A318099 -id:A318099 - cp's OEIS frontend

A319621 Number of non-isomorphic connected antichain covers of n vertices by distinct sets whose dual is also an antichain of (not necessarily distinct) sets.

1, 1, 1, 2, 7, 73

Offset: 0

Gus Wiseman, Sep 25 2018

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.

			Non-isomorphic representatives of the a(1) = 1 through a(4) = 7 antichain covers:
  {{1}}  {{1,2}}  {{1,2,3}}            {{1,2,3,4}}
                  {{1,2},{1,3},{2,3}}  {{1,2},{1,3,4},{2,3,4}}
                                       {{1,2},{1,3},{2,4},{3,4}}
                                       {{1,2},{1,3},{1,4},{2,3,4}}
                                       {{1,3},{1,4},{2,3},{2,4},{3,4}}
                                       {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
                                       {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}

Cf. A006126, A007716, A007718, A049311, A056156, A059201, A316980, A316983, A318099, A319557, A319565, A319616-A319646, A300913.

A319622 Number of non-isomorphic connected weight-n antichains of distinct sets whose dual is also an antichain of (not necessarily distinct) sets.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 1, 3, 2, 7

Offset: 0

Gus Wiseman, Sep 25 2018

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks 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.

			Non-isomorphic representatives of the a(1) = 1 through a(10) = 7 antichains:
1:  {{1}}
2:  {{1,2}}
3:  {{1,2,3}}
4:  {{1,2,3,4}}
5:  {{1,2,3,4,5}}
6:  {{1,2,3,4,5,6}}
    {{1,2},{1,3},{2,3}}
7:  {{1,2,3,4,5,6,7}}
8:  {{1,2,3,4,5,6,7,8}}
    {{1,2},{1,3,4},{2,3,4}}
    {{1,2},{1,3},{2,4},{3,4}}
9:  {{1,2,3,4,5,6,7,8,9}}
    {{1,2},{1,3},{1,4},{2,3,4}}
10: {{1,2,3,4,5,6,7,8,9,10}}
    {{1,2},{1,3,4,5},{2,3,4,5}}
    {{1,2,3},{1,4,5},{2,3,4,5}}
    {{1,2},{1,3},{2,4,5},{3,4,5}}
    {{1,3},{2,4},{1,2,5},{3,4,5}}
    {{1,2},{1,3},{2,4},{3,5},{4,5}}
    {{1,3},{1,4},{2,3},{2,4},{3,4}}

Cf. A006126, A007716, A007718, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319565, A319616-A319646, A300913.

A319623 Number of connected antichain covers of n vertices by distinct sets whose dual is also an antichain of distinct sets.

Original entry on oeis.org

1, 1, 0, 1, 15, 1957

Offset: 0

Gus Wiseman, Sep 25 2018

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.

			Non-isomorphic representatives of the a(1) = 1 through a(4) = 15 antichain covers:
1: {{1}}
3: {{1,2},{1,3},{2,3}}
4: {{1,2},{1,3},{2,4},{3,4}}
   {{1,3},{1,4},{2,3},{2,4}}
   {{1,2},{1,4},{2,3},{3,4}}
   {{1,4},{2,4},{3,4},{1,2,3}}
   {{1,3},{2,3},{3,4},{1,2,4}}
   {{1,2},{2,3},{2,4},{1,3,4}}
   {{1,2},{1,3},{1,4},{2,3,4}}
   {{1,3},{1,4},{2,3},{2,4},{3,4}}
   {{1,2},{1,4},{2,3},{2,4},{3,4}}
   {{1,2},{1,3},{2,3},{2,4},{3,4}}
   {{1,2},{1,3},{1,4},{2,4},{3,4}}
   {{1,2},{1,3},{1,4},{2,3},{3,4}}
   {{1,2},{1,3},{1,4},{2,3},{2,4}}
   {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
   {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}

Cf. A006126, A007716, A007718, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319558, A319565, A319616-A319646, A300913.

