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A320331 Number of strict T_0 multiset partitions of integer partitions of n. 7
1, 1, 2, 4, 8, 17, 30, 61, 110, 207, 381, 711, 1250 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. The T_0 condition means the dual is strict.
LINKS
EXAMPLE
The a(1) = 1 through a(5) = 17 multiset partitions:
{{1}} {{2}} {{3}} {{4}} {{5}}
{{1,1}} {{1,1,1}} {{2,2}} {{1,1,3}}
{{1},{2}} {{1,1,2}} {{1,2,2}}
{{1},{1,1}} {{1},{3}} {{1},{4}}
{{1,1,1,1}} {{2},{3}}
{{1},{1,2}} {{1,1,1,2}}
{{2},{1,1}} {{1},{1,3}}
{{1},{1,1,1}} {{1},{2,2}}
{{2},{1,2}}
{{3},{1,1}}
{{1,1,1,1,1}}
{{1},{1,1,2}}
{{1,1},{1,2}}
{{2},{1,1,1}}
{{1},{1,1,1,1}}
{{1,1},{1,1,1}}
{{1},{2},{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]]]];
dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}];
Table[Length[Select[Join@@mps/@IntegerPartitions[n], And[UnsameQ@@#, UnsameQ@@dual[#]]&]], {n, 8}]
CROSSREFS
Sequence in context: A342773 A080281 A172446 * A289322 A349842 A049962
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Oct 11 2018
STATUS
approved

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Last modified May 19 12:47 EDT 2024. Contains 372692 sequences. (Running on oeis4.)