Identifier
-
Mp00322:
Integer partitions
—Loehr-Warrington⟶
Integer partitions
St001564: Integer partitions ⟶ ℤ
Values
[1] => [1] => 1
[2] => [1,1] => 3
[1,1] => [2] => 1
[3] => [1,1,1] => 10
[2,1] => [3] => 1
[1,1,1] => [2,1] => 6
[4] => [1,1,1,1] => 35
[3,1] => [2,1,1] => 30
[2,2] => [4] => 1
[2,1,1] => [2,2] => 3
[1,1,1,1] => [3,1] => 6
[5] => [1,1,1,1,1] => 126
[4,1] => [2,1,1,1] => 140
[3,2] => [5] => 1
[3,1,1] => [4,1] => 6
[2,2,1] => [2,2,1] => 30
[2,1,1,1] => [3,1,1] => 30
[1,1,1,1,1] => [3,2] => 6
[6] => [1,1,1,1,1,1] => 462
[5,1] => [2,1,1,1,1] => 630
[4,2] => [2,2,1,1] => 210
[4,1,1] => [3,1,1,1] => 140
[3,3] => [6] => 1
[3,2,1] => [5,1] => 6
[3,1,1,1] => [3,3] => 3
[2,2,2] => [2,2,2] => 10
[2,2,1,1] => [4,1,1] => 30
[2,1,1,1,1] => [4,2] => 6
[1,1,1,1,1,1] => [3,2,1] => 60
[7] => [1,1,1,1,1,1,1] => 1716
[6,1] => [2,1,1,1,1,1] => 2772
[5,2] => [2,2,1,1,1] => 1260
[5,1,1] => [3,1,1,1,1] => 630
[4,3] => [7] => 1
[4,2,1] => [5,1,1] => 30
[4,1,1,1] => [3,2,1,1] => 420
[3,3,1] => [6,1] => 6
[3,2,2] => [2,2,2,1] => 140
[3,2,1,1] => [5,2] => 6
[3,1,1,1,1] => [3,2,2] => 30
[2,2,2,1] => [4,1,1,1] => 140
[2,2,1,1,1] => [4,3] => 6
[2,1,1,1,1,1] => [3,3,1] => 30
[1,1,1,1,1,1,1] => [4,2,1] => 60
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Description
The value of the forgotten symmetric functions when all variables set to 1.
Let $f_\lambda(x)$ denote the forgotten symmetric functions.
Then the statistic associated with $\lambda$, where $\lambda$ has $\ell$ parts,
is $f_\lambda(1,1,\dotsc,1)$ where there are $\ell$ variables substituted by $1$.
Let $f_\lambda(x)$ denote the forgotten symmetric functions.
Then the statistic associated with $\lambda$, where $\lambda$ has $\ell$ parts,
is $f_\lambda(1,1,\dotsc,1)$ where there are $\ell$ variables substituted by $1$.
Map
Loehr-Warrington
Description
Return a partition whose diagonal inversion number is the length of the preimage.
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