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A367902
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Number of sets of nonempty subsets of {1..n} satisfying a strict version of the axiom of choice.
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64
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OFFSET
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0,2
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COMMENTS
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The axiom of choice says that, given any set of nonempty sets Y, it is possible to choose a set containing an element from each. The strict version requires this set to have the same cardinality as Y, meaning no element is chosen more than once.
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LINKS
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FORMULA
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EXAMPLE
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The a(2) = 7 set-systems:
{}
{{1}}
{{2}}
{{1,2}}
{{1},{2}}
{{1},{1,2}}
{{2},{1,2}}
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MATHEMATICA
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Table[Length[Select[Subsets[Subsets[Range[n]]], Select[Tuples[#], UnsameQ@@#&]!={}&]], {n, 0, 3}]
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CROSSREFS
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The version without singletons is A367770.
The complement allowing empty edges is A367901.
These set-systems have ranks A367906.
A059201 counts covering T_0 set-systems.
A323818 counts covering connected set-systems.
A326031 gives weight of the set-system with BII-number n.
Cf. A007716, A083323, A092918, A102896, A283877, A306445, A355739, A355740, A367862, A367905, A370636.
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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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