Identifier
-
Mp00255:
Decorated permutations
—lower permutation⟶
Permutations
St001569: Permutations ⟶ ℤ
Values
=>
[+,+]=>[1,2]=>0
[-,+]=>[2,1]=>1
[+,-]=>[1,2]=>0
[-,-]=>[1,2]=>0
[2,1]=>[1,2]=>0
[+,+,+]=>[1,2,3]=>0
[-,+,+]=>[2,3,1]=>1
[+,-,+]=>[1,3,2]=>1
[+,+,-]=>[1,2,3]=>0
[-,-,+]=>[3,1,2]=>1
[-,+,-]=>[2,1,3]=>1
[+,-,-]=>[1,2,3]=>0
[-,-,-]=>[1,2,3]=>0
[+,3,2]=>[1,2,3]=>0
[-,3,2]=>[2,1,3]=>1
[2,1,+]=>[1,3,2]=>1
[2,1,-]=>[1,2,3]=>0
[2,3,1]=>[1,2,3]=>0
[3,1,2]=>[1,2,3]=>0
[3,+,1]=>[2,1,3]=>1
[3,-,1]=>[1,3,2]=>1
[+,+,+,+]=>[1,2,3,4]=>0
[-,+,+,+]=>[2,3,4,1]=>1
[+,-,+,+]=>[1,3,4,2]=>2
[+,+,-,+]=>[1,2,4,3]=>1
[+,+,+,-]=>[1,2,3,4]=>0
[-,-,+,+]=>[3,4,1,2]=>2
[-,+,-,+]=>[2,4,1,3]=>2
[-,+,+,-]=>[2,3,1,4]=>2
[+,-,-,+]=>[1,4,2,3]=>2
[+,-,+,-]=>[1,3,2,4]=>1
[+,+,-,-]=>[1,2,3,4]=>0
[-,-,-,+]=>[4,1,2,3]=>1
[-,-,+,-]=>[3,1,2,4]=>2
[-,+,-,-]=>[2,1,3,4]=>1
[+,-,-,-]=>[1,2,3,4]=>0
[-,-,-,-]=>[1,2,3,4]=>0
[+,+,4,3]=>[1,2,3,4]=>0
[-,+,4,3]=>[2,3,1,4]=>2
[+,-,4,3]=>[1,3,2,4]=>1
[-,-,4,3]=>[3,1,2,4]=>2
[+,3,2,+]=>[1,2,4,3]=>1
[-,3,2,+]=>[2,4,1,3]=>2
[+,3,2,-]=>[1,2,3,4]=>0
[-,3,2,-]=>[2,1,3,4]=>1
[+,3,4,2]=>[1,2,3,4]=>0
[-,3,4,2]=>[2,1,3,4]=>1
[+,4,2,3]=>[1,2,3,4]=>0
[-,4,2,3]=>[2,3,1,4]=>2
[+,4,+,2]=>[1,3,2,4]=>1
[-,4,+,2]=>[3,2,1,4]=>2
[+,4,-,2]=>[1,2,4,3]=>1
[-,4,-,2]=>[2,1,4,3]=>1
[2,1,+,+]=>[1,3,4,2]=>2
[2,1,-,+]=>[1,4,2,3]=>2
[2,1,+,-]=>[1,3,2,4]=>1
[2,1,-,-]=>[1,2,3,4]=>0
[2,1,4,3]=>[1,3,2,4]=>1
[2,3,1,+]=>[1,4,2,3]=>2
[2,3,1,-]=>[1,2,3,4]=>0
[2,3,4,1]=>[1,2,3,4]=>0
[2,4,1,3]=>[1,3,2,4]=>1
[2,4,+,1]=>[3,1,2,4]=>2
[2,4,-,1]=>[1,2,4,3]=>1
[3,1,2,+]=>[1,2,4,3]=>1
[3,1,2,-]=>[1,2,3,4]=>0
[3,1,4,2]=>[1,2,3,4]=>0
[3,+,1,+]=>[2,1,4,3]=>1
[3,-,1,+]=>[1,4,3,2]=>2
[3,+,1,-]=>[2,1,3,4]=>1
[3,-,1,-]=>[1,3,2,4]=>1
