- FindStat

Identifier

Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00284: Standard tableaux —rows⟶ Set partitions
St000211: Set partitions ⟶ ℤ

Values

[1] => [[1]] => {{1}} => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The rank of the set partition.
This is defined as the number of elements in the set partition minus the number of blocks, or, equivalently, the number of arcs in the one-line diagram associated to the set partition.

Map

rows

Description

The set partition whose blocks are the rows of the tableau.

Map

Robinson-Schensted recording tableau

Description

Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.