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A002773 Number of nonisomorphic simple matroids (or geometries) with n points.
(Formerly M1197 N0462)
7
1, 1, 1, 2, 4, 9, 26, 101, 950, 376467 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, p. 138.

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).

LINKS

Table of n, a(n) for n=0..9.

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.

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

CROSSREFS

Cf. A055545, A056642. Row sums of A058730.

Sequence in context: A087378 A004252 A114957 * A112706 A110138 A148085

Adjacent sequences:  A002770 A002771 A002772 * A002774 A002775 A002776

KEYWORD

nonn,nice,more,changed

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(9) from Gordon Royle, Dec 23 2006

STATUS

approved

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Last modified October 22 18:16 EDT 2019. Contains 328319 sequences. (Running on oeis4.)