A056642 Number of linear spaces on n (labeled) points.

1, 1, 2, 6, 32, 353, 8390, 433039, 50166354, 13480967630

Offset: 1

Author

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

Keywords

• nice
• more
• nonn

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 linéaires non isomorphes de n points, Bull. Soc. Math. Belg. 19 (1967), 421-437.
• J. A. Thas, Sur le nombre d'espaces linéaires non isomorphes de n points, Bull. Soc. Math. Belg. 21 (1969), 57-66.

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. Dukes, Bounds on the number of generalized partitions and some applications, Australas. J. Combin. 28 (2003), 257-261.
• W. M. B. Dukes, On the number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004.
• Index entries for sequences related to matroids

Crossrefs

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

Extensions

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