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A001200 Number of linear geometries on n (unlabeled) points.
(Formerly M0726 N0271)
7
1, 1, 1, 2, 3, 5, 10, 24, 69, 384, 5250, 232929, 28872973 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

For the labeled case see A056642.

Also a(n) = 1 + number of non-isomorphic simple rank-3 matroids on n elements (see A058731); a(n) = number of non-isomorphic 2-partitions of a set of size n. For 1-partitions see A000041.

REFERENCES

Blackburn et al., A catalogue of combinatorial geometries, Math. Comp 27 1973 155-166.

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

CRC Handbook of Combinatorial Designs, 1996, pp. 216, 697.

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

D. G. Glynn, Rings of geometries II, J. Combin. Theory, A 49 (1988), 26-66.

D. G. Glynn, A geometrical isomorphism algorithm, Bull. ICA 7 (1993), 36-38.

G. Heathcote, Linear spaces on 16 points, J. Combin. Designs, 1 (1993), 359-378.

Ch. Pietsch, On the classification of linear spaces of order 11, J. Comb. Designs, 3 (1995), 185-193.

P. Robillard, On the weighted finite linear spaces. Bull. Soc. Math. Belg. 22 (1970), 227-241.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..12.

A. Betten and D. Betten, Linear spaces with at most 12 points, J. Combinatorial Designs, Volume 7, 1999, pp. 119 - 145.

CROSSREFS

Cf. A000041, A056642, A058731.

Sequence in context: A101163 A155587 A125658 * A050837 A107578 A011827

Adjacent sequences:  A001197 A001198 A001199 * A001201 A001202 A001203

KEYWORD

nonn,hard,more,nice

AUTHOR

N. J. A. Sloane, D.Glynn(AT)math.canterbury.ac.nz

EXTENSIONS

Dead link to Betten paper replaced with CiteSeer entry (which has full text as cached PDF) Robert Munafo, Dec 13 2009

STATUS

approved

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Last modified October 31 17:56 EDT 2014. Contains 248868 sequences.