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A055545 Number of unlabeled matroids on n points. 6
1, 2, 4, 8, 17, 38, 98, 306, 1724, 383172 (list; graph; refs; listen; history; text; internal format)
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
J. G. Oxley, Matroid Theory. Oxford, England: Oxford University Press, 1993. See p. 473.
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
Cf. A002773, A058673 (labeled matroids), A058718.
Row sums of A053534.
Sequence in context: A325921 A049312 A132043 * A241671 A036375 A036376
a(9) from Gordon Royle, Dec 23 2006
Name clarified by Lorenzo Sauras Altuzarra, Aug 10 2023

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Last modified December 8 17:58 EST 2023. Contains 367680 sequences. (Running on oeis4.)