

A055545


Number of matroids on n points.


6




OFFSET

0,2


COMMENTS

This is the total number of pairwise nonisomorphic (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 hvector of a matroid simplicial complex is a pure Osequence. 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], 20162017.
Jesus DeLoera, Yvonne Kemper, and Steven Klee, hvectors 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), 415431.
Gordon Royle and Dillon Mayhew, 9element 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), 313316.  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



