- FindStat

Identifier

Mp00287: Ordered set partitions —to composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St001587: Integer partitions ⟶ ℤ

Values

[{1,2},{3}] => [2,1] => [[2,2],[1]] => [1] => 0

[{1,3},{2}] => [2,1] => [[2,2],[1]] => [1] => 0

[{2,3},{1}] => [2,1] => [[2,2],[1]] => [1] => 0

[{1},{2,3},{4}] => [1,2,1] => [[2,2,1],[1]] => [1] => 0

[{1},{2,4},{3}] => [1,2,1] => [[2,2,1],[1]] => [1] => 0

[{1},{3,4},{2}] => [1,2,1] => [[2,2,1],[1]] => [1] => 0

[{2},{1,3},{4}] => [1,2,1] => [[2,2,1],[1]] => [1] => 0

[{2},{1,4},{3}] => [1,2,1] => [[2,2,1],[1]] => [1] => 0

[{3},{1,2},{4}] => [1,2,1] => [[2,2,1],[1]] => [1] => 0

[{4},{1,2},{3}] => [1,2,1] => [[2,2,1],[1]] => [1] => 0

[{3},{1,4},{2}] => [1,2,1] => [[2,2,1],[1]] => [1] => 0

[{4},{1,3},{2}] => [1,2,1] => [[2,2,1],[1]] => [1] => 0

[{2},{3,4},{1}] => [1,2,1] => [[2,2,1],[1]] => [1] => 0

[{3},{2,4},{1}] => [1,2,1] => [[2,2,1],[1]] => [1] => 0

[{4},{2,3},{1}] => [1,2,1] => [[2,2,1],[1]] => [1] => 0

[{1,2},{3},{4}] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0

[{1,2},{4},{3}] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0

[{1,3},{2},{4}] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0

[{1,4},{2},{3}] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0

[{1,3},{4},{2}] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0

[{1,4},{3},{2}] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0

[{2,3},{1},{4}] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0

[{2,4},{1},{3}] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0

[{3,4},{1},{2}] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0

[{2,3},{4},{1}] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0

[{2,4},{3},{1}] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0

[{3,4},{2},{1}] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0

[{1,2},{3,4}] => [2,2] => [[3,2],[1]] => [1] => 0

[{1,3},{2,4}] => [2,2] => [[3,2],[1]] => [1] => 0

[{1,4},{2,3}] => [2,2] => [[3,2],[1]] => [1] => 0

[{2,3},{1,4}] => [2,2] => [[3,2],[1]] => [1] => 0

[{2,4},{1,3}] => [2,2] => [[3,2],[1]] => [1] => 0

[{3,4},{1,2}] => [2,2] => [[3,2],[1]] => [1] => 0

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

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

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

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

[{1},{2},{3,4},{5}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{1},{2},{3,5},{4}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{1},{2},{4,5},{3}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{1},{3},{2,4},{5}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{1},{3},{2,5},{4}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{1},{4},{2,3},{5}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{1},{5},{2,3},{4}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{1},{4},{2,5},{3}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{1},{5},{2,4},{3}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{1},{3},{4,5},{2}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{1},{4},{3,5},{2}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{1},{5},{3,4},{2}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{2},{1},{3,4},{5}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{2},{1},{3,5},{4}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{2},{1},{4,5},{3}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{3},{1},{2,4},{5}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{3},{1},{2,5},{4}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{4},{1},{2,3},{5}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{5},{1},{2,3},{4}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{4},{1},{2,5},{3}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{5},{1},{2,4},{3}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{3},{1},{4,5},{2}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{4},{1},{3,5},{2}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{5},{1},{3,4},{2}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{2},{3},{1,4},{5}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{2},{3},{1,5},{4}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{2},{4},{1,3},{5}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{2},{5},{1,3},{4}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{2},{4},{1,5},{3}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{2},{5},{1,4},{3}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{3},{2},{1,4},{5}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{3},{2},{1,5},{4}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{4},{2},{1,3},{5}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{5},{2},{1,3},{4}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{4},{2},{1,5},{3}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{5},{2},{1,4},{3}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{3},{4},{1,2},{5}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{3},{5},{1,2},{4}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{4},{3},{1,2},{5}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{5},{3},{1,2},{4}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{4},{5},{1,2},{3}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{5},{4},{1,2},{3}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{3},{4},{1,5},{2}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{3},{5},{1,4},{2}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{4},{3},{1,5},{2}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{5},{3},{1,4},{2}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{4},{5},{1,3},{2}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{5},{4},{1,3},{2}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{2},{3},{4,5},{1}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{2},{4},{3,5},{1}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{2},{5},{3,4},{1}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{3},{2},{4,5},{1}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{4},{2},{3,5},{1}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{5},{2},{3,4},{1}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{3},{4},{2,5},{1}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{3},{5},{2,4},{1}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{4},{3},{2,5},{1}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{5},{3},{2,4},{1}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{4},{5},{2,3},{1}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{5},{4},{2,3},{1}] => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0

[{1},{2,3},{4},{5}] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 0

[{1},{2,3},{5},{4}] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 0

[{1},{2,4},{3},{5}] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 0

[{1},{2,5},{3},{4}] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 0

>>> Load all 3818 entries. <<<

search for individual values

searching the database for the individual values of this statistic

Description

Half of the largest even part of an integer partition.
The largest even part is recorded by St000995The largest even part of an integer partition..

Map

to ribbon

Description

The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.

Map

inner shape

Description

The inner shape of a skew partition.

Map

to composition

Description

Return the sizes of the blocks as a composition.