A322441 Number of pairs of set partitions of {1,...,n} where no block of one is a subset or equal to any block of the other.

1, 0, 0, 0, 6, 60, 630, 9660, 192906

Offset: 0

Author

Gus Wiseman, Dec 08 2018

Keywords

• nonn
• more

Comments

For any pair (X,Y) meeting the requirement, so does the pair (Y,X) which must be distinct from (X,Y), except for X = Y = {} when n = 0. Therefore all a(n) are even for n > 0. - M. F. Hasler, Dec 30 2020

Examples

			The a(4) = 6 pairs of set partitions:
  {{1,2},{3,4}} and {{1,3},{2,4}},
  {{1,2},{3,4}} and {{1,4},{2,3}},
  {{1,3},{2,4}} and {{1,2},{3,4}},
  {{1,3},{2,4}} and {{1,4},{2,3}},
  {{1,4},{2,3}} and {{1,2},{3,4}},
  {{1,4},{2,3}} and {{1,3},{2,4}}.
		

Crossrefs

Cf. A000110, A000258, A001247, A008277, A059849, A060639, A181939, A318393, A321760 (unlabeled version), A322435, A322442.

Programs

Mathematica

sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
stabQ[u_]:=stabQ[u,SubsetQ];stabQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
Table[Length[Select[Tuples[sps[Range[n]],2],And[UnsameQ@@Join@@#,stabQ[Join@@#]]&]],{n,6}]