Identifier
-
Mp00044:
Integer partitions
—conjugate⟶
Integer partitions
St001127: Integer partitions ⟶ ℤ
Values
[1] => [1] => 1
[2] => [1,1] => 2
[1,1] => [2] => 4
[3] => [1,1,1] => 3
[2,1] => [2,1] => 5
[1,1,1] => [3] => 9
[4] => [1,1,1,1] => 4
[3,1] => [2,1,1] => 6
[2,2] => [2,2] => 8
[2,1,1] => [3,1] => 10
[1,1,1,1] => [4] => 16
[5] => [1,1,1,1,1] => 5
[4,1] => [2,1,1,1] => 7
[3,2] => [2,2,1] => 9
[3,1,1] => [3,1,1] => 11
[2,2,1] => [3,2] => 13
[2,1,1,1] => [4,1] => 17
[1,1,1,1,1] => [5] => 25
[6] => [1,1,1,1,1,1] => 6
[5,1] => [2,1,1,1,1] => 8
[4,2] => [2,2,1,1] => 10
[4,1,1] => [3,1,1,1] => 12
[3,3] => [2,2,2] => 12
[3,2,1] => [3,2,1] => 14
[3,1,1,1] => [4,1,1] => 18
[2,2,2] => [3,3] => 18
[2,2,1,1] => [4,2] => 20
[2,1,1,1,1] => [5,1] => 26
[1,1,1,1,1,1] => [6] => 36
[7] => [1,1,1,1,1,1,1] => 7
[6,1] => [2,1,1,1,1,1] => 9
[5,2] => [2,2,1,1,1] => 11
[5,1,1] => [3,1,1,1,1] => 13
[4,3] => [2,2,2,1] => 13
[4,2,1] => [3,2,1,1] => 15
[4,1,1,1] => [4,1,1,1] => 19
[3,3,1] => [3,2,2] => 17
[3,2,2] => [3,3,1] => 19
[3,2,1,1] => [4,2,1] => 21
[3,1,1,1,1] => [5,1,1] => 27
[2,2,2,1] => [4,3] => 25
[2,2,1,1,1] => [5,2] => 29
[2,1,1,1,1,1] => [6,1] => 37
[1,1,1,1,1,1,1] => [7] => 49
[8] => [1,1,1,1,1,1,1,1] => 8
[7,1] => [2,1,1,1,1,1,1] => 10
[6,2] => [2,2,1,1,1,1] => 12
[6,1,1] => [3,1,1,1,1,1] => 14
[5,3] => [2,2,2,1,1] => 14
[5,2,1] => [3,2,1,1,1] => 16
[5,1,1,1] => [4,1,1,1,1] => 20
[4,4] => [2,2,2,2] => 16
[4,3,1] => [3,2,2,1] => 18
[4,2,2] => [3,3,1,1] => 20
[4,2,1,1] => [4,2,1,1] => 22
[4,1,1,1,1] => [5,1,1,1] => 28
[3,3,2] => [3,3,2] => 22
[3,3,1,1] => [4,2,2] => 24
[3,2,2,1] => [4,3,1] => 26
[3,2,1,1,1] => [5,2,1] => 30
[3,1,1,1,1,1] => [6,1,1] => 38
[2,2,2,2] => [4,4] => 32
[2,2,2,1,1] => [5,3] => 34
[2,2,1,1,1,1] => [6,2] => 40
[2,1,1,1,1,1,1] => [7,1] => 50
[1,1,1,1,1,1,1,1] => [8] => 64
[9] => [1,1,1,1,1,1,1,1,1] => 9
[8,1] => [2,1,1,1,1,1,1,1] => 11
[7,2] => [2,2,1,1,1,1,1] => 13
[7,1,1] => [3,1,1,1,1,1,1] => 15
[6,3] => [2,2,2,1,1,1] => 15
[6,2,1] => [3,2,1,1,1,1] => 17
[6,1,1,1] => [4,1,1,1,1,1] => 21
[5,4] => [2,2,2,2,1] => 17
[5,3,1] => [3,2,2,1,1] => 19
[5,2,2] => [3,3,1,1,1] => 21
[5,2,1,1] => [4,2,1,1,1] => 23
[5,1,1,1,1] => [5,1,1,1,1] => 29
[4,4,1] => [3,2,2,2] => 21
[4,3,2] => [3,3,2,1] => 23
[4,3,1,1] => [4,2,2,1] => 25
[4,2,2,1] => [4,3,1,1] => 27
[4,2,1,1,1] => [5,2,1,1] => 31
[4,1,1,1,1,1] => [6,1,1,1] => 39
[3,3,3] => [3,3,3] => 27
[3,3,2,1] => [4,3,2] => 29
[3,3,1,1,1] => [5,2,2] => 33
[3,2,2,2] => [4,4,1] => 33
[3,2,2,1,1] => [5,3,1] => 35
[3,2,1,1,1,1] => [6,2,1] => 41
[3,1,1,1,1,1,1] => [7,1,1] => 51
[2,2,2,2,1] => [5,4] => 41
[2,2,2,1,1,1] => [6,3] => 45
[2,2,1,1,1,1,1] => [7,2] => 53
[2,1,1,1,1,1,1,1] => [8,1] => 65
[1,1,1,1,1,1,1,1,1] => [9] => 81
[10] => [1,1,1,1,1,1,1,1,1,1] => 10
[9,1] => [2,1,1,1,1,1,1,1,1] => 12
[8,2] => [2,2,1,1,1,1,1,1] => 14
[8,1,1] => [3,1,1,1,1,1,1,1] => 16
[7,3] => [2,2,2,1,1,1,1] => 16
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Description
The sum of the squares of the parts of a partition.
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
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