cp's OEIS Frontend

A322011 Number of distinct chromatic symmetric functions of spanning hypergraphs (or antichain covers) on n vertices.

%I A322011 #5 Nov 24 2018 08:15:42
%S A322011 1,2,5,19,121
%N A322011 Number of distinct chromatic symmetric functions of spanning hypergraphs (or antichain covers) on n vertices.
%C A322011 A stable partition of a graph is a set partition of the vertices where no edge has both ends in the same block. The chromatic symmetric function is given by X_G = Sum_p m(t(p)) where the sum is over all stable partitions of G, t(p) is the integer partition whose parts are the block-sizes of p, and m is the augmented monomial symmetric function basis (see A321895).
%e A322011 The a(3) = 5 chromatic symmetric functions:
%e A322011                   m(111)
%e A322011           m(21) + m(111)
%e A322011          2m(21) + m(111)
%e A322011          3m(21) + m(111)
%e A322011   m(3) + 3m(21) + m(111)
%t A322011 chromSF[g_]:=Sum[m[Sort[Length/@stn,Greater]],{stn,spsu[Select[Subsets[Union@@g],Select[DeleteCases[g,{_}],Function[ed,Complement[ed,#]=={}]]=={}&],Union@@g]}];
%t A322011 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]]]];
%t A322011 hyps[n_]:=Select[stableSets[Rest[Subsets[Range[n]]],SubsetQ],Union@@#==Range[n]&];
%t A322011 Table[Length[Union[chromSF/@hyps[n]]],{n,5}]
%Y A322011 Cf. A000569, A006125, A229048, A240936, A245883, A277203, A030019, A321750, A321895, A321911, A321994.
%K A322011 nonn,more
%O A322011 1,2
%A A322011 _Gus Wiseman_, Nov 24 2018