A055545 Number of unlabeled matroids on n points.

1, 2, 4, 8, 17, 38, 98, 306, 1724, 383172

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. - Jonathan Vos Post, Apr 25 2010

References

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

Links

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

Dragan M. Acketa, On the enumeration of matroids of rank-2, Zbornik radova Prirodnomatematickog fakulteta-Univerzitet u Novom Sadu 8 (1978): 83-90. - N. J. A. Sloane, Dec 04 2022

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.

S. C. Locke, Matroids

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, A058673 (labeled matroids), A058718.

Row sums of A053534.

Sequence in context: A325921 A049312 A132043 * A241671 A368095 A036375

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

Name clarified by Lorenzo Sauras Altuzarra, Aug 10 2023

Status

approved