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A056642 Number of linear spaces on n (labeled) points. 6
1, 1, 2, 6, 32, 353, 8390, 433039, 50166354, 13480967630 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Alternatively, number of linear geometries on n (labeled) points. For the unlabeled case see A001200.

Also a(n) = 1 + number of simple rank-3 matroids on n (labeled) elements; a(n) = number of 2-partitions of a set of size n.

REFERENCES

L. M. Batten and A. Beutelspacher: The theory of finite linear spaces, Cambridge Univ. Press, 1993 (see the Appendix).

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 303, #42.

J. Doyen, Sur le nombre d'espaces lineaires non isomorphes de n points. Bull. Soc. Math. Belg. 19 1967 421-437.

LINKS

Table of n, a(n) for n=1..10.

W. M. B. Dukes, Tables of matroids

W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000.

Index entries for sequences related to matroids

CROSSREFS

Corrected version of A001199. Cf. A002773, A001200, A031436, A058731.

Sequence in context: A005742 A055612 A236691 * A001199 A232469 A034997

Adjacent sequences:  A056639 A056640 A056641 * A056643 A056644 A056645

KEYWORD

nice,more,nonn

AUTHOR

W. M. B. Dukes (dukes(AT)stp.dias.ie), Aug 28 2000

EXTENSIONS

a(9) and a(10) from Gordon Royle, May 29 2006

STATUS

approved

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Last modified November 21 11:01 EST 2018. Contains 317447 sequences. (Running on oeis4.)