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

0,5

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

Links

Table of n, a(n) for n=0..8.

Example

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}}.

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}]

Crossrefs

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

Sequence in context: A136893 A090019 A186676 * A186674 A186672 A295503

Adjacent sequences: A322438 A322439 A322440 * A322442 A322443 A322444

Keyword

nonn,more

Author

Gus Wiseman, Dec 08 2018

Status

approved