A321405 - OEIS

A321405

Number of non-isomorphic self-dual set systems of weight n.

1, 1, 1, 2, 2, 3, 6, 9, 16, 28, 47

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OFFSET

0,4

COMMENTS

Also the number of (0,1) symmetric matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, in which the rows are all different.

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.

LINKS

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

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(8) = 16 set systems:

{{1}} {{1}{2}} {{2}{12}} {{1}{3}{23}} {{2}{13}{23}}

{{1}{2}{3}} {{1}{2}{3}{4}} {{1}{2}{4}{34}}

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

{{12}{13}{23}} {{13}{23}{123}} {{1}{13}{14}{234}}

{{3}{23}{123}} {{1}{23}{24}{34}} {{12}{13}{24}{34}}

{{1}{3}{24}{34}} {{1}{4}{34}{234}} {{1}{24}{34}{234}}

{{2}{4}{12}{34}} {{2}{13}{24}{34}} {{2}{14}{34}{234}}

{{1}{2}{3}{5}{45}} {{3}{4}{14}{234}} {{3}{4}{134}{234}}

{{1}{2}{3}{4}{5}{6}} {{1}{2}{4}{35}{45}} {{4}{13}{14}{234}}

{{1}{3}{5}{23}{45}} {{1}{2}{34}{35}{45}}

{{1}{2}{3}{4}{6}{56}} {{1}{2}{5}{45}{345}}

{{1}{2}{3}{4}{5}{6}{7}} {{1}{3}{24}{35}{45}}

{{1}{4}{5}{25}{345}}

{{2}{4}{12}{35}{45}}

{{4}{5}{13}{23}{45}}

{{1}{2}{3}{5}{46}{56}}

{{1}{2}{4}{6}{34}{56}}

{{1}{2}{3}{4}{5}{7}{67}}

{{1}{2}{3}{4}{5}{6}{7}{8}}

CROSSREFS

Cf. A000219, A007716, A045778, A049311, A135588, A138178, A283877, A316980, A316983, A319616.

Cf. A320796, A320797, A321401, A321403, A321406.

Sequence in context: A019465 A077074 A163493 * A054200 A137216 A369424

Adjacent sequences: A321402 A321403 A321404 * A321406 A321407 A321408

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 15 2018

STATUS

approved