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A319769 Number of non-isomorphic intersecting set multipartitions (multisets of sets) of weight n whose dual is also an intersecting set multipartition. 6
1, 1, 2, 3, 5, 7, 12, 16, 26, 38, 61 (list; graph; refs; listen; history; text; internal format)



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 weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

A multiset partition is intersecting iff no two parts are disjoint. The dual of a multiset partition is intersecting iff every pair of distinct vertices appear together in some part.


Table of n, a(n) for n=0..10.


Non-isomorphic representatives of the a(1) = 1 through a(5) = 7 set multipartitions:

1: {{1}}

2: {{1,2}}


3: {{1,2,3}}



4: {{1,2,3,4}}





5: {{1,2,3,4,5}}








Cf. A007716, A281116, A283877, A305854, A306006,  A316980, A316983, A317757, A319616.

Cf. A319752, A319765, A319766, A319767, A319768, A319773, A319774.

Sequence in context: A275592 A319635 A179822 * A326083 A027959 A060730

Adjacent sequences:  A319766 A319767 A319768 * A319770 A319771 A319772




Gus Wiseman, Sep 27 2018



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Last modified December 14 17:41 EST 2019. Contains 329979 sequences. (Running on oeis4.)