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A281574
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Number of geometric lattices on n nodes.
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0
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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
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1,8
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COMMENTS
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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
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LINKS
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EXAMPLE
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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)
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CROSSREFS
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Cf. A229202 (semimodular lattices).
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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