OFFSET
0,3
COMMENTS
The dual of a set-system has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. The T_0 condition means that the dual is strict (no repeated edges).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..11
FORMULA
Logarithmic transform of A059201.
EXAMPLE
The a(3) = 86 set-systems:
{12}{13} {1}{2}{13}{123} {1}{2}{3}{13}{23}
{12}{23} {1}{2}{23}{123} {1}{2}{3}{13}{123}
{13}{23} {1}{3}{12}{13} {1}{2}{3}{23}{123}
{1}{2}{123} {1}{3}{12}{23} {1}{2}{12}{13}{23}
{1}{3}{123} {1}{3}{12}{123} {1}{2}{12}{13}{123}
{1}{12}{13} {1}{3}{13}{23} {1}{2}{12}{23}{123}
{1}{12}{23} {1}{3}{13}{123} {1}{2}{13}{23}{123}
{1}{12}{123} {1}{3}{23}{123} {1}{3}{12}{13}{23}
{1}{13}{23} {1}{12}{13}{23} {1}{3}{12}{13}{123}
{1}{13}{123} {1}{12}{13}{123} {1}{3}{12}{23}{123}
{2}{3}{123} {1}{12}{23}{123} {1}{3}{13}{23}{123}
{2}{12}{13} {1}{13}{23}{123} {1}{12}{13}{23}{123}
{2}{12}{23} {2}{3}{12}{13} {2}{3}{12}{13}{23}
{2}{12}{123} {2}{3}{12}{23} {2}{3}{12}{13}{123}
{2}{13}{23} {2}{3}{12}{123} {2}{3}{12}{23}{123}
{2}{23}{123} {2}{3}{13}{23} {2}{3}{13}{23}{123}
{3}{12}{13} {2}{3}{13}{123} {2}{12}{13}{23}{123}
{3}{12}{23} {2}{3}{23}{123} {3}{12}{13}{23}{123}
{3}{13}{23} {2}{12}{13}{23} {1}{2}{3}{12}{13}{23}
{3}{13}{123} {2}{12}{13}{123} {1}{2}{3}{12}{13}{123}
{3}{23}{123} {2}{12}{23}{123} {1}{2}{3}{12}{23}{123}
{12}{13}{23} {2}{13}{23}{123} {1}{2}{3}{13}{23}{123}
{12}{13}{123} {3}{12}{13}{23} {1}{2}{12}{13}{23}{123}
{12}{23}{123} {3}{12}{13}{123} {1}{3}{12}{13}{23}{123}
{13}{23}{123} {3}{12}{23}{123} {2}{3}{12}{13}{23}{123}
{1}{2}{3}{123} {3}{13}{23}{123} {1}{2}{3}{12}{13}{23}{123}
{1}{2}{12}{13} {12}{13}{23}{123}
{1}{2}{12}{23} {1}{2}{3}{12}{13}
{1}{2}{12}{123} {1}{2}{3}{12}{23}
{1}{2}{13}{23} {1}{2}{3}{12}{123}
MATHEMATICA
dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}];
csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];
Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], Union@@#==Range[n]&&Length[csm[#]]<=1&&UnsameQ@@dual[#]&]], {n, 0, 3}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 08 2019
STATUS
approved