OFFSET
0,3
LINKS
Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, Journal of Integer Sequences, Vol. 7 (2004).
EXAMPLE
The a(1) = 1 through a(5) = 17 antichains:
{{1}} {{2}} {{3}} {{4}} {{5}}
{{1,1}} {{1,2}} {{1,3}} {{1,4}}
{{1},{1}} {{1,1,1}} {{2,2}} {{2,3}}
{{1},{2}} {{1,1,2}} {{1,1,3}}
{{1},{1},{1}} {{1},{3}} {{1,2,2}}
{{2},{2}} {{1},{4}}
{{1,1,1,1}} {{2},{3}}
{{2},{1,1}} {{1,1,1,2}}
{{1,1},{1,1}} {{1},{2,2}}
{{1},{1},{2}} {{3},{1,1}}
{{1},{1},{1},{1}} {{1,1,1,1,1}}
{{1,1},{1,2}}
{{1},{1},{3}}
{{1},{2},{2}}
{{2},{1,1,1}}
{{1},{1},{1},{2}}
{{1},{1},{1},{1},{1}}
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
submultisetQ[M_, N_]:=Or[Length[M]==0, MatchQ[{Sort[List@@M], Sort[List@@N]}, {{x_, Z___}, {___, x_, W___}}/; submultisetQ[{Z}, {W}]]];
antiQ[s_]:=Select[Tuples[s, 2], And[UnsameQ@@#, submultisetQ@@#]&]=={};
Table[Length[Select[Join@@mps/@IntegerPartitions[n], antiQ]], {n, 8}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Oct 11 2018
STATUS
approved