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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 (list; graph; refs; listen; history; text; internal format)
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 join-irreducible element is an atom.
a(n) is the number of simple matroids with n flats, up to isomorphism. - Harry Richman, Jul 27 2022
LINKS
J. Kohonen, Generating modular lattices up to 30 elements, arXiv:1708.03750 [math.CO], 2017-2018.
M. Malandro, The unlabeled lattices on <=15 nodes, (listing of lattices; geometric lattices are a subset of these).
EXAMPLE
From Peter Luschny, Jan 24 2017: (Start)
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).
Sequence in context: A086289 A077807 A280152 * A191784 A261350 A259177
KEYWORD
nonn,more,hard
AUTHOR
Jukka Kohonen, Jan 24 2017
EXTENSIONS
a(16)-a(34) from Kohonen (2017), by Jukka Kohonen, Aug 15 2017
a(35)-a(37) by Jukka Kohonen, Jul 07 2020
STATUS
approved

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Last modified June 19 17:11 EDT 2024. Contains 373504 sequences. (Running on oeis4.)