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A326901
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Number of set-systems (without {}) on n vertices that are closed under intersection.
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7
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OFFSET
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0,2
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COMMENTS
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A set-system is a finite set of finite nonempty sets, so no two edges of a set-system that is closed under intersection can be disjoint.
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LINKS
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FORMULA
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EXAMPLE
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The a(3) = 32 set-systems:
{} {{1}} {{1}{12}} {{1}{12}{13}} {{1}{12}{13}{123}}
{{2}} {{1}{13}} {{2}{12}{23}} {{2}{12}{23}{123}}
{{3}} {{2}{12}} {{3}{13}{23}} {{3}{13}{23}{123}}
{{12}} {{2}{23}} {{1}{12}{123}}
{{13}} {{3}{13}} {{1}{13}{123}}
{{23}} {{3}{23}} {{2}{12}{123}}
{{123}} {{1}{123}} {{2}{23}{123}}
{{2}{123}} {{3}{13}{123}}
{{3}{123}} {{3}{23}{123}}
{{12}{123}}
{{13}{123}}
{{23}{123}}
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MATHEMATICA
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Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], SubsetQ[#, Intersection@@@Tuples[#, 2]]&]], {n, 0, 3}]
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CROSSREFS
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The case with union instead of intersection is A102896.
The case closed under union and intersection is A326900.
The BII-numbers of these set-systems are A326905.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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