A002773
Number of nonisomorphic simple matroids (or geometries) with n points.
Original entry on oeis.org
1, 1, 1, 2, 4, 9, 26, 101, 950, 376467
Offset: 0
- Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, p. 138.
- Knuth, Donald E. "The asymptotic number of geometries." Journal of Combinatorial Theory, Series A 16.3 (1974): 398-400.
- 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).
- N. Bansal, R. Pendavingh, and J. G. van der Pol, On the number of matroids, arXiv:1206.6270v1 [math.CO], 2012.
- Nikhil Bansal, Rudi A. Pendavingh, and Jorn G. van der Pol, On the number of matroids, Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM, 2013; full version in Combinatorica, 35:3 (2015), 253-277.
- J. E. Blackburn, H. H. Crapo, and D. A. Higgs, A catalogue of combinatorial geometries, Math. Comp 27 (1973), 155-166.
- Henry H. Crapo and Gian-Carlo Rota, On the foundations of combinatorial theory. II. Combinatorial geometries, Studies in Appl. Math. 49 (1970), 109-133.
- 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]
- 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.
- Dillon Mayhew and Gordon F. Royle, Matroids with nine elements, J. Combin. Theory Ser. B 98(2) (2008), 415-431.
- M. J. Piff, An upper bound for the number of matroids, J. Combinatorial Theory Ser. B, vol 14 (1973), pp. 241-245.
- Gordon Royle and Dillon Mayhew, 9-element matroids.
- N. J. A. Sloane, Initial terms (* denotes 5 points in general position in 4-space).
- Eric Weisstein's World of Mathematics, Matroid.
- Index entries for sequences related to matroids
A058720
Triangle T(n,k) giving the number of simple matroids of rank k on n labeled points (n >= 2, 2 <= k <= n).
Original entry on oeis.org
1, 1, 1, 1, 5, 1, 1, 31, 16, 1, 1, 352, 337, 42, 1, 1, 8389, 18700, 2570, 99, 1, 1, 433038, 7642631, 907647, 16865, 219, 1
Offset: 2
Triangle T(n,k) (with rows n >= 2 and columns k >= 2) begins as follows:
1;
1, 1;
1, 5, 1;
1, 31, 16, 1;
1, 352, 337, 42, 1;
1, 8389, 18700, 2570, 99, 1;
1, 433038, 7642631, 907647, 16865, 219, 1;
...
- Mohamed Barakat, Reimer Behrends, Christopher Jefferson, Lukas Kühne, and Martin Leuner, On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture, arXiv:1907.01073 [math.CO], 2019.
- 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. [See p. 11.]
- Index entries for sequences related to matroids
A058731
Number of nonisomorphic simple matroids of rank 3 on n unlabeled points.
Original entry on oeis.org
0, 0, 0, 1, 2, 4, 9, 23, 68, 383, 5249, 232928, 28872972
Offset: 0
- 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.
- Crapo, Henry H.; Rota, Gian-Carlo; 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]
- W. M. B. Dukes, Tables of matroids
- W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000.
- Index entries for sequences related to matroids
Equals
A001200 - 1 (see that entry for further information).
A058733
Number of nonisomorphic simple matroids of rank 4 on n labeled points.
Original entry on oeis.org
1, 3, 11, 49, 617, 185981
Offset: 4
- 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.]
- Gordon Royle and Dillon Mayhew, 9-element matroids.
- Index entries for sequences related to matroids
Showing 1-4 of 4 results.
