A229202 -id:A229202 - cp's OEIS frontend

A278691 Number of graded lattices on n nodes.

1, 1, 1, 2, 4, 9, 22, 60, 176, 565, 1980, 7528, 30843, 135248, 630004, 3097780, 15991395, 86267557, 484446620, 2822677523, 17017165987

Offset: 1

Jukka Kohonen, Nov 26 2016

A finite lattice is graded if, for any element, all paths from the bottom to that element have the same length.

J. Heitzig and J. Reinhold, Counting finite lattices, Algebra Universalis, 48 (2002), 43-53.
J. Kohonen, Generating modular lattices up to 30 elements, arXiv:1708.03750 [math.CO] preprint (2017).
M. Malandro, The unlabeled lattices on <=15 nodes, (listing of lattices; graded lattices are a subset of these).

Cf. A006966 (lattices), A229202 (semimodular lattices).

a(16)-a(21) from Kohonen (2017), by Jukka Kohonen, Aug 15 2017

A281574 Number of geometric lattices on n nodes.

Original entry on oeis.org

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

Offset: 1

Jukka Kohonen, Jan 24 2017

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

			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)

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).
Wikipedia, Geometric lattice

Cf. A229202 (semimodular lattices).

a(16)-a(34) from Kohonen (2017), by Jukka Kohonen, Aug 15 2017

a(35)-a(37) by Jukka Kohonen, Jul 07 2020

cp's OEIS Frontend

A278691 Number of graded lattices on n nodes.

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