Identifier
-
Mp00322:
Integer partitions
—Loehr-Warrington⟶
Integer partitions
St000511: Integer partitions ⟶ ℤ
Values
[1] => [1] => 2
[2] => [1,1] => 4
[1,1] => [2] => 2
[3] => [1,1,1] => 8
[2,1] => [3] => 2
[1,1,1] => [2,1] => 4
[4] => [1,1,1,1] => 16
[3,1] => [2,1,1] => 8
[2,2] => [4] => 2
[2,1,1] => [2,2] => 4
[1,1,1,1] => [3,1] => 4
[5] => [1,1,1,1,1] => 32
[4,1] => [2,1,1,1] => 16
[3,2] => [5] => 2
[3,1,1] => [4,1] => 4
[2,2,1] => [2,2,1] => 8
[2,1,1,1] => [3,1,1] => 8
[1,1,1,1,1] => [3,2] => 4
[6] => [1,1,1,1,1,1] => 64
[5,1] => [2,1,1,1,1] => 32
[4,2] => [2,2,1,1] => 16
[4,1,1] => [3,1,1,1] => 16
[3,3] => [6] => 2
[3,2,1] => [5,1] => 4
[3,1,1,1] => [3,3] => 4
[2,2,2] => [2,2,2] => 8
[2,2,1,1] => [4,1,1] => 8
[2,1,1,1,1] => [4,2] => 4
[1,1,1,1,1,1] => [3,2,1] => 8
[7] => [1,1,1,1,1,1,1] => 128
[6,1] => [2,1,1,1,1,1] => 64
[5,2] => [2,2,1,1,1] => 32
[5,1,1] => [3,1,1,1,1] => 32
[4,3] => [7] => 2
[4,2,1] => [5,1,1] => 8
[4,1,1,1] => [3,2,1,1] => 16
[3,3,1] => [6,1] => 4
[3,2,2] => [2,2,2,1] => 16
[3,2,1,1] => [5,2] => 4
[3,1,1,1,1] => [3,2,2] => 8
[2,2,2,1] => [4,1,1,1] => 16
[2,2,1,1,1] => [4,3] => 4
[2,1,1,1,1,1] => [3,3,1] => 8
[1,1,1,1,1,1,1] => [4,2,1] => 8
[8] => [1,1,1,1,1,1,1,1] => 256
[7,1] => [2,1,1,1,1,1,1] => 128
[6,2] => [2,2,1,1,1,1] => 64
[6,1,1] => [3,1,1,1,1,1] => 64
[5,3] => [2,2,2,1,1] => 32
[5,2,1] => [4,1,1,1,1] => 32
[5,1,1,1] => [3,2,1,1,1] => 32
[4,4] => [8] => 2
[4,3,1] => [7,1] => 4
[4,2,2] => [6,1,1] => 8
[4,2,1,1] => [4,4] => 4
[4,1,1,1,1] => [5,2,1] => 8
[3,3,2] => [2,2,2,2] => 16
[3,3,1,1] => [6,2] => 4
[3,2,2,1] => [3,2,2,1] => 16
[3,2,1,1,1] => [3,3,1,1] => 16
[3,1,1,1,1,1] => [4,2,1,1] => 16
[2,2,2,2] => [5,1,1,1] => 16
[2,2,2,1,1] => [5,3] => 4
[2,2,1,1,1,1] => [3,3,2] => 8
[2,1,1,1,1,1,1] => [4,2,2] => 8
[1,1,1,1,1,1,1,1] => [4,3,1] => 8
[9] => [1,1,1,1,1,1,1,1,1] => 512
[8,1] => [2,1,1,1,1,1,1,1] => 256
[7,2] => [2,2,1,1,1,1,1] => 128
[7,1,1] => [3,1,1,1,1,1,1] => 128
[6,3] => [2,2,2,1,1,1] => 64
[6,2,1] => [4,1,1,1,1,1] => 64
[6,1,1,1] => [3,2,1,1,1,1] => 64
[5,4] => [9] => 2
[5,3,1] => [3,2,2,1,1] => 32
[5,2,2] => [6,1,1,1] => 16
[5,2,1,1] => [3,3,1,1,1] => 32
[5,1,1,1,1] => [4,2,1,1,1] => 32
[4,4,1] => [8,1] => 4
[4,3,2] => [7,1,1] => 8
[4,3,1,1] => [7,2] => 4
[4,2,2,1] => [6,3] => 4
[4,2,1,1,1] => [6,2,1] => 8
[4,1,1,1,1,1] => [4,4,1] => 8
[3,3,3] => [2,2,2,2,1] => 32
[3,3,2,1] => [3,2,2,2] => 16
[3,3,1,1,1] => [5,2,1,1] => 16
[3,2,2,2] => [5,1,1,1,1] => 32
[3,2,2,1,1] => [3,3,3] => 8
[3,2,1,1,1,1] => [5,2,2] => 8
[3,1,1,1,1,1,1] => [5,3,1] => 8
[2,2,2,2,1] => [5,4] => 4
[2,2,2,1,1,1] => [3,3,2,1] => 16
[2,2,1,1,1,1,1] => [4,2,2,1] => 16
[2,1,1,1,1,1,1,1] => [4,3,1,1] => 16
[1,1,1,1,1,1,1,1,1] => [4,3,2] => 8
[10] => [1,1,1,1,1,1,1,1,1,1] => 1024
[9,1] => [2,1,1,1,1,1,1,1,1] => 512
[8,2] => [2,2,1,1,1,1,1,1] => 256
[8,1,1] => [3,1,1,1,1,1,1,1] => 256
[7,3] => [2,2,2,1,1,1,1] => 128
>>> Load all 272 entries. <<<
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Description
The number of invariant subsets when acting with a permutation of given cycle type.
Map
Loehr-Warrington
Description
Return a partition whose diagonal inversion number is the length of the preimage.
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