OFFSET
0,2
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
Wikipedia, Axiom of choice.
FORMULA
a(n) = A370636(2^n-1). - Alois P. Heinz, Mar 09 2024
EXAMPLE
The a(2) = 7 set-systems:
{}
{{1}}
{{2}}
{{1,2}}
{{1},{2}}
{{1},{1,2}}
{{2},{1,2}}
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n]]], Select[Tuples[#], UnsameQ@@#&]!={}&]], {n, 0, 3}]
CROSSREFS
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.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Dec 05 2023
EXTENSIONS
a(6)-a(8) from Christian Sievers, Jul 25 2024
STATUS
approved