A058673 - OEIS

A058673

Number of matroids on n labeled points.

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

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OFFSET

0,2

COMMENTS

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

a(n) <= A014466(n).

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

LINKS

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

EXAMPLE

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}}

CROSSREFS

Row sums of A058669. Closely related to A114491.

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

KEYWORD

nonn,nice,more

AUTHOR

STATUS

approved