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

1, 2, 5, 19, 121

Offset

1,2

Comments

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).

Links

Table of n, a(n) for n=1..5.

Example

The a(3) = 5 chromatic symmetric functions:
                  m(111)
          m(21) + m(111)
         2m(21) + m(111)
         3m(21) + m(111)
  m(3) + 3m(21) + m(111)

Mathematica

chromSF[g_]:=Sum[m[Sort[Length/@stn, Greater]], {stn, spsu[Select[Subsets[Union@@g], Select[DeleteCases[g, {_}], Function[ed, Complement[ed, #]=={}]]=={}&], Union@@g]}];
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]]]];
hyps[n_]:=Select[stableSets[Rest[Subsets[Range[n]]], SubsetQ], Union@@#==Range[n]&];
Table[Length[Union[chromSF/@hyps[n]]], {n, 5}]

Crossrefs

Cf. A000569, A006125, A229048, A240936, A245883, A277203, A030019, A321750, A321895, A321911, A321994.

Sequence in context: A113346 A198945 A324168 * A355519 A342435 A341036

Adjacent sequences: A322008 A322009 A322010 * A322012 A322013 A322014

Keyword

nonn,more

Author

Gus Wiseman, Nov 24 2018

Status

approved