- FindStat

Identifier

Mp00289: Ordered set partitions —complement⟶ Ordered set partitions
Mp00285: Ordered set partitions —to set partition⟶ Set partitions

Images

[{1}] => [{1}] => {{1}}

[{1},{2}] => [{2},{1}] => {{1},{2}}

[{2},{1}] => [{1},{2}] => {{1},{2}}

[{1,2}] => [{1,2}] => {{1,2}}

[{1},{2},{3}] => [{3},{2},{1}] => {{1},{2},{3}}

[{1},{3},{2}] => [{3},{1},{2}] => {{1},{2},{3}}

[{2},{1},{3}] => [{2},{3},{1}] => {{1},{2},{3}}

[{3},{1},{2}] => [{1},{3},{2}] => {{1},{2},{3}}

[{2},{3},{1}] => [{2},{1},{3}] => {{1},{2},{3}}

[{3},{2},{1}] => [{1},{2},{3}] => {{1},{2},{3}}

[{1},{2,3}] => [{3},{1,2}] => {{1,2},{3}}

[{2},{1,3}] => [{2},{1,3}] => {{1,3},{2}}

[{3},{1,2}] => [{1},{2,3}] => {{1},{2,3}}

[{1,2},{3}] => [{2,3},{1}] => {{1},{2,3}}

[{1,3},{2}] => [{1,3},{2}] => {{1,3},{2}}

[{2,3},{1}] => [{1,2},{3}] => {{1,2},{3}}

[{1,2,3}] => [{1,2,3}] => {{1,2,3}}

[{1},{2},{3},{4}] => [{4},{3},{2},{1}] => {{1},{2},{3},{4}}

[{1},{2},{4},{3}] => [{4},{3},{1},{2}] => {{1},{2},{3},{4}}

[{1},{3},{2},{4}] => [{4},{2},{3},{1}] => {{1},{2},{3},{4}}

[{1},{4},{2},{3}] => [{4},{1},{3},{2}] => {{1},{2},{3},{4}}

[{1},{3},{4},{2}] => [{4},{2},{1},{3}] => {{1},{2},{3},{4}}

[{1},{4},{3},{2}] => [{4},{1},{2},{3}] => {{1},{2},{3},{4}}

[{2},{1},{3},{4}] => [{3},{4},{2},{1}] => {{1},{2},{3},{4}}

[{2},{1},{4},{3}] => [{3},{4},{1},{2}] => {{1},{2},{3},{4}}

[{3},{1},{2},{4}] => [{2},{4},{3},{1}] => {{1},{2},{3},{4}}

[{4},{1},{2},{3}] => [{1},{4},{3},{2}] => {{1},{2},{3},{4}}

[{3},{1},{4},{2}] => [{2},{4},{1},{3}] => {{1},{2},{3},{4}}

[{4},{1},{3},{2}] => [{1},{4},{2},{3}] => {{1},{2},{3},{4}}

[{2},{3},{1},{4}] => [{3},{2},{4},{1}] => {{1},{2},{3},{4}}

[{2},{4},{1},{3}] => [{3},{1},{4},{2}] => {{1},{2},{3},{4}}

[{3},{2},{1},{4}] => [{2},{3},{4},{1}] => {{1},{2},{3},{4}}

[{4},{2},{1},{3}] => [{1},{3},{4},{2}] => {{1},{2},{3},{4}}

[{3},{4},{1},{2}] => [{2},{1},{4},{3}] => {{1},{2},{3},{4}}

[{4},{3},{1},{2}] => [{1},{2},{4},{3}] => {{1},{2},{3},{4}}

[{2},{3},{4},{1}] => [{3},{2},{1},{4}] => {{1},{2},{3},{4}}

[{2},{4},{3},{1}] => [{3},{1},{2},{4}] => {{1},{2},{3},{4}}

[{3},{2},{4},{1}] => [{2},{3},{1},{4}] => {{1},{2},{3},{4}}

[{4},{2},{3},{1}] => [{1},{3},{2},{4}] => {{1},{2},{3},{4}}

[{3},{4},{2},{1}] => [{2},{1},{3},{4}] => {{1},{2},{3},{4}}

[{4},{3},{2},{1}] => [{1},{2},{3},{4}] => {{1},{2},{3},{4}}

[{1},{2},{3,4}] => [{4},{3},{1,2}] => {{1,2},{3},{4}}

[{1},{3},{2,4}] => [{4},{2},{1,3}] => {{1,3},{2},{4}}

[{1},{4},{2,3}] => [{4},{1},{2,3}] => {{1},{2,3},{4}}

[{2},{1},{3,4}] => [{3},{4},{1,2}] => {{1,2},{3},{4}}

[{3},{1},{2,4}] => [{2},{4},{1,3}] => {{1,3},{2},{4}}

[{4},{1},{2,3}] => [{1},{4},{2,3}] => {{1},{2,3},{4}}

[{2},{3},{1,4}] => [{3},{2},{1,4}] => {{1,4},{2},{3}}

[{2},{4},{1,3}] => [{3},{1},{2,4}] => {{1},{2,4},{3}}

[{3},{2},{1,4}] => [{2},{3},{1,4}] => {{1,4},{2},{3}}

[{4},{2},{1,3}] => [{1},{3},{2,4}] => {{1},{2,4},{3}}

[{3},{4},{1,2}] => [{2},{1},{3,4}] => {{1},{2},{3,4}}