[3,+,4,1]=>[2,1,3,4]=>1
[3,-,4,1]=>[1,3,2,4]=>1
[3,4,1,2]=>[1,2,3,4]=>0
[3,4,2,1]=>[2,1,3,4]=>1
[4,1,2,3]=>[1,2,3,4]=>0
[4,1,+,2]=>[1,3,2,4]=>1
[4,1,-,2]=>[1,2,4,3]=>1
[4,+,1,3]=>[2,1,3,4]=>1
[4,-,1,3]=>[1,3,4,2]=>2
[4,+,+,1]=>[2,3,1,4]=>2
[4,-,+,1]=>[3,1,4,2]=>2
[4,+,-,1]=>[2,1,4,3]=>1
[4,-,-,1]=>[1,4,2,3]=>2
[4,3,1,2]=>[1,2,4,3]=>1
[4,3,2,1]=>[2,1,4,3]=>1
[+,+,+,+,+]=>[1,2,3,4,5]=>0
[-,+,+,+,+]=>[2,3,4,5,1]=>1
[+,-,+,+,+]=>[1,3,4,5,2]=>2
[+,+,-,+,+]=>[1,2,4,5,3]=>2
[+,+,+,-,+]=>[1,2,3,5,4]=>1
[+,+,+,+,-]=>[1,2,3,4,5]=>0
[-,-,+,+,+]=>[3,4,5,1,2]=>2
[-,+,-,+,+]=>[2,4,5,1,3]=>2
[-,+,+,-,+]=>[2,3,5,1,4]=>2
[-,+,+,+,-]=>[2,3,4,1,5]=>2
[+,-,-,+,+]=>[1,4,5,2,3]=>2
[+,-,+,-,+]=>[1,3,5,2,4]=>2
[+,-,+,+,-]=>[1,3,4,2,5]=>2
[+,+,-,-,+]=>[1,2,5,3,4]=>2
[+,+,-,+,-]=>[1,2,4,3,5]=>1
[+,+,+,-,-]=>[1,2,3,4,5]=>0
[-,-,-,+,+]=>[4,5,1,2,3]=>2
[-,-,+,-,+]=>[3,5,1,2,4]=>2
[-,-,+,+,-]=>[3,4,1,2,5]=>2
[-,+,-,-,+]=>[2,5,1,3,4]=>2
[-,+,-,+,-]=>[2,4,1,3,5]=>2
[-,+,+,-,-]=>[2,3,1,4,5]=>2
[+,-,-,-,+]=>[1,5,2,3,4]=>2
[+,-,-,+,-]=>[1,4,2,3,5]=>2
[+,-,+,-,-]=>[1,3,2,4,5]=>1
[+,+,-,-,-]=>[1,2,3,4,5]=>0
[-,-,-,-,+]=>[5,1,2,3,4]=>1
[-,-,-,+,-]=>[4,1,2,3,5]=>2
[-,-,+,-,-]=>[3,1,2,4,5]=>2
[-,+,-,-,-]=>[2,1,3,4,5]=>1
[+,-,-,-,-]=>[1,2,3,4,5]=>0
[-,-,-,-,-]=>[1,2,3,4,5]=>0
[+,+,+,5,4]=>[1,2,3,4,5]=>0
[-,+,+,5,4]=>[2,3,4,1,5]=>2
[+,-,+,5,4]=>[1,3,4,2,5]=>2
[+,+,-,5,4]=>[1,2,4,3,5]=>1
[-,-,+,5,4]=>[3,4,1,2,5]=>2
[-,+,-,5,4]=>[2,4,1,3,5]=>2
[+,-,-,5,4]=>[1,4,2,3,5]=>2
[-,-,-,5,4]=>[4,1,2,3,5]=>2
[+,+,4,3,+]=>[1,2,3,5,4]=>1
[-,+,4,3,+]=>[2,3,5,1,4]=>2
[+,-,4,3,+]=>[1,3,5,2,4]=>2
[+,+,4,3,-]=>[1,2,3,4,5]=>0
[-,-,4,3,+]=>[3,5,1,2,4]=>2
[-,+,4,3,-]=>[2,3,1,4,5]=>2
[+,-,4,3,-]=>[1,3,2,4,5]=>1
[-,-,4,3,-]=>[3,1,2,4,5]=>2
[+,+,4,5,3]=>[1,2,3,4,5]=>0
