Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001629
Mapping
Mp00255: Decorated permutations —lower permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St001629: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[-,4,+,2] => [3,2,1,4] => [1,1,2] => [2,1] => 0
[-,4,-,2] => [2,1,4,3] => [1,2,1] => [1,1,1] => 1
[3,+,1,+] => [2,1,4,3] => [1,2,1] => [1,1,1] => 1
[3,-,1,+] => [1,4,3,2] => [2,1,1] => [1,2] => 0
[4,-,+,1] => [3,1,4,2] => [1,2,1] => [1,1,1] => 1
[4,+,-,1] => [2,1,4,3] => [1,2,1] => [1,1,1] => 1
[4,3,2,1] => [2,1,4,3] => [1,2,1] => [1,1,1] => 1
[-,+,5,+,3] => [2,4,3,1,5] => [2,1,2] => [1,1,1] => 1
[+,-,5,+,3] => [1,4,3,2,5] => [2,1,2] => [1,1,1] => 1
[-,-,5,+,3] => [4,3,1,2,5] => [1,1,3] => [2,1] => 0
[-,+,5,-,3] => [2,3,1,5,4] => [2,2,1] => [2,1] => 0
[+,-,5,-,3] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[-,-,5,-,3] => [3,1,2,5,4] => [1,3,1] => [1,1,1] => 1
[-,3,5,+,2] => [4,2,1,3,5] => [1,1,3] => [2,1] => 0
[-,3,5,-,2] => [2,1,3,5,4] => [1,3,1] => [1,1,1] => 1
[+,4,+,2,+] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[-,4,+,2,+] => [3,2,5,1,4] => [1,2,2] => [1,2] => 0
[+,4,-,2,+] => [1,2,5,4,3] => [3,1,1] => [1,2] => 0
[-,4,-,2,+] => [2,5,1,4,3] => [2,2,1] => [2,1] => 0
[-,4,+,2,-] => [3,2,1,4,5] => [1,1,3] => [2,1] => 0
[-,4,-,2,-] => [2,1,4,3,5] => [1,2,2] => [1,2] => 0
[-,4,+,5,2] => [3,2,1,4,5] => [1,1,3] => [2,1] => 0
[-,4,-,5,2] => [2,1,4,3,5] => [1,2,2] => [1,2] => 0
[-,4,5,3,2] => [3,2,1,4,5] => [1,1,3] => [2,1] => 0
[-,5,2,+,3] => [2,4,3,1,5] => [2,1,2] => [1,1,1] => 1
[-,5,2,-,3] => [2,3,1,5,4] => [2,2,1] => [2,1] => 0
[-,5,+,2,4] => [3,2,4,1,5] => [1,2,2] => [1,2] => 0
[-,5,-,2,4] => [2,4,1,5,3] => [2,2,1] => [2,1] => 0
[-,5,+,+,2] => [3,4,2,1,5] => [2,1,2] => [1,1,1] => 1
[+,5,-,+,2] => [1,4,2,5,3] => [2,2,1] => [2,1] => 0
[+,5,+,-,2] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[-,5,-,+,2] => [4,2,1,5,3] => [1,1,2,1] => [2,1,1] => 1
[-,5,+,-,2] => [3,2,1,5,4] => [1,1,2,1] => [2,1,1] => 1
[-,5,-,-,2] => [2,1,5,3,4] => [1,2,2] => [1,2] => 0
[-,5,4,2,3] => [2,3,1,5,4] => [2,2,1] => [2,1] => 0
[+,5,4,3,2] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[-,5,4,3,2] => [3,2,1,5,4] => [1,1,2,1] => [2,1,1] => 1
[2,1,5,+,3] => [1,4,3,2,5] => [2,1,2] => [1,1,1] => 1
[2,1,5,-,3] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[2,4,+,1,+] => [3,1,5,2,4] => [1,2,2] => [1,2] => 0
[2,4,-,1,+] => [1,5,2,4,3] => [2,2,1] => [2,1] => 0
[2,5,1,+,3] => [1,4,3,2,5] => [2,1,2] => [1,1,1] => 1
[2,5,1,-,3] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[2,5,+,1,4] => [3,1,4,2,5] => [1,2,2] => [1,2] => 0
[2,5,-,1,4] => [1,4,2,5,3] => [2,2,1] => [2,1] => 0
[2,5,-,+,1] => [4,1,2,5,3] => [1,3,1] => [1,1,1] => 1
[2,5,+,-,1] => [3,1,2,5,4] => [1,3,1] => [1,1,1] => 1
[2,5,4,1,3] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[2,5,4,3,1] => [3,1,2,5,4] => [1,3,1] => [1,1,1] => 1
[3,+,1,+,+] => [2,1,4,5,3] => [1,3,1] => [1,1,1] => 1
Description
The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles.