login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A321406 Number of non-isomorphic self-dual set systems of weight n with no singletons. 5
1, 0, 0, 0, 0, 0, 1, 1, 1, 2, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

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 and none sums to 1.

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(6) = 1 through a(10) = 4 set systems:

   6: {{1,2},{1,3},{2,3}}

   7: {{1,3},{2,3},{1,2,3}}

   8: {{1,2},{1,3},{2,4},{3,4}}

   9: {{1,2},{1,3},{1,4},{2,3,4}}

   9: {{1,2},{1,4},{3,4},{2,3,4}}

  10: {{1,2},{2,4},{1,3,4},{2,3,4}}

  10: {{1,3},{2,4},{1,3,4},{2,3,4}}

  10: {{1,4},{2,4},{3,4},{1,2,3,4}}

  10: {{1,2},{1,3},{2,4},{3,5},{4,5}}

CROSSREFS

Cf. A000219, A007716, A045778, A049311, A135588, A138178, A283877, A302545, A316980, A316983.

Cf. A320796, A320797, A321401, A321402, A321403, A321405.

Sequence in context: A216979 A334822 A082871 * A166926 A266296 A028573

Adjacent sequences:  A321403 A321404 A321405 * A321407 A321408 A321409

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 15 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 5 00:40 EDT 2020. Contains 335457 sequences. (Running on oeis4.)