[-,+,4,5,3]=>[2,3,1,4,5]=>2
[+,-,4,5,3]=>[1,3,2,4,5]=>1
[-,-,4,5,3]=>[3,1,2,4,5]=>2
[+,+,5,3,4]=>[1,2,3,4,5]=>0
[-,+,5,3,4]=>[2,3,4,1,5]=>2
[+,-,5,3,4]=>[1,3,4,2,5]=>2
[-,-,5,3,4]=>[3,4,1,2,5]=>2
[+,+,5,+,3]=>[1,2,4,3,5]=>1
[-,+,5,+,3]=>[2,4,3,1,5]=>2
[+,-,5,+,3]=>[1,4,3,2,5]=>2
[+,+,5,-,3]=>[1,2,3,5,4]=>1
[-,-,5,+,3]=>[4,3,1,2,5]=>2
[-,+,5,-,3]=>[2,3,1,5,4]=>2
[+,-,5,-,3]=>[1,3,2,5,4]=>1
[-,-,5,-,3]=>[3,1,2,5,4]=>2
[+,3,2,+,+]=>[1,2,4,5,3]=>2
[-,3,2,+,+]=>[2,4,5,1,3]=>2
[+,3,2,-,+]=>[1,2,5,3,4]=>2
[+,3,2,+,-]=>[1,2,4,3,5]=>1
[-,3,2,-,+]=>[2,5,1,3,4]=>2
[-,3,2,+,-]=>[2,4,1,3,5]=>2
[+,3,2,-,-]=>[1,2,3,4,5]=>0
[-,3,2,-,-]=>[2,1,3,4,5]=>1
[+,3,2,5,4]=>[1,2,4,3,5]=>1
[-,3,2,5,4]=>[2,4,1,3,5]=>2
[+,3,4,2,+]=>[1,2,5,3,4]=>2
[-,3,4,2,+]=>[2,5,1,3,4]=>2
[+,3,4,2,-]=>[1,2,3,4,5]=>0
[-,3,4,2,-]=>[2,1,3,4,5]=>1
[+,3,4,5,2]=>[1,2,3,4,5]=>0
[-,3,4,5,2]=>[2,1,3,4,5]=>1
[+,3,5,2,4]=>[1,2,4,3,5]=>1
[-,3,5,2,4]=>[2,4,1,3,5]=>2
[+,3,5,+,2]=>[1,4,2,3,5]=>2
[-,3,5,+,2]=>[4,2,1,3,5]=>2
[+,3,5,-,2]=>[1,2,3,5,4]=>1
[-,3,5,-,2]=>[2,1,3,5,4]=>1
[+,4,2,3,+]=>[1,2,3,5,4]=>1
[-,4,2,3,+]=>[2,3,5,1,4]=>2
[+,4,2,3,-]=>[1,2,3,4,5]=>0
[-,4,2,3,-]=>[2,3,1,4,5]=>2
[+,4,2,5,3]=>[1,2,3,4,5]=>0
[-,4,2,5,3]=>[2,3,1,4,5]=>2
[+,4,+,2,+]=>[1,3,2,5,4]=>1
[-,4,+,2,+]=>[3,2,5,1,4]=>2
[+,4,-,2,+]=>[1,2,5,4,3]=>2
[+,4,+,2,-]=>[1,3,2,4,5]=>1
[-,4,-,2,+]=>[2,5,1,4,3]=>2
[-,4,+,2,-]=>[3,2,1,4,5]=>2
[+,4,-,2,-]=>[1,2,4,3,5]=>1
[-,4,-,2,-]=>[2,1,4,3,5]=>1
[+,4,+,5,2]=>[1,3,2,4,5]=>1
[-,4,+,5,2]=>[3,2,1,4,5]=>2
[+,4,-,5,2]=>[1,2,4,3,5]=>1
[-,4,-,5,2]=>[2,1,4,3,5]=>1
[+,4,5,2,3]=>[1,2,3,4,5]=>0
[-,4,5,2,3]=>[2,3,1,4,5]=>2
[+,4,5,3,2]=>[1,3,2,4,5]=>1
[-,4,5,3,2]=>[3,2,1,4,5]=>2
[+,5,2,3,4]=>[1,2,3,4,5]=>0
[-,5,2,3,4]=>[2,3,4,1,5]=>2
[+,5,2,+,3]=>[1,2,4,3,5]=>1
