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A055545
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Number of matroids on n points.
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4
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OFFSET
| 0,2
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COMMENTS
| This is the total number of pairwise non-isomorphic (i.e. "unlabeled") matroids on n points, with no restrictions on loops, parallel elements etc.
Partial sums of A058718. Partial sums of number of nonisomorphic loopless matroids on n unlabeled points. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 25 2010]
Abstract DeLoera et al: "Stanley conjectured in 1977 that the h-vector of a matroid simplicial complex is a pure O-sequence. We give simple constructive proofs that the conjecture is true for matroids of rank less than or equal to 3, and corank 2. We used computers [Dillon Mayhew and Gordon Royle constructed a computer database of all 385,369 matroids on at most nine elements] to verify that Stanley’s conjecture holds for all matroids on at most nine elements." [From Jonathan Vos Post, Jun 15 2011]
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REFERENCES
| Oxley, J. G., Matroid Theory. Oxford, England: Oxford University Press, 1993.
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LINKS
| Gordon Royle and Dillon Mayhew, 9-element matroids
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to matroids
Jesus DeLoera, Yvonne Kemper, Steven Klee, h-vectors of small matroid complexes, arXiv:1106.2576 [math.CO], June 13, 2011.
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CROSSREFS
| Cf. A002773.
Cf. A058718. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 25 2010]
Sequence in context: A118928 A049312 A132043 * A036375 A036376 A000598
Adjacent sequences: A055542 A055543 A055544 * A055546 A055547 A055548
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KEYWORD
| nonn,nice
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| a(9) from Gordon Royle, Dec 23 2006
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