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A058673 Number of matroids on n labeled points. 6
1, 2, 5, 16, 68, 406, 3807, 75164, 10607540 (list; graph; refs; listen; history; text; internal format)
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, 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
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.
Sequence in context: A002631 A107948 A220840 * A296675 A059295 A259408
KEYWORD
nonn,nice,more
AUTHOR
N. J. A. Sloane, Dec 30 2000
STATUS
approved

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Last modified March 1 15:55 EST 2024. Contains 370442 sequences. (Running on oeis4.)