[-,5,2,+,3]=>[2,4,3,1,5]=>2
[+,5,2,-,3]=>[1,2,3,5,4]=>1
[-,5,2,-,3]=>[2,3,1,5,4]=>2
[+,5,+,2,4]=>[1,3,2,4,5]=>1
[-,5,+,2,4]=>[3,2,4,1,5]=>2
[+,5,-,2,4]=>[1,2,4,5,3]=>2
[-,5,-,2,4]=>[2,4,1,5,3]=>2
[+,5,+,+,2]=>[1,3,4,2,5]=>2
[-,5,+,+,2]=>[3,4,2,1,5]=>2
[+,5,-,+,2]=>[1,4,2,5,3]=>2
[+,5,+,-,2]=>[1,3,2,5,4]=>1
[-,5,-,+,2]=>[4,2,1,5,3]=>2
[-,5,+,-,2]=>[3,2,1,5,4]=>2
[+,5,-,-,2]=>[1,2,5,3,4]=>2
[-,5,-,-,2]=>[2,1,5,3,4]=>2
[+,5,4,2,3]=>[1,2,3,5,4]=>1
[-,5,4,2,3]=>[2,3,1,5,4]=>2
[+,5,4,3,2]=>[1,3,2,5,4]=>1
[-,5,4,3,2]=>[3,2,1,5,4]=>2
[2,1,+,+,+]=>[1,3,4,5,2]=>2
[2,1,-,+,+]=>[1,4,5,2,3]=>2
[2,1,+,-,+]=>[1,3,5,2,4]=>2
[2,1,+,+,-]=>[1,3,4,2,5]=>2
[2,1,-,-,+]=>[1,5,2,3,4]=>2
[2,1,-,+,-]=>[1,4,2,3,5]=>2
[2,1,+,-,-]=>[1,3,2,4,5]=>1
[2,1,-,-,-]=>[1,2,3,4,5]=>0
[2,1,+,5,4]=>[1,3,4,2,5]=>2
[2,1,-,5,4]=>[1,4,2,3,5]=>2
[2,1,4,3,+]=>[1,3,5,2,4]=>2
[2,1,4,3,-]=>[1,3,2,4,5]=>1
[2,1,4,5,3]=>[1,3,2,4,5]=>1
[2,1,5,3,4]=>[1,3,4,2,5]=>2
[2,1,5,+,3]=>[1,4,3,2,5]=>2
[2,1,5,-,3]=>[1,3,2,5,4]=>1
[2,3,1,+,+]=>[1,4,5,2,3]=>2
[2,3,1,-,+]=>[1,5,2,3,4]=>2
[2,3,1,+,-]=>[1,4,2,3,5]=>2
[2,3,1,-,-]=>[1,2,3,4,5]=>0
[2,3,1,5,4]=>[1,4,2,3,5]=>2
[2,3,4,1,+]=>[1,5,2,3,4]=>2
[2,3,4,1,-]=>[1,2,3,4,5]=>0
[2,3,4,5,1]=>[1,2,3,4,5]=>0
[2,3,5,1,4]=>[1,4,2,3,5]=>2
[2,3,5,+,1]=>[4,1,2,3,5]=>2
[2,3,5,-,1]=>[1,2,3,5,4]=>1
[2,4,1,3,+]=>[1,3,5,2,4]=>2
[2,4,1,3,-]=>[1,3,2,4,5]=>1
[2,4,1,5,3]=>[1,3,2,4,5]=>1
[2,4,+,1,+]=>[3,1,5,2,4]=>2
[2,4,-,1,+]=>[1,5,2,4,3]=>2
[2,4,+,1,-]=>[3,1,2,4,5]=>2
[2,4,-,1,-]=>[1,2,4,3,5]=>1
[2,4,+,5,1]=>[3,1,2,4,5]=>2
[2,4,-,5,1]=>[1,2,4,3,5]=>1
[2,4,5,1,3]=>[1,3,2,4,5]=>1
[2,4,5,3,1]=>[3,1,2,4,5]=>2
[2,5,1,3,4]=>[1,3,4,2,5]=>2
[2,5,1,+,3]=>[1,4,3,2,5]=>2
[2,5,1,-,3]=>[1,3,2,5,4]=>1
[2,5,+,1,4]=>[3,1,4,2,5]=>2
