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A326943
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Number of T_0 sets of subsets of {1..n} that cover all n vertices and are closed under intersection.
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11
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OFFSET
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0,1
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COMMENTS
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The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. The T_0 condition means that the dual is strict (no repeated edges).
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LINKS
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FORMULA
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Inverse binomial transform of A326945.
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EXAMPLE
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The a(0) = 2 through a(3) = 6 sets of subsets:
{} {{1}} {{1},{1,2}}
{{}} {{},{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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dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}];
Table[Length[Select[Subsets[Subsets[Range[n]]], Union@@#==Range[n]&&UnsameQ@@dual[#]&&SubsetQ[#, Intersection@@@Tuples[#, 2]]&]], {n, 0, 3}]
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CROSSREFS
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The case without empty edges is A309615.
The non-covering version is A326945.
The version not closed under intersection is A326939.
Cf. A003180, A003181, A003465, A059052, A059201, A245567, A316978, A319564, A319637, A326940, A326941, A326942, A326947.
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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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