A058673 Number of matroids on n labeled points.

1, 2, 5, 16, 68, 406, 3807, 75164, 10607540

Offset: 0

Author

N. J. A. Sloane, Dec 30 2000

Keywords

• nonn
• nice
• more

Comments

From Lorenzo Sauras Altuzarra, Aug 10 2023: (Start)

a(n) <= A014466(n).

a(n) <= A306020(n). (End)

Examples

			The 16 possible sets E such that ({1, 2, 3}, E) is a matroid:
  {{}}
  {{}, {1}}
  {{}, {2}}
  {{}, {3}}
  {{}, {1}, {2}}
  {{}, {1}, {3}}
  {{}, {2}, {3}}
  {{}, {1}, {2}, {3}}
  {{}, {1}, {2}, {1, 2}}
  {{}, {1}, {3}, {1, 3}}
  {{}, {2}, {3}, {2, 3}}
  {{}, {1}, {2}, {3}, {1, 2}, {1, 3}}
  {{}, {1}, {2}, {3}, {1, 2}, {2, 3}}
  {{}, {1}, {2}, {3}, {1, 3}, {2, 3}}
  {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}}
  {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
		

Links

• W. M. B. Dukes, Tables of matroids.
• W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000.
• 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
• Index entries for sequences related to matroids

Crossrefs

Row sums of A058669. Closely related to A114491.

Cf. A014466 (abstract simplicial complexes), A055545 (unlabeled matroids), A306020.