- FindStat

Identifier

Mp00083: Standard tableaux —shape⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001595: Skew partitions ⟶ ℤ

Values

[[1]] => [1] => [[1],[]] => 1

[[1,2]] => [2] => [[2],[]] => 1

[[1],[2]] => [1,1] => [[1,1],[]] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,4,5],[2],[3]] => [3,1,1] => [[3,1,1],[]] => 6

[[1,3,5],[2],[4]] => [3,1,1] => [[3,1,1],[]] => 6

[[1,2,5],[3],[4]] => [3,1,1] => [[3,1,1],[]] => 6

[[1,3,4],[2],[5]] => [3,1,1] => [[3,1,1],[]] => 6

[[1,2,4],[3],[5]] => [3,1,1] => [[3,1,1],[]] => 6

[[1,2,3],[4],[5]] => [3,1,1] => [[3,1,1],[]] => 6

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

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

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

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

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

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

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

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

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

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

[[1,2,3,4,5,6]] => [6] => [[6],[]] => 1

[[1,3,4,5,6],[2]] => [5,1] => [[5,1],[]] => 5

[[1,2,4,5,6],[3]] => [5,1] => [[5,1],[]] => 5

[[1,2,3,5,6],[4]] => [5,1] => [[5,1],[]] => 5

[[1,2,3,4,6],[5]] => [5,1] => [[5,1],[]] => 5

[[1,2,3,4,5],[6]] => [5,1] => [[5,1],[]] => 5

[[1,3,5,6],[2,4]] => [4,2] => [[4,2],[]] => 9

[[1,2,5,6],[3,4]] => [4,2] => [[4,2],[]] => 9

[[1,3,4,6],[2,5]] => [4,2] => [[4,2],[]] => 9

[[1,2,4,6],[3,5]] => [4,2] => [[4,2],[]] => 9

[[1,2,3,6],[4,5]] => [4,2] => [[4,2],[]] => 9

[[1,3,4,5],[2,6]] => [4,2] => [[4,2],[]] => 9

[[1,2,4,5],[3,6]] => [4,2] => [[4,2],[]] => 9

[[1,2,3,5],[4,6]] => [4,2] => [[4,2],[]] => 9

[[1,2,3,4],[5,6]] => [4,2] => [[4,2],[]] => 9

[[1,4,5,6],[2],[3]] => [4,1,1] => [[4,1,1],[]] => 10

[[1,3,5,6],[2],[4]] => [4,1,1] => [[4,1,1],[]] => 10

[[1,2,5,6],[3],[4]] => [4,1,1] => [[4,1,1],[]] => 10

[[1,3,4,6],[2],[5]] => [4,1,1] => [[4,1,1],[]] => 10

[[1,2,4,6],[3],[5]] => [4,1,1] => [[4,1,1],[]] => 10

[[1,2,3,6],[4],[5]] => [4,1,1] => [[4,1,1],[]] => 10

[[1,3,4,5],[2],[6]] => [4,1,1] => [[4,1,1],[]] => 10

[[1,2,4,5],[3],[6]] => [4,1,1] => [[4,1,1],[]] => 10

[[1,2,3,5],[4],[6]] => [4,1,1] => [[4,1,1],[]] => 10

[[1,2,3,4],[5],[6]] => [4,1,1] => [[4,1,1],[]] => 10

[[1,3,5],[2,4,6]] => [3,3] => [[3,3],[]] => 5

[[1,2,5],[3,4,6]] => [3,3] => [[3,3],[]] => 5

[[1,3,4],[2,5,6]] => [3,3] => [[3,3],[]] => 5

[[1,2,4],[3,5,6]] => [3,3] => [[3,3],[]] => 5

[[1,2,3],[4,5,6]] => [3,3] => [[3,3],[]] => 5

[[1,4,6],[2,5],[3]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,3,6],[2,5],[4]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,2,6],[3,5],[4]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,3,6],[2,4],[5]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,2,6],[3,4],[5]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,4,5],[2,6],[3]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,3,5],[2,6],[4]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,2,5],[3,6],[4]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,3,4],[2,6],[5]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,2,4],[3,6],[5]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,2,3],[4,6],[5]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,3,5],[2,4],[6]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,2,5],[3,4],[6]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,3,4],[2,5],[6]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,2,4],[3,5],[6]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,2,3],[4,5],[6]] => [3,2,1] => [[3,2,1],[]] => 16

[[1,5,6],[2],[3],[4]] => [3,1,1,1] => [[3,1,1,1],[]] => 10

[[1,4,6],[2],[3],[5]] => [3,1,1,1] => [[3,1,1,1],[]] => 10

[[1,3,6],[2],[4],[5]] => [3,1,1,1] => [[3,1,1,1],[]] => 10

[[1,2,6],[3],[4],[5]] => [3,1,1,1] => [[3,1,1,1],[]] => 10

[[1,4,5],[2],[3],[6]] => [3,1,1,1] => [[3,1,1,1],[]] => 10

[[1,3,5],[2],[4],[6]] => [3,1,1,1] => [[3,1,1,1],[]] => 10

[[1,2,5],[3],[4],[6]] => [3,1,1,1] => [[3,1,1,1],[]] => 10

[[1,3,4],[2],[5],[6]] => [3,1,1,1] => [[3,1,1,1],[]] => 10

[[1,2,4],[3],[5],[6]] => [3,1,1,1] => [[3,1,1,1],[]] => 10

[[1,2,3],[4],[5],[6]] => [3,1,1,1] => [[3,1,1,1],[]] => 10

[[1,4],[2,5],[3,6]] => [2,2,2] => [[2,2,2],[]] => 5

[[1,3],[2,5],[4,6]] => [2,2,2] => [[2,2,2],[]] => 5

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Description

The number of standard Young tableaux of the skew partition.

Map

to skew partition

Description

The partition regarded as a skew partition.

Map

shape

Description

Sends a tableau to its shape.