A322111 - OEIS

A322111

Number of non-isomorphic self-dual connected multiset partitions of weight n with multiset density -1.

1, 1, 1, 2, 2, 5, 5, 13, 13, 37, 37

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OFFSET

0,4

COMMENTS

The multiset density of a multiset partition is the sum of the numbers of distinct vertices in each part minus the number of parts minus the number of vertices.

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}}. A multiset partition is self-dual if it is isomorphic to its dual. For example, {{1,1},{1,2,2},{2,3,3}} is self-dual, as it is isomorphic to its dual {{1,1,2},{2,2,3},{3,3}}.

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

LINKS

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

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(8) = 13 multiset partitions:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

CROSSREFS

Cf. A000272, A007716, A007718, A030019, A052888, A134954, A304867, A304887, A316983, A318697, A319616, A321155, A321255.

Sequence in context: A364486 A178115 A094967 * A321395 A056505 A056506

Adjacent sequences: A322108 A322109 A322110 * A322112 A322113 A322114

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 26 2018

STATUS

approved