[2,5,-,1,4]=>[1,4,2,5,3]=>2
[2,5,+,+,1]=>[3,4,1,2,5]=>2
[2,5,-,+,1]=>[4,1,2,5,3]=>2
[2,5,+,-,1]=>[3,1,2,5,4]=>2
[2,5,-,-,1]=>[1,2,5,3,4]=>2
[2,5,4,1,3]=>[1,3,2,5,4]=>1
[2,5,4,3,1]=>[3,1,2,5,4]=>2
[3,1,2,+,+]=>[1,2,4,5,3]=>2
[3,1,2,-,+]=>[1,2,5,3,4]=>2
[3,1,2,+,-]=>[1,2,4,3,5]=>1
[3,1,2,-,-]=>[1,2,3,4,5]=>0
[3,1,2,5,4]=>[1,2,4,3,5]=>1
[3,1,4,2,+]=>[1,2,5,3,4]=>2
[3,1,4,2,-]=>[1,2,3,4,5]=>0
[3,1,4,5,2]=>[1,2,3,4,5]=>0
[3,1,5,2,4]=>[1,2,4,3,5]=>1
[3,1,5,+,2]=>[1,4,2,3,5]=>2
[3,1,5,-,2]=>[1,2,3,5,4]=>1
[3,+,1,+,+]=>[2,1,4,5,3]=>2
[3,-,1,+,+]=>[1,4,5,3,2]=>2
[3,+,1,-,+]=>[2,1,5,3,4]=>2
[3,+,1,+,-]=>[2,1,4,3,5]=>1
[3,-,1,-,+]=>[1,5,3,2,4]=>2
[3,-,1,+,-]=>[1,4,3,2,5]=>2
[3,+,1,-,-]=>[2,1,3,4,5]=>1
[3,-,1,-,-]=>[1,3,2,4,5]=>1
[3,+,1,5,4]=>[2,1,4,3,5]=>1
[3,-,1,5,4]=>[1,4,3,2,5]=>2
[3,+,4,1,+]=>[2,1,5,3,4]=>2
[3,-,4,1,+]=>[1,5,3,2,4]=>2
[3,+,4,1,-]=>[2,1,3,4,5]=>1
[3,-,4,1,-]=>[1,3,2,4,5]=>1
[3,+,4,5,1]=>[2,1,3,4,5]=>1
[3,-,4,5,1]=>[1,3,2,4,5]=>1
[3,+,5,1,4]=>[2,1,4,3,5]=>1
[3,-,5,1,4]=>[1,4,3,2,5]=>2
[3,+,5,+,1]=>[2,4,1,3,5]=>2
[3,-,5,+,1]=>[4,1,3,2,5]=>2
[3,+,5,-,1]=>[2,1,3,5,4]=>1
[3,-,5,-,1]=>[1,3,2,5,4]=>1
[3,4,1,2,+]=>[1,2,5,3,4]=>2
[3,4,1,2,-]=>[1,2,3,4,5]=>0
[3,4,1,5,2]=>[1,2,3,4,5]=>0
[3,4,2,1,+]=>[2,1,5,3,4]=>2
[3,4,2,1,-]=>[2,1,3,4,5]=>1
[3,4,2,5,1]=>[2,1,3,4,5]=>1
[3,4,5,1,2]=>[1,2,3,4,5]=>0
[3,4,5,2,1]=>[2,1,3,4,5]=>1
[3,5,1,2,4]=>[1,2,4,3,5]=>1
[3,5,1,+,2]=>[1,4,2,3,5]=>2
[3,5,1,-,2]=>[1,2,3,5,4]=>1
[3,5,2,1,4]=>[2,1,4,3,5]=>1
[3,5,2,+,1]=>[2,4,1,3,5]=>2
[3,5,2,-,1]=>[2,1,3,5,4]=>1
[3,5,4,1,2]=>[1,2,3,5,4]=>1
[3,5,4,2,1]=>[2,1,3,5,4]=>1
[4,1,2,3,+]=>[1,2,3,5,4]=>1
[4,1,2,3,-]=>[1,2,3,4,5]=>0
[4,1,2,5,3]=>[1,2,3,4,5]=>0
[4,1,+,2,+]=>[1,3,2,5,4]=>1
[4,1,-,2,+]=>[1,2,5,4,3]=>2
[4,1,+,2,-]=>[1,3,2,4,5]=>1
