OFFSET
0,5
COMMENTS
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.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
Eric Weisstein's World of Mathematics, Graph Loop.
ProofWiki, Definition:Loop-Graph
FORMULA
EXAMPLE
The a(4) = 6 set-systems:
{{1},{2},{1,2},{3,4}}
{{1},{3},{1,3},{2,4}}
{{1},{4},{1,4},{2,3}}
{{2},{3},{1,4},{2,3}}
{{2},{4},{1,3},{2,4}}
{{3},{4},{1,2},{3,4}}
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {1, 2}], {n}], Union@@#==Range[n] && Length[Select[Tuples[#], UnsameQ@@#&]]==0&]], {n, 0, 5}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 04 2024
EXTENSIONS
Terms a(7) and beyond from Andrew Howroyd, Jan 10 2024
STATUS
approved