A342132 - OEIS

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A342132

Number of unlabeled vertically indecomposable modular lattices on n nodes.

1, 1, 0, 1, 1, 2, 3, 7, 12, 28, 54, 127, 266, 614, 1356, 3134, 7091, 16482, 37929, 88622, 206295, 484445, 1136897, 2682451, 6333249, 15005945, 35595805, 84649515, 201560350, 480845007, 1148537092, 2747477575, 6579923491, 15777658535, 37871501929

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OFFSET

1,6

COMMENTS

A lattice is vertically decomposable if it has an element that is comparable to all elements and is neither the bottom nor the top element. Otherwise the lattice is vertically indecomposable.

LINKS

Table of n, a(n) for n=1..35.

P. Jipsen and N. Lawless, Generating all finite modular lattices of a given size, Algebra universalis, 74 (2015), 253-264.

J. Kohonen, Generating modular lattices of up to 30 elements, Order, 36 (2019), 423-435.

J. Kohonen, Cartesian lattice counting by the vertical 2-sum, arXiv:2007.03232 [math.CO] preprint (2020).

EXAMPLE

a(7)=3: These are the three lattices.

o o __o__

/ \ /|\ / /|\ \

o o o o o o o o o o

/|\ / / \|/ \_\|/_/

o o o o o o