- FindStat

Identifier

Mp00077: Semistandard tableaux —shape⟶ Integer partitions
St000812: Integer partitions ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

[[1,1],[2]] => [2,1] => 6

[[1,2],[2]] => [2,1] => 6

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

[[2,4]] => [2] => 2

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

[[4,4]] => [2] => 2

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

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

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

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

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

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

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

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

[[3,3,3]] => [3] => 3

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

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

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

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

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

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

[[1],[2],[3]] => [1,1,1] => 10

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

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

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

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

[[1,1,1],[2]] => [3,1] => 12

[[1,1,2],[2]] => [3,1] => 12

[[1,2,2],[2]] => [3,1] => 12

[[1,1],[2,2]] => [2,2] => 16

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

[[2,5]] => [2] => 2

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

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

[[5,5]] => [2] => 2

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

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

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

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

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

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

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

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

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

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

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

[[3,3,4]] => [3] => 3

[[3,4,4]] => [3] => 3

[[4,4,4]] => [3] => 3

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

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

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

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

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

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

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

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

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

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

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

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

[[1],[2],[4]] => [1,1,1] => 10

[[1],[3],[4]] => [1,1,1] => 10

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

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

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

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

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

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

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

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

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

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

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

[[1,1,1],[3]] => [3,1] => 12

[[1,1,2],[3]] => [3,1] => 12

[[1,1,3],[2]] => [3,1] => 12

[[1,1,3],[3]] => [3,1] => 12

[[1,2,2],[3]] => [3,1] => 12

[[1,2,3],[2]] => [3,1] => 12

[[1,2,3],[3]] => [3,1] => 12

[[1,3,3],[2]] => [3,1] => 12

[[1,3,3],[3]] => [3,1] => 12

[[2,2,2],[3]] => [3,1] => 12

[[2,2,3],[3]] => [3,1] => 12

[[2,3,3],[3]] => [3,1] => 12

[[1,1],[2,3]] => [2,2] => 16

[[1,1],[3,3]] => [2,2] => 16

[[1,2],[2,3]] => [2,2] => 16

[[1,2],[3,3]] => [2,2] => 16

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Description

The sum of the entries in the column specified by the partition of the change of basis matrix from complete homogeneous symmetric functions to monomial symmetric functions.
For example, $h_{11} = 2m_{11} + m_2$, so the statistic on the partition $11$ is 3.

Map

shape

Description

Return the shape of a tableau.