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 A317074 Number of antichains of multisets with multiset-join a strongly normal multiset of size n. 5
 1, 1, 3, 13, 148, 7685 (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 strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities. The multiset-join of a multiset system 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) = 13 antichains of multisets:   (111),   (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}]]]; strnorm[n_]:=Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n]; auu[m_]:=Select[stableSets[Union[Rest[Subsets[m]]], submultisetQ], multijoin@@#==m&]; Table[Length[Join@@Table[auu[m], {m, strnorm[n]}]], {n, 5}] CROSSREFS Cf. A048143, A285572, A293993, A293994, A303837, A303838, A304998, A305001. Cf. A317073, A317076, A317078, A317079. Sequence in context: A108554 A287029 A339025 * A230036 A014376 A224990 Adjacent sequences:  A317071 A317072 A317073 * A317075 A317076 A317077 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 20 2018 STATUS approved

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Last modified August 9 21:08 EDT 2022. Contains 356026 sequences. (Running on oeis4.)