Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001818
Mapping
St001818: Decorated permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+] => 0
[-] => 0
[+,+] => 0
[-,+] => 1
[+,-] => 1
[-,-] => 0
[2,1] => 0
[+,+,+] => 0
[-,+,+] => 2
[+,-,+] => 2
[+,+,-] => 2
[-,-,+] => 2
[-,+,-] => 2
[+,-,-] => 2
[-,-,-] => 0
[+,3,2] => 1
[-,3,2] => 1
[2,1,+] => 1
[2,1,-] => 1
[2,3,1] => 0
[3,1,2] => 0
[3,+,1] => 1
[3,-,1] => 1
[+,+,+,+] => 0
[-,+,+,+] => 3
[+,-,+,+] => 3
[+,+,-,+] => 3
[+,+,+,-] => 3
[-,-,+,+] => 4
[-,+,-,+] => 4
[-,+,+,-] => 4
[+,-,-,+] => 4
[+,-,+,-] => 4
[+,+,-,-] => 4
[-,-,-,+] => 3
[-,-,+,-] => 3
[-,+,-,-] => 3
[+,-,-,-] => 3
[-,-,-,-] => 0
[+,+,4,3] => 2
[-,+,4,3] => 3
[+,-,4,3] => 3
[-,-,4,3] => 2
[+,3,2,+] => 2
[-,3,2,+] => 3
[+,3,2,-] => 3
[-,3,2,-] => 2
[+,3,4,2] => 2
[-,3,4,2] => 1
[+,4,2,3] => 1
Description
The number of alignments of a decorated permutation. An alignment in a decorated permutation $w$ is a pair of directed edges $(i\mapsto w(i), j\mapsto w(j))$ which can be drawn as distinct noncrossing arcs oriented in the same direction in the circular chord diagram. According to [1], the number of alignments of a decorated permutation on $n$ letters with $k$ anit-exceedances equals and associated Grassmann interval $[u, v]$ equals $k(n - k) - [\ell(v) − \ell(u)]$.