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A302250
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The number of antichains in the lattice of set partitions of an n-element set.
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5
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OFFSET
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1,1
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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 includes the empty antichain consisting of no set partitions.
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LINKS
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EXAMPLE
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For n = 3 the a(3) = 10 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() for n in range(4)]
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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