OFFSET
0,4
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
EXAMPLE
The a(3) = 3 set-systems:
{{1},{2},{1,2}}
{{1},{3},{1,3}}
{{2},{3},{2,3}}
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {1, 2}], {n}], Length[Select[Tuples[#], UnsameQ@@#&]]==0&]], {n, 0, 5}]
CROSSREFS
The complement appears to be A333331.
For covering pairs we have A367868.
The covering case is A368730.
The unlabeled version is A368835.
A000085 counts set partitions into singletons or pairs.
A100861 counts set partitions into singletons or pairs by number of pairs.
A111924 counts set partitions into singletons or pairs by length.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 04 2024
EXTENSIONS
Terms a(7) and beyond from Andrew Howroyd, Jan 10 2024
STATUS
approved