A319624 Number of non-isomorphic connected antichain covers of n vertices by distinct sets whose dual is also an antichain of distinct sets.

Original entry on oeis.org

1, 1, 0, 1, 5, 63

Offset: 0

Gus Wiseman, Sep 25 2018

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.

			Non-isomorphic representatives of the a(1) = 1 through a(4) = 5 antichain covers:
1: {{1}}
3: {{1,2},{1,3},{2,3}}
4: {{1,2},{1,3},{2,4},{3,4}}
   {{1,2},{1,3},{1,4},{2,3,4}}
   {{1,3},{1,4},{2,3},{2,4},{3,4}}
   {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
   {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}

Cf. A006126, A007716, A007718, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319558, A319565, A319616-A319646, A300913.

A319631 Number of non-isomorphic weight-n antichains of multisets whose dual is a chain of distinct multisets.

Original entry on oeis.org

1, 1, 2, 3, 5, 5, 13, 11, 25, 31, 54

Offset: 0

Gus Wiseman, Sep 25 2018

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks 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.

			Non-isomorphic representatives of the a(1) = 1 through a(5) = 5 antichains:
1: {{1}}
2: {{1,1}}
   {{1},{1}}
3: {{1,1,1}}
   {{1,2,2}}
   {{1},{1},{1}}
4: {{1,1,1,1}}
   {{1,2,2,2}}
   {{1,1},{1,1}}
   {{1,2},{2,2}}
   {{1},{1},{1},{1}}
5: {{1,1,1,1,1}}
   {{1,1,2,2,2}}
   {{1,2,2,2,2}}
   {{1,2},{2,2,2}}
   {{1},{1},{1},{1},{1}}

Cf. A000219, A006126, A007716, A059201, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913.

A319632 Number of non-isomorphic weight-n antichains of (not necessarily distinct) sets whose dual is also an antichain of (not necessarily distinct) sets.

Original entry on oeis.org

1, 1, 3, 5, 11, 17, 35, 53, 100, 154, 275

Offset: 0

Gus Wiseman, Sep 25 2018

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks 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.

			Non-isomorphic representatives of the a(1) = 1 through a(4) = 11 set systems:
1: {{1}}
2: {{1,2}}
   {{1},{1}}
   {{1},{2}}
3: {{1,2,3}}
   {{1},{2,3}}
   {{1},{1},{1}}
   {{1},{2},{2}}
   {{1},{2},{3}}
4: {{1,2,3,4}}
   {{1},{2,3,4}}
   {{1,2},{1,2}}
   {{1,2},{3,4}}
   {{1},{1},{2,3}}
   {{1},{2},{3,4}}
   {{1},{1},{1},{1}}
   {{1},{1},{2},{2}}
   {{1},{2},{2},{2}}
   {{1},{2},{3},{3}}
   {{1},{2},{3},{4}}

Cf. A006126, A007716, A049311, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913.

A319633 Number of antichain covers of n vertices by distinct sets whose dual is also an antichain of (not necessarily distinct) sets.

Original entry on oeis.org

1, 1, 2, 6, 40, 2309

Offset: 0

Gus Wiseman, Sep 25 2018

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.

			The a(3) = 6 antichain covers:
   {{1,2,3}}
   {{3},{1,2}}
   {{2},{1,3}}
   {{1},{2,3}}
   {{1},{2},{3}}
   {{1,2},{1,3},{2,3}}

Cf. A006126, A007716, A049311, A059201, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913.

A319634 Number of non-isomorphic antichain covers of n vertices by distinct sets whose dual is also an antichain of (not necessarily distinct) sets.

Original entry on oeis.org

1, 1, 2, 4, 12, 87

Offset: 0

Gus Wiseman, Sep 25 2018

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.

