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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.
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).
LINKS
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.
Eric Weisstein's World of Mathematics, Matroid.
FORMULA
Limit_{ n -> oo } (log_2 log_2 a(n))/n = 1. [Knuth]
2^n/n^(3/2) << log a(n) << 2^n/n, proved by Knuth and Piff respectively. - Charles R Greathouse IV, Mar 20 2021
Bansal, Pendavingh, & van der Pol prove an upper bound almost matching the lower bound above: log a(n) <= 2*sqrt(2/Pi)*2^n/n^(3/2)*(1 + o(1)). - Charles R Greathouse IV, Mar 20 2021
CROSSREFS
Cf. A055545, A056642. Row sums of A058730.
Sequence in context: A087378 A004252 A114957 * A112706 A359502 A110138
KEYWORD
nonn,nice,more
AUTHOR
EXTENSIONS
a(9) from Gordon Royle, Dec 23 2006
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)