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 A317076 Number of connected antichains of multisets with multiset-join a strongly normal multiset of size n. 5
 1, 1, 2, 8, 110, 7047 (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) = 8 connected antichains of multisets: (111), (112), (11)(12), (123), (13)(23), (12)(23), (12)(13), (12)(13)(23). 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}]]]; csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Union[Append[Delete[s, List/@c[[1]]], multijoin@@s[[c[[1]]]]]]]]]; strnorm[n_]:=Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n]; cuu[m_]:=Select[stableSets[Union[Rest[Subsets[m]]], submultisetQ], And[multijoin@@#==m, Length[csm[#]]==1]&]; Table[Length[Join@@Table[cuu[m], {m, strnorm[n]}]], {n, 5}] CROSSREFS Cf. A048143, A255906, A286520, A303837, A303838, A304716, A305001, A305078. Cf. A317074, A317075, A317078, A317080. Sequence in context: A132523 A012554 A012665 * A211938 A331405 A005787 Adjacent sequences: A317073 A317074 A317075 * A317077 A317078 A317079 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 20 2018 STATUS approved

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Last modified December 2 05:20 EST 2022. Contains 358485 sequences. (Running on oeis4.)