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A002773
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Number of nonisomorphic simple matroids (or geometries) with n points.
(Formerly M1197 N0462)
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7
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OFFSET
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0,4
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REFERENCES
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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).
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LINKS
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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.
Eric Weisstein's World of Mathematics, Matroid.
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FORMULA
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Limit_{ n -> oo } (log_2 log_2 a(n))/n = 1. [Knuth]
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
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CROSSREFS
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KEYWORD
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nonn,nice,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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