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A327019 Number of non-isomorphic set-systems of weight n whose dual is a (strict) antichain. 1
1, 1, 1, 1, 2, 2, 5, 7, 15, 26, 61 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Also the number of non-isomorphic set-systems where every vertex is the unique common element of some subset of the edges, also called non-isomorphic T_1 set-systems.

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}}.

An antichain is a set of sets, none of which is a 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(8) = 15 multiset partitions:

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

                          {1}{2}{3}{4}  {1}{2}{3}{4}{5}  {1}{2}{13}{23}

                                                         {1}{2}{3}{123}

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

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

.

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

  {3}{12}{13}{23}        {2}{13}{14}{234}

  {1}{2}{3}{13}{23}      {1}{2}{13}{24}{34}

  {1}{2}{3}{24}{34}      {1}{2}{3}{14}{234}

  {1}{2}{3}{4}{234}      {1}{2}{3}{23}{123}

  {1}{2}{3}{4}{5}{45}    {1}{2}{3}{4}{1234}

  {1}{2}{3}{4}{5}{6}{7}  {1}{2}{34}{35}{45}

                         {1}{4}{23}{24}{34}

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

                         {1}{2}{3}{4}{12}{34}

                         {1}{2}{3}{4}{24}{34}

                         {1}{2}{3}{4}{35}{45}

                         {1}{2}{3}{4}{5}{345}

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

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

CROSSREFS

Cf. A007716, A059523, A283877, A293993, A326961, A326965, A326974, A326976, A326977, A326979, A327012, A327018.

Sequence in context: A195964 A047083 A238422 * A035085 A208238 A127413

Adjacent sequences:  A327016 A327017 A327018 * A327020 A327021 A327022

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 15 2019

STATUS

approved

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Last modified January 26 08:18 EST 2020. Contains 331278 sequences. (Running on oeis4.)