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A302251
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The number of nonempty antichains in the lattice of set partitions.
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1
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OFFSET
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1,2
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COMMENTS
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Computing terms in this sequence is analogous to Dedekind's problem which asks for the number of antichains in the Boolean algebra.
This count excludes the empty antichain consisting of no set partitions.
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LINKS
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Table of n, a(n) for n=1..5.
Sebastian Bozlee, Bob Kuo, and Adrian Neff, A classification of modular compactifications of the space of pointed elliptic curves by Gorenstein curves, arXiv:2105.10582 [math.AG], 2021.
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EXAMPLE
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For n = 3 the a(3) = 9 nonempty antichains are:
{1/2/3}
{1/23}
{12/3}
{13/2}
{1/23, 12/3}
{1/23, 13/2}
{12/3, 13/2}
{1/23, 12/3, 13/2}
{123}
Here we have used the usual shorthand notation for set partitions where 1/23 denotes {{1}, {2,3}}.
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PROG
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(Sage)
[Posets.SetPartitions(n).antichains().cardinality() - 1 for n in range(4)]
# minus removes the empty antichain
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CROSSREFS
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Equals A302250 - 1, Cf. A000372, A007153, A003182, A014466.
Sequence in context: A005271 A258668 A012938 * A013093 A013169 A012991
Adjacent sequences: A302248 A302249 A302250 * A302252 A302253 A302254
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KEYWORD
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nonn,hard,more
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AUTHOR
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John Machacek, Apr 04 2018
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STATUS
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approved
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