

A281574


Number of geometric lattices on n nodes.


0



1, 1, 0, 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 3, 5, 3, 4, 5, 6, 6, 8, 9, 16, 16, 21, 29, 45, 50, 95, 136, 220, 392, 680, 1270, 2530, 4991
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OFFSET

1,8


COMMENTS

A finite lattice is geometric if it is semimodular and atomistic. Atomistic (or atomic in Stanley's terminology) means that every element is a join of some atoms; or equivalently, that every joinirreducible element is an atom.
a(n) is the number of simple matroids with n flats, up to isomorphism.  Harry Richman, Jul 27 2022


LINKS



EXAMPLE

The only two geometric lattices on 8 nodes:
7
/  \
/  \ _ _ 7_ _
3 5 6 / / /\ \ \
\/ \/ / / / \ \ \
/\ /\ 1 2 3 4 5 6
1 2 4 \ \ \ / / /
\  / \_\_\/_/_/
\/ 0
0
(End)


CROSSREFS

Cf. A229202 (semimodular lattices).


KEYWORD

nonn,more,hard


AUTHOR



EXTENSIONS



STATUS

approved



