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 A317080 Number of unlabeled connected antichains of multisets with multiset-join a multiset of size n. 5
 1, 1, 2, 6, 34, 392 (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. 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 Non-isomorphic representatives of the a(3) = 6 connected antichains of multisets:   (111),   (122), (12)(22),   (123), (13)(23), (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]; sysnorm[m_]:=First[Sort[sysnorm[m, 1]]]; sysnorm[m_, aft_]:=If[Length[Union@@m]<=aft, {m}, With[{mx=Table[Count[m, i, {2}], {i, Select[Union@@m, #>=aft&]}]}, Union@@(sysnorm[#, aft+1]&/@Union[Table[Map[Sort, m/.{par+aft-1->aft, aft->par+aft-1}, {0, 1}], {par, First/@Position[mx, Max[mx]]}]])]]; cuu[m_]:=Select[stableSets[Union[Rest[Subsets[m]]], submultisetQ], And[multijoin@@#==m, Length[csm[#]]==1]&]; Table[Length[Union[sysnorm/@Join@@Table[cuu[m], {m, strnorm[n]}]]], {n, 5}] CROSSREFS Cf. A007716, A007718, A048143, A261006, A286520, A293993, A293994, A304716, A304998. Cf. A317073, A317074, A317075, A317076, A317077, A317078, A317079. Sequence in context: A191742 A181082 A118186 * A075272 A224913 A327038 Adjacent sequences:  A317077 A317078 A317079 * A317081 A317082 A317083 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 20 2018 STATUS approved

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Last modified February 29 05:25 EST 2020. Contains 332353 sequences. (Running on oeis4.)