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
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
CROSSREFS
KEYWORD
nonn,nice,more
AUTHOR
EXTENSIONS
a(9) from Gordon Royle, Dec 23 2006
Name clarified by Lorenzo Sauras Altuzarra, Aug 10 2023
STATUS
approved