- FindStat

Identifier

Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000714: Integer partitions ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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search for individual values

searching the database for the individual values of this statistic

Description

The number of semistandard Young tableau of given shape, with entries at most 2.
This is also the dimension of the corresponding irreducible representation of

$GL_2$ .

Map

first row removal

Description

Removes the first entry of an integer partition

Map

inner shape

Description

The inner shape of a skew 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.