			Non-isomorphic representatives of the a(1) = 1 through a(4) = 12 antichain covers:
  {{1}}   {{1,2}}     {{1,2,3}}              {{1,2,3,4}}
         {{1},{2}}   {{1},{2,3}}            {{1},{2,3,4}}
                    {{1},{2},{3}}           {{1,2},{3,4}}
                 {{1,2},{1,3},{2,3}}       {{1},{2},{3,4}}
                                          {{1},{2},{3},{4}}
                                       {{1,2},{1,3,4},{2,3,4}}
                                       {{1},{2,3},{2,4},{3,4}}
                                      {{1,2},{1,3},{2,4},{3,4}}
                                     {{1,2},{1,3},{1,4},{2,3,4}}
                                   {{1,3},{1,4},{2,3},{2,4},{3,4}}
                                  {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
                                {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}

Cf. A006126, A007716, A049311, A059201, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913.

A319635 Number of non-isomorphic weight-n antichains of distinct multisets whose dual is also an antichain of (not necessarily distinct) multisets.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 12, 16, 26, 36, 58

Offset: 0

Gus Wiseman, Sep 25 2018

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks 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.

			Non-isomorphic representatives of the a(1) = 1 through a(5) = 7 antichains:
1: {{1}}
2: {{1,2}}
   {{1},{2}}
3: {{1,2,3}}
   {{1},{2,3}}
   {{1},{2},{3}}
4: {{1,2,3,4}}
   {{1},{2,3,4}}
   {{1,2},{3,4}}
   {{1},{2},{3,4}}
   {{1},{2},{3},{4}}
5: {{1,2,3,4,5}}
   {{1},{2,3,4,5}}
   {{1,2},{3,4,5}}
   {{1},{2},{3,4,5}}
   {{1},{2,3},{4,5}}
   {{1},{2},{3},{4,5}}
   {{1},{2},{3},{4},{5}}

Cf. A006126, A007716, A049311, A059201, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913.

A319640 Number of non-isomorphic antichain covers of n vertices by distinct sets whose dual is also an antichain of distinct sets.

Original entry on oeis.org

1, 1, 1, 2, 7, 70

Offset: 0

Gus Wiseman, Sep 25 2018

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.

			Non-isomorphic representatives of the a(1) = 1 through a(4) = 7 antichains:
1: {{1}}
2: {{1},{2}}
3: {{1},{2},{3}}
   {{1,2},{1,3},{2,3}}
4: {{1},{2},{3},{4}}
   {{1},{2,3},{2,4},{3,4}}
   {{1,2},{1,3},{1,4},{2,3,4}}
   {{1,2},{1,3},{2,4},{3,4}}
   {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
   {{1,3},{1,4},{2,3},{2,4},{3,4}}
   {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}

Cf. A006126, A007716, A049311, A059201, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913.

cp's OEIS Frontend

A319621 Number of non-isomorphic connected antichain covers of n vertices by distinct sets whose dual is also an antichain of (not necessarily distinct) sets.

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A319622 Number of non-isomorphic connected weight-n antichains of distinct sets whose dual is also an antichain of (not necessarily distinct) sets.

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A319623 Number of connected antichain covers of n vertices by distinct sets whose dual is also an antichain of distinct sets.

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A319624 Number of non-isomorphic connected antichain covers of n vertices by distinct sets whose dual is also an antichain of distinct sets.

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A319631 Number of non-isomorphic weight-n antichains of multisets whose dual is a chain of distinct multisets.

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A319632 Number of non-isomorphic weight-n antichains of (not necessarily distinct) sets whose dual is also an antichain of (not necessarily distinct) sets.

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A319633 Number of antichain covers of n vertices by distinct sets whose dual is also an antichain of (not necessarily distinct) sets.

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A319634 Number of non-isomorphic antichain covers of n vertices by distinct sets whose dual is also an antichain of (not necessarily distinct) sets.

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A319635 Number of non-isomorphic weight-n antichains of distinct multisets whose dual is also an antichain of (not necessarily distinct) multisets.

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A319640 Number of non-isomorphic antichain covers of n vertices by distinct sets whose dual is also an antichain of distinct sets.

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