[{4},{3},{1,2}] => [{1},{2},{3,4}] => {{1},{2},{3,4}}

[{1},{2,3},{4}] => [{4},{2,3},{1}] => {{1},{2,3},{4}}

[{1},{2,4},{3}] => [{4},{1,3},{2}] => {{1,3},{2},{4}}

[{1},{3,4},{2}] => [{4},{1,2},{3}] => {{1,2},{3},{4}}

[{2},{1,3},{4}] => [{3},{2,4},{1}] => {{1},{2,4},{3}}

[{2},{1,4},{3}] => [{3},{1,4},{2}] => {{1,4},{2},{3}}

[{3},{1,2},{4}] => [{2},{3,4},{1}] => {{1},{2},{3,4}}

[{4},{1,2},{3}] => [{1},{3,4},{2}] => {{1},{2},{3,4}}

[{3},{1,4},{2}] => [{2},{1,4},{3}] => {{1,4},{2},{3}}

[{4},{1,3},{2}] => [{1},{2,4},{3}] => {{1},{2,4},{3}}

[{2},{3,4},{1}] => [{3},{1,2},{4}] => {{1,2},{3},{4}}

[{3},{2,4},{1}] => [{2},{1,3},{4}] => {{1,3},{2},{4}}

[{4},{2,3},{1}] => [{1},{2,3},{4}] => {{1},{2,3},{4}}

[{1},{2,3,4}] => [{4},{1,2,3}] => {{1,2,3},{4}}

[{2},{1,3,4}] => [{3},{1,2,4}] => {{1,2,4},{3}}

[{3},{1,2,4}] => [{2},{1,3,4}] => {{1,3,4},{2}}

[{4},{1,2,3}] => [{1},{2,3,4}] => {{1},{2,3,4}}

[{1,2},{3},{4}] => [{3,4},{2},{1}] => {{1},{2},{3,4}}

[{1,2},{4},{3}] => [{3,4},{1},{2}] => {{1},{2},{3,4}}

[{1,3},{2},{4}] => [{2,4},{3},{1}] => {{1},{2,4},{3}}

[{1,4},{2},{3}] => [{1,4},{3},{2}] => {{1,4},{2},{3}}

[{1,3},{4},{2}] => [{2,4},{1},{3}] => {{1},{2,4},{3}}

[{1,4},{3},{2}] => [{1,4},{2},{3}] => {{1,4},{2},{3}}

[{2,3},{1},{4}] => [{2,3},{4},{1}] => {{1},{2,3},{4}}

[{2,4},{1},{3}] => [{1,3},{4},{2}] => {{1,3},{2},{4}}

[{3,4},{1},{2}] => [{1,2},{4},{3}] => {{1,2},{3},{4}}

[{2,3},{4},{1}] => [{2,3},{1},{4}] => {{1},{2,3},{4}}

[{2,4},{3},{1}] => [{1,3},{2},{4}] => {{1,3},{2},{4}}

[{3,4},{2},{1}] => [{1,2},{3},{4}] => {{1,2},{3},{4}}

[{1,2},{3,4}] => [{3,4},{1,2}] => {{1,2},{3,4}}

[{1,3},{2,4}] => [{2,4},{1,3}] => {{1,3},{2,4}}

[{1,4},{2,3}] => [{1,4},{2,3}] => {{1,4},{2,3}}

[{2,3},{1,4}] => [{2,3},{1,4}] => {{1,4},{2,3}}

[{2,4},{1,3}] => [{1,3},{2,4}] => {{1,3},{2,4}}

[{3,4},{1,2}] => [{1,2},{3,4}] => {{1,2},{3,4}}

[{1,2,3},{4}] => [{2,3,4},{1}] => {{1},{2,3,4}}

[{1,2,4},{3}] => [{1,3,4},{2}] => {{1,3,4},{2}}

[{1,3,4},{2}] => [{1,2,4},{3}] => {{1,2,4},{3}}

[{2,3,4},{1}] => [{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}] => [{5},{4},{3},{2},{1}] => {{1},{2},{3},{4},{5}}

[{1},{2},{3},{5},{4}] => [{5},{4},{3},{1},{2}] => {{1},{2},{3},{4},{5}}

[{1},{2},{4},{3},{5}] => [{5},{4},{2},{3},{1}] => {{1},{2},{3},{4},{5}}

[{1},{2},{5},{3},{4}] => [{5},{4},{1},{3},{2}] => {{1},{2},{3},{4},{5}}

[{1},{2},{4},{5},{3}] => [{5},{4},{2},{1},{3}] => {{1},{2},{3},{4},{5}}

[{1},{2},{5},{4},{3}] => [{5},{4},{1},{2},{3}] => {{1},{2},{3},{4},{5}}

[{1},{3},{2},{4},{5}] => [{5},{3},{4},{2},{1}] => {{1},{2},{3},{4},{5}}

[{1},{3},{2},{5},{4}] => [{5},{3},{4},{1},{2}] => {{1},{2},{3},{4},{5}}

[{1},{4},{2},{3},{5}] => [{5},{2},{4},{3},{1}] => {{1},{2},{3},{4},{5}}

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Map

complement

Description

Return the ordered set partition obtained by complementing each entry.

Map

to set partition

Description

Return the underlying set partition