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A321405
Number of non-isomorphic self-dual set systems of weight n.
26
1, 1, 1, 2, 2, 3, 6, 9, 16, 28, 47
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.
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}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 15 2018
STATUS
approved