A001200 Number of linear geometries on n (unlabeled) points. (Formerly M0726 N0271)

1, 1, 1, 2, 3, 5, 10, 24, 69, 384, 5250, 232929, 28872973

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

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 linéaires non isomorphes de n points. Bull. Soc. Math. Belg. 19 1967 421-437.

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.

Mohamed Barakat, Reimer Behrends, Christopher Jefferson, Lukas Kühne, Martin Leuner, On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture, arXiv:1907.01073 [math.CO], 2019.

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

J. E. Blackburn, H. H. Crapo, and D. A. Higgs, A catalogue of combinatorial geometries, Math. Comp 27 1973 155-166.

J. Doyen, Sur le nombre d'espaces linéaires non isomorphes de n points [Annotated and scanned copy]

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.

Robert Haas, Cographs, arXiv:1905.12627 [math.GM], 2019.

G. Heathcote, Linear spaces on 16 points, J. Combin. Designs, Vol. 1, No. 5 (1993), 359-378.

Kaplan, Nathan; Kimport, Susie; Lawrence, Rachel; Peilen, Luke; Weinreich, Max Counting arcs in projective planes via Glynn’s algorithm. J. Geom. 108, No. 3, 1013-1029 (2017).

Ch. Pietsch, On the classification of linear spaces of order 11, J. Comb. Designs, Vol. 3, No. 3 (1995), 185-193.

Crossrefs

Cf. A000041, A056642, A058731, A001548.

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

Status

approved