Bounds on the number of generalized partitions and some applications, Australas. J. Combin. 28 (2003), 257-261.
- W. M. B. Dukes, On the number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004.
- Index entries for sequences related to matroids
A058730
Triangle T(n,k) giving number of nonisomorphic simple matroids of rank k on n labeled points (n >= 2, 2 <= k <= n).
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 9, 11, 4, 1, 1, 23, 49, 22, 5, 1, 1, 68, 617, 217, 40, 6, 1, 1, 383, 185981, 188936, 1092, 66, 7, 1, 1, 5249, 4884573865
Offset: 2
Triangle T(n,k) (with rows n >= 2 and columns k >= 2) begins as follows:
1;
1, 1;
1, 2, 1;
1, 4, 3, 1;
1, 9, 11, 4, 1;
1, 23, 49, 22, 5, 1;
1, 68, 617, 217, 40, 6, 1;
1, 383, 185981, 188936, 1092, 66, 7, 1;
...
From _Petros Hadjicostas_, Oct 09 2019: (Start)
Matsumoto et al. (2012, p. 36) gave an incomplete row n = 10 (starting at k = 2):
1, 5249, 4884573865, *, 4886374072, 9742, 104, 8, 1;
They also gave incomplete rows for n = 11 and n = 12.
(End)
- Henry H. Crapo and Gian-Carlo Rota, On the foundations of combinatorial theory. II. Combinatorial geometries, Studies in Appl. Math. 49 (1970), 109-133. [Annotated scanned copy of pages 126 and 127 only]
- Henry H. Crapo and Gian-Carlo Rota, On the foundations of combinatorial theory. II. Combinatorial geometries, Studies in Appl. Math. 49 (1970), 109-133.
- W. M. B. Dukes, Tables of matroids.
- W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000.
- W. M. B. Dukes, The number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004.
- W. M. B. Dukes, On the number of matroids on a finite set, Séminaire Lotharingien de Combinatoire 51 (2004), Article B51g.
- Dillon Mayhew and Gordon F. Royle, Matroids with nine elements, arXiv:math/0702316 [math.CO], 2007. [See Table 2, p. 9.]
- Dillon Mayhew and Gordon F. Royle, Matroids with nine elements, J. Combin. Theory Ser. B 98(2) (2008), 415-431. [See Table 2, p. 420.]
- Y. Matsumoto, S. Moriyama, H. Imai, and D. Bremmer, Matroid enumeration for incidence geometry, Discrete Comput. Geom. 47 (2012), 17-43.
- Gordon Royle and Dillon Mayhew, 9-element matroids.
- Index entries for sequences related to matroids
Showing 1-3 of 3 results.
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