|
|
EXAMPLE
|
The a(4) = 23 intersecting antichains with empty intersection:
{{1,2},{1,3},{2,3,4}}
{{1,2},{1,4},{2,3,4}}
{{1,2},{2,3},{1,3,4}}
{{1,2},{2,4},{1,3,4}}
{{1,3},{1,4},{2,3,4}}
{{1,3},{2,3},{1,2,4}}
{{1,3},{3,4},{1,2,4}}
{{1,4},{2,4},{1,2,3}}
{{1,4},{3,4},{1,2,3}}
{{2,3},{2,4},{1,3,4}}
{{2,3},{3,4},{1,2,4}}
{{2,4},{3,4},{1,2,3}}
{{1,2},{1,3,4},{2,3,4}}
{{1,3},{1,2,4},{2,3,4}}
{{1,4},{1,2,3},{2,3,4}}
{{2,3},{1,2,4},{1,3,4}}
{{2,4},{1,2,3},{1,3,4}}
{{3,4},{1,2,3},{1,2,4}}
{{1,2},{1,3},{1,4},{2,3,4}}
{{1,2},{2,3},{2,4},{1,3,4}}
{{1,3},{2,3},{3,4},{1,2,4}}
{{1,4},{2,4},{3,4},{1,2,3}}
{{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
|
|
|
MATHEMATICA
|
stableSets[u_, Q_]:=If[Length[u]==0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r==w||Q[r, w]||Q[w, r]], Q]]]];
Table[Length[Select[stableSets[Subsets[Range[n], {1, n}], Or[Intersection[#1, #2]=={}, SubsetQ[#1, #2]]&], And[Union@@#==Range[n], #=={}||Intersection@@#=={}]&]], {n, 0, 4}]
|
