- FindStat

Identifier

Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00258: Set partitions —Standard tableau associated to a set partition⟶ Standard tableaux
St000738: Standard tableaux ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The first entry in the last row of a standard tableau.
For the last entry in the first row, see St000734The last entry in the first row of a standard tableau..

Map

Standard tableau associated to a set partition

Description

Sends a set partition to the associated standard tableau.
The $j$th column of the standard tableau associated to a set partition is the set of $j$th smallest elements of its blocks arranged in increassing order.

Map

weak exceedance partition

Description

The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.