The On-Line Encyclopedia of Integer Sequences (OEIS)

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A319762

Number of non-isomorphic intersecting set multipartitions (multisets of sets) of weight n with empty intersection.
(history; published version)

#5 by Susanna Cuyler at Fri Sep 28 15:22:11 EDT 2018

STATUS

proposed

approved

#4 by Gus Wiseman at Thu Sep 27 22:29:14 EDT 2018

STATUS

editing

proposed

#3 by Gus Wiseman at Thu Sep 27 22:29:04 EDT 2018

CROSSREFS

Cf. A319752, A319759, A319763, A319764, A319765, A319779, A319781.

#2 by Gus Wiseman at Thu Sep 27 12:55:22 EDT 2018

NAME

allocated for Gus WisemanNumber of non-isomorphic intersecting set multipartitions (multisets of sets) of weight n with empty intersection.

DATA

1, 0, 0, 0, 0, 0, 1, 1, 4, 9, 24

OFFSET

0,9

COMMENTS

A set multipartition is intersecting if no two parts are disjoint. The weight of a set multipartition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

EXAMPLE

Non-isomorphic representatives of the a(6) = 1 through a(9) = 9 set multipartitions:

6: {{1,2},{1,3},{2,3}}

7: {{1,3},{1,4},{2,3,4}}

8: {{1,2},{1,3,4},{2,3,4}}

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

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

{{1,2},{1,3},{2,3},{2,3}}

9: {{1,3},{1,4,5},{2,3,4,5}}

{{1,5},{1,6},{2,3,4,5,6}}

{{2,5},{1,2,6},{3,4,5,6}}

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

{{1,3,5},{2,3,6},{4,5,6}}

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

{{1,2},{1,3},{2,3},{1,2,3}}

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

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

CROSSREFS

Cf. A007716, A049311, A281116, A283877, A305854, A306006, A316980, A317757, A318715, A318717.

KEYWORD

allocated

nonn,more

AUTHOR

Gus Wiseman, Sep 27 2018

STATUS

approved

editing

#1 by Gus Wiseman at Thu Sep 27 12:55:22 EDT 2018

NAME

allocated for Gus Wiseman

KEYWORD

allocated

STATUS

approved