Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001606
Mp00253: Decorated permutations permutationPermutations
Mp00060: Permutations Robinson-Schensted tableau shapeInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St001606: Integer partitions ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
[2,1] => [2,1] => [1,1]
=> [1]
=> 1
[+,3,2] => [1,3,2] => [2,1]
=> [1]
=> 1
[-,3,2] => [1,3,2] => [2,1]
=> [1]
=> 1
[2,1,+] => [2,1,3] => [2,1]
=> [1]
=> 1
[2,1,-] => [2,1,3] => [2,1]
=> [1]
=> 1
[2,3,1] => [2,3,1] => [2,1]
=> [1]
=> 1
[3,1,2] => [3,1,2] => [2,1]
=> [1]
=> 1
[3,+,1] => [3,2,1] => [1,1,1]
=> [1,1]
=> 0
[3,-,1] => [3,2,1] => [1,1,1]
=> [1,1]
=> 0
[+,+,4,3] => [1,2,4,3] => [3,1]
=> [1]
=> 1
[-,+,4,3] => [1,2,4,3] => [3,1]
=> [1]
=> 1
[+,-,4,3] => [1,2,4,3] => [3,1]
=> [1]
=> 1
[-,-,4,3] => [1,2,4,3] => [3,1]
=> [1]
=> 1
[+,3,2,+] => [1,3,2,4] => [3,1]
=> [1]
=> 1
[-,3,2,+] => [1,3,2,4] => [3,1]
=> [1]
=> 1
[+,3,2,-] => [1,3,2,4] => [3,1]
=> [1]
=> 1
[-,3,2,-] => [1,3,2,4] => [3,1]
=> [1]
=> 1
[+,3,4,2] => [1,3,4,2] => [3,1]
=> [1]
=> 1
[-,3,4,2] => [1,3,4,2] => [3,1]
=> [1]
=> 1
[+,4,2,3] => [1,4,2,3] => [3,1]
=> [1]
=> 1
[-,4,2,3] => [1,4,2,3] => [3,1]
=> [1]
=> 1
[+,4,+,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 0
[-,4,+,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 0
[+,4,-,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 0
[-,4,-,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 0
[2,1,+,+] => [2,1,3,4] => [3,1]
=> [1]
=> 1
[2,1,-,+] => [2,1,3,4] => [3,1]
=> [1]
=> 1
[2,1,+,-] => [2,1,3,4] => [3,1]
=> [1]
=> 1
[2,1,-,-] => [2,1,3,4] => [3,1]
=> [1]
=> 1
[2,1,4,3] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[2,3,1,+] => [2,3,1,4] => [3,1]
=> [1]
=> 1
[2,3,1,-] => [2,3,1,4] => [3,1]
=> [1]
=> 1
[2,3,4,1] => [2,3,4,1] => [3,1]
=> [1]
=> 1
[2,4,1,3] => [2,4,1,3] => [2,2]
=> [2]
=> 2
[2,4,+,1] => [2,4,3,1] => [2,1,1]
=> [1,1]
=> 0
[2,4,-,1] => [2,4,3,1] => [2,1,1]
=> [1,1]
=> 0
[3,1,2,+] => [3,1,2,4] => [3,1]
=> [1]
=> 1
[3,1,2,-] => [3,1,2,4] => [3,1]
=> [1]
=> 1
[3,1,4,2] => [3,1,4,2] => [2,2]
=> [2]
=> 2
[3,+,1,+] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 0
[3,-,1,+] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 0
[3,+,1,-] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 0
[3,-,1,-] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 0
[3,+,4,1] => [3,2,4,1] => [2,1,1]
=> [1,1]
=> 0
[3,-,4,1] => [3,2,4,1] => [2,1,1]
=> [1,1]
=> 0
[3,4,1,2] => [3,4,1,2] => [2,2]
=> [2]
=> 2
[3,4,2,1] => [3,4,2,1] => [2,1,1]
=> [1,1]
=> 0
[4,1,2,3] => [4,1,2,3] => [3,1]
=> [1]
=> 1
[4,1,+,2] => [4,1,3,2] => [2,1,1]
=> [1,1]
=> 0
[4,1,-,2] => [4,1,3,2] => [2,1,1]
=> [1,1]
=> 0
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions.