A055545 Number of unlabeled matroids on n points.

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

Offset: 0

Author

Eric W. Weisstein

Keywords

• nonn
• nice
• more

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

• 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.

Extensions

a(9) from Gordon Royle, Dec 23 2006

Name clarified by Lorenzo Sauras Altuzarra, Aug 10 2023