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 A317073 Number of antichains of multisets with multiset-join a normal multiset of size n. 9
 1, 1, 3, 16, 198, 9890 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS An antichain of multisets is a finite set of finite nonempty multisets, none of which is a submultiset of any other. A multiset is normal if it spans an initial interval of positive integers. The multiset-join of a set of multisets has the same vertices with multiplicities equal to the maxima of the multiplicities in the edges. LINKS Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, Journal of Integer Sequences, Vol. 7 (2004). EXAMPLE The a(3) = 16 antichains of multisets:   (111),   (122), (12)(22), (1)(22),   (112), (11)(12), (2)(11),   (123), (13)(23), (12)(23), (12)(13), (12)(13)(23), (3)(12), (2)(13), (1)(23), (1)(2)(3). 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]]]]; multijoin[mss__]:=Join@@Table[Table[x, {Max[Count[#, x]&/@{mss}]}], {x, Union[mss]}] submultisetQ[M_, N_]:=Or[Length[M]==0, MatchQ[{Sort[List@@M], Sort[List@@N]}, {{x_, Z___}, {___, x_, W___}}/; submultisetQ[{Z}, {W}]]]; allnorm[n_]:=Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1]; auu[m_]:=Select[stableSets[Union[Rest[Subsets[m]]], submultisetQ], multijoin@@#==m&]; Table[Length[Join@@Table[auu[m], {m, allnorm[n]}]], {n, 5}] CROSSREFS Cf. A048143, A255906, A285572, A303837, A303838, A304998, A305001. Cf. A317074, A317075, A317077, A317079. Sequence in context: A174137 A166860 A196562 * A272658 A326903 A113597 Adjacent sequences:  A317070 A317071 A317072 * A317074 A317075 A317076 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 20 2018 STATUS approved

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Last modified January 22 04:27 EST 2020. Contains 331133 sequences. (Running on oeis4.)