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A326866
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Number of connectedness systems on n vertices.
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26
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OFFSET
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0,2
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COMMENTS
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We define a connectedness system (investigated by Vim van Dam in 2002) to be a set of finite nonempty sets (edges) that is closed under taking the union of two overlapping edges.
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LINKS
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FORMULA
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EXAMPLE
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The a(0) = 1 through a(2) = 8 connectedness systems:
{} {} {}
{{1}} {{1}}
{{2}}
{{1,2}}
{{1},{2}}
{{1},{1,2}}
{{2},{1,2}}
{{1},{2},{1,2}}
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MATHEMATICA
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Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], SubsetQ[#, Union@@@Select[Tuples[#, 2], Intersection@@#!={}&]]&]], {n, 0, 3}]
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CROSSREFS
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The case without singletons is A072446.
Binomial transform of A326870 (the covering case).
The BII-numbers of these set-systems are A326872.
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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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