OFFSET
1,18
COMMENTS
A finitary set is transitive if every element is also a subset. A set system is maximal if the union is also a member.
LINKS
EXAMPLE
The a(23)=3 maximal transitive finitary sets are:
(()(())(()(()))((())(()(())))(()(())(()(())))),
(()(())((()))(((())))(()((())))(()(())((())))),
(()(())((()))(()(()))(()((())))(()(())((())))).
MATHEMATICA
maxtransfins[n_]:=If[n===1, {}, Select[Union@@FixedPointList[Complement[Union@@Function[fin, Cases[Complement[Subsets[fin], fin], sub_:>With[{nov=Sort[Append[fin, sub]]}, nov/; Count[Union[nov, {Union@@nov}], _List, {0, Infinity}]<=n]]]/@#, #]&, {{}}], And[Count[#, _List, {0, Infinity}]===n, MemberQ[#, Union@@#]]&]];
Table[Length[maxtransfins[n]], {n, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 21 2016
STATUS
approved