A327018 Number of non-isomorphic set-systems of weight n whose dual is a weak antichain.

1, 1, 2, 3, 6, 8, 17, 24, 51, 80, 180

Offset

0,3

Comments

A set-system is a finite set of finite nonempty sets. The dual of a set-system has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. A weak antichain is a multiset of sets, none of which is a proper subset of any other.

Links

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

Example

Non-isomorphic representatives of the a(1) = 1 through a(6) = 17 multiset partitions:
  {1}  {12}    {123}      {1234}        {12345}          {123456}
       {1}{2}  {1}{23}    {1}{234}      {1}{2345}        {1}{23456}
               {1}{2}{3}  {12}{34}      {12}{345}        {12}{3456}
                          {1}{2}{12}    {1}{2}{345}      {123}{456}
                          {1}{2}{34}    {1}{23}{45}      {12}{13}{23}
                          {1}{2}{3}{4}  {1}{2}{3}{23}    {1}{23}{123}
                                        {1}{2}{3}{45}    {1}{2}{3456}
                                        {1}{2}{3}{4}{5}  {1}{23}{456}
                                                         {12}{34}{56}
                                                         {1}{2}{13}{23}
                                                         {1}{2}{3}{123}
                                                         {1}{2}{3}{456}
                                                         {1}{2}{34}{56}
                                                         {3}{4}{12}{34}
                                                         {1}{2}{3}{4}{34}
                                                         {1}{2}{3}{4}{56}
                                                         {1}{2}{3}{4}{5}{6}

Crossrefs

Cf. A007716, A283877, A293993, A319643, A319721, A326966, A326968, A326970, A326972, A326973, A326974, A326975, A326978, A327017, A327019.

Sequence in context: A057574 A198296 A276033 * A329128 A368687 A330442

Adjacent sequences: A327015 A327016 A327017 * A327019 A327020 A327021

Keyword

nonn,more

Author

Gus Wiseman, Aug 15 2019

Status

approved