Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001544
Mapping
St001544: Decorated permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+,+] => 0
[-,+] => 0
[+,-] => 1
[-,-] => 0
[2,1] => 0
[+,+,+] => 0
[-,+,+] => 0
[+,-,+] => 1
[+,+,-] => 2
[-,-,+] => 0
[-,+,-] => 1
[+,-,-] => 2
[-,-,-] => 0
[+,3,2] => 1
[-,3,2] => 0
[2,1,+] => 0
[2,1,-] => 1
[2,3,1] => 0
[3,1,2] => 0
[3,+,1] => 1
[3,-,1] => 1
[+,+,+,+] => 0
[-,+,+,+] => 0
[+,-,+,+] => 1
[+,+,-,+] => 2
[+,+,+,-] => 3
[-,-,+,+] => 0
[-,+,-,+] => 1
[-,+,+,-] => 2
[+,-,-,+] => 2
[+,-,+,-] => 3
[+,+,-,-] => 4
[-,-,-,+] => 0
[-,-,+,-] => 1
[-,+,-,-] => 2
[+,-,-,-] => 3
[-,-,-,-] => 0
[+,+,4,3] => 2
[-,+,4,3] => 1
[+,-,4,3] => 2
[-,-,4,3] => 0
[+,3,2,+] => 1
[-,3,2,+] => 0
[+,3,2,-] => 3
[-,3,2,-] => 1
[+,3,4,2] => 2
[-,3,4,2] => 0
[+,4,2,3] => 1
[-,4,2,3] => 0
[+,4,+,2] => 2
Description
The inversion number of the associated bounded affine permutation. The inversion number is given by $\ell(f) = |\{(i, j) \in [n] \times \mathbb Z \; | \; i < j \text{ and } f(i) > f(j)\}|$