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A055545 Number of matroids on n points. 6
1, 2, 4, 8, 17, 38, 98, 306, 1724, 383172 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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. - Jonathan Vos Post, Apr 25 2010

Abstract from 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." - Jonathan Vos Post, Jun 15 2011

REFERENCES

Oxley, J. G., Matroid Theory. Oxford, England: Oxford University Press, 1993. See p. 473.

LINKS

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

Jayant Apte and J. M. Walsh, Constrained Linear Representability of Polymatroids and Algorithms for Computing Achievability Proofs in Network Coding, arXiv preprint arXiv:1605.04598 [cs.IT], 2016-2017.

Jesus DeLoera, Yvonne Kemper, and Steven Klee, h-vectors of small matroid complexes, arXiv:1106.2576 [math.CO], 2011.

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.

Eric Weisstein's World of Mathematics, Matroid.

Eric Weisstein's World of Mathematics, Graph Vertex.

D. J. A. Welsh, A bound for the number of matroids, J. Combinat. Theory, Ser. A, 6 (1969), 313-316. - From N. J. A. Sloane, May 06 2012

Index entries for sequences related to matroids

CROSSREFS

Cf. A002773, A058718.

Row sums of A053534.

Sequence in context: A325921 A049312 A132043 * A241671 A036375 A036376

Adjacent sequences:  A055542 A055543 A055544 * A055546 A055547 A055548

KEYWORD

nonn,nice,more

AUTHOR

Eric W. Weisstein

EXTENSIONS

a(9) from Gordon Royle, Dec 23 2006

STATUS

approved

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Last modified June 2 14:10 EDT 2020. Contains 334781 sequences. (Running on oeis4.)