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A322442 Number of pairs of set partitions of {1,...,n} where every block of one is a subset or superset of some block of the other. 9
1, 1, 4, 25, 195, 1894, 22159, 303769 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..7.

EXAMPLE

The a(3) = 25 pairs of set partitions (these are actually all pairs of set partitions of {1,2,3}):

  (1)(2)(3)|(1)(2)(3)

  (1)(2)(3)|(1)(23)

  (1)(2)(3)|(12)(3)

  (1)(2)(3)|(13)(2)

  (1)(2)(3)|(123)

    (1)(23)|(1)(2)(3)

    (1)(23)|(1)(23)

    (1)(23)|(12)(3)

    (1)(23)|(13)(2)

    (1)(23)|(123)

    (12)(3)|(1)(2)(3)

    (12)(3)|(1)(23)

    (12)(3)|(12)(3)

    (12)(3)|(13)(2)

    (12)(3)|(123)

    (13)(2)|(1)(2)(3)

    (13)(2)|(1)(23)

    (13)(2)|(12)(3)

    (13)(2)|(13)(2)

    (13)(2)|(123)

      (123)|(1)(2)(3)

      (123)|(1)(23)

      (123)|(12)(3)

      (123)|(13)(2)

      (123)|(123)

Non-isomorphic representatives of the pairs of set partitions of {1,2,3,4} for which the condition fails:

    (12)(34)|(13)(24)

    (12)(34)|(1)(3)(24)

  (1)(2)(34)|(13)(24)

MATHEMATICA

sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];

costabQ[s_, t_]:=And@@Cases[s, x_:>Select[t, SubsetQ[x, #]||SubsetQ[#, x]&]!={}];

Table[Length[Select[Tuples[sps[Range[n]], 2], And[costabQ@@#, costabQ@@Reverse[#]]&]], {n, 5}]

CROSSREFS

Cf. A000110, A000258, A001247, A008277, A059849, A060639, A181939, A318393, A322435, A322437, A322439, A322440, A322441.

Sequence in context: A199494 A171791 A060908 * A036449 A051500 A206179

Adjacent sequences:  A322439 A322440 A322441 * A322443 A322444 A322445

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Dec 08 2018

STATUS

approved

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Last modified July 11 01:19 EDT 2020. Contains 335600 sequences. (Running on oeis4.)