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A327011
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Number of unlabeled sets of subsets covering n vertices where every vertex is the unique common element of some subset of the edges, also called unlabeled covering T_1 sets of subsets.
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1
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OFFSET
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0,1
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COMMENTS
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Alternatively, these are unlabeled sets of subsets covering n vertices whose dual is a (strict) antichain. The dual of a set of subsets has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. An antichain is a set of subsets where no edge is a subset of any other.
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LINKS
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FORMULA
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EXAMPLE
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Non-isomorphic representatives of the a(0) = 1 through a(2) = 4 sets of subsets:
{} {{1}} {{1},{2}}
{{}} {{},{1}} {{},{1},{2}}
{{1},{2},{1,2}}
{{},{1},{2},{1,2}}
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CROSSREFS
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Unlabeled covering sets of subsets are A003181.
The same with T_0 instead of T_1 is A326942.
The non-covering version is A326951 (partial sums).
The case without empty edges is A326974.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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