|
Search: id:A056642
|
|
|
| A056642 |
|
Number of linear spaces on n (labeled) points. |
|
+0
7
|
|
| 1, 1, 2, 6, 32, 353, 8390, 433039, 50166354, 13480967630
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
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
|
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.
Adjacent sequences: A056639 A056640 A056641 this_sequence A056643 A056644 A056645
Sequence in context: A123903 A005742 A055612 this_sequence A001199 A034997 A067735
|
|
KEYWORD
|
nice,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
|
|
|
Search completed in 0.002 seconds
|
