Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001564
Mapping
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001564: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [1,1]
 => [1]
 => 1
[1,2,3] => [1,3,2] => [2,1]
 => [1]
 => 1
[1,3,2] => [1,3,2] => [2,1]
 => [1]
 => 1
[2,1,3] => [2,1,3] => [2,1]
 => [1]
 => 1
[3,2,1] => [3,2,1] => [2,1]
 => [1]
 => 1
[1,2,3,4] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 3
[1,2,4,3] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 3
[1,3,2,4] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 3
[1,3,4,2] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 3
[1,4,2,3] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 3
[1,4,3,2] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 3
[2,1,3,4] => [2,1,4,3] => [2,2]
 => [2]
 => 1
[2,1,4,3] => [2,1,4,3] => [2,2]
 => [2]
 => 1
[2,3,4,1] => [2,4,3,1] => [3,1]
 => [1]
 => 1
[2,4,3,1] => [2,4,3,1] => [3,1]
 => [1]
 => 1
[3,2,1,4] => [3,2,1,4] => [2,1,1]
 => [1,1]
 => 3
[3,2,4,1] => [3,2,4,1] => [3,1]
 => [1]
 => 1
[3,4,1,2] => [3,4,1,2] => [2,2]
 => [2]
 => 1
[4,1,2,3] => [4,1,3,2] => [3,1]
 => [1]
 => 1
[4,1,3,2] => [4,1,3,2] => [3,1]
 => [1]
 => 1
[4,2,1,3] => [4,2,1,3] => [3,1]
 => [1]
 => 1
[4,2,3,1] => [4,2,3,1] => [2,1,1]
 => [1,1]
 => 3
[4,3,2,1] => [4,3,2,1] => [2,2]
 => [2]
 => 1
[1,2,3,4,5] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,2,3,5,4] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,2,4,3,5] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,2,4,5,3] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,2,5,3,4] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,2,5,4,3] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,3,2,4,5] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,3,2,5,4] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,3,4,2,5] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,3,4,5,2] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,3,5,2,4] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,3,5,4,2] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,4,2,3,5] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,4,2,5,3] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,4,3,2,5] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,4,3,5,2] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,4,5,2,3] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,4,5,3,2] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,5,2,3,4] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,5,2,4,3] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,5,3,2,4] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,5,3,4,2] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,5,4,2,3] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[1,5,4,3,2] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 6
[2,1,3,4,5] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 6
[2,1,3,5,4] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 6
[2,1,4,3,5] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 6
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 $1$.