[4,1,-,2,-]=>[1,2,4,3,5]=>1
[4,1,+,5,2]=>[1,3,2,4,5]=>1
[4,1,-,5,2]=>[1,2,4,3,5]=>1
[4,1,5,2,3]=>[1,2,3,4,5]=>0
[4,1,5,3,2]=>[1,3,2,4,5]=>1
[4,+,1,3,+]=>[2,1,3,5,4]=>1
[4,-,1,3,+]=>[1,3,5,4,2]=>2
[4,+,1,3,-]=>[2,1,3,4,5]=>1
[4,-,1,3,-]=>[1,3,4,2,5]=>2
[4,+,1,5,3]=>[2,1,3,4,5]=>1
[4,-,1,5,3]=>[1,3,4,2,5]=>2
[4,+,+,1,+]=>[2,3,1,5,4]=>2
[4,-,+,1,+]=>[3,1,5,4,2]=>2
[4,+,-,1,+]=>[2,1,5,4,3]=>2
[4,+,+,1,-]=>[2,3,1,4,5]=>2
[4,-,-,1,+]=>[1,5,4,2,3]=>2
[4,-,+,1,-]=>[3,1,4,2,5]=>2
[4,+,-,1,-]=>[2,1,4,3,5]=>1
[4,-,-,1,-]=>[1,4,2,3,5]=>2
[4,+,+,5,1]=>[2,3,1,4,5]=>2
[4,-,+,5,1]=>[3,1,4,2,5]=>2
[4,+,-,5,1]=>[2,1,4,3,5]=>1
[4,-,-,5,1]=>[1,4,2,3,5]=>2
[4,+,5,1,3]=>[2,1,3,4,5]=>1
[4,-,5,1,3]=>[1,3,4,2,5]=>2
[4,+,5,3,1]=>[2,3,1,4,5]=>2
[4,-,5,3,1]=>[3,1,4,2,5]=>2
[4,3,1,2,+]=>[1,2,5,4,3]=>2
[4,3,1,2,-]=>[1,2,4,3,5]=>1
[4,3,1,5,2]=>[1,2,4,3,5]=>1
[4,3,2,1,+]=>[2,1,5,4,3]=>2
[4,3,2,1,-]=>[2,1,4,3,5]=>1
[4,3,2,5,1]=>[2,1,4,3,5]=>1
[4,3,5,1,2]=>[1,2,4,3,5]=>1
[4,3,5,2,1]=>[2,1,4,3,5]=>1
[4,5,1,2,3]=>[1,2,3,4,5]=>0
[4,5,1,3,2]=>[1,3,2,4,5]=>1
[4,5,2,1,3]=>[2,1,3,4,5]=>1
[4,5,2,3,1]=>[2,3,1,4,5]=>2
[4,5,+,1,2]=>[3,1,2,4,5]=>2
[4,5,-,1,2]=>[1,2,4,5,3]=>2
[4,5,+,2,1]=>[3,2,1,4,5]=>2
[4,5,-,2,1]=>[2,1,4,5,3]=>2
[5,1,2,3,4]=>[1,2,3,4,5]=>0
[5,1,2,+,3]=>[1,2,4,3,5]=>1
[5,1,2,-,3]=>[1,2,3,5,4]=>1
[5,1,+,2,4]=>[1,3,2,4,5]=>1
[5,1,-,2,4]=>[1,2,4,5,3]=>2
[5,1,+,+,2]=>[1,3,4,2,5]=>2
[5,1,-,+,2]=>[1,4,2,5,3]=>2
[5,1,+,-,2]=>[1,3,2,5,4]=>1
[5,1,-,-,2]=>[1,2,5,3,4]=>2
[5,1,4,2,3]=>[1,2,3,5,4]=>1
[5,1,4,3,2]=>[1,3,2,5,4]=>1
[5,+,1,3,4]=>[2,1,3,4,5]=>1
[5,-,1,3,4]=>[1,3,4,5,2]=>2
[5,+,1,+,3]=>[2,1,4,3,5]=>1
[5,-,1,+,3]=>[1,4,3,5,2]=>2
[5,+,1,-,3]=>[2,1,3,5,4]=>1
[5,-,1,-,3]=>[1,3,5,2,4]=>2
[5,+,+,1,4]=>[2,3,1,4,5]=>2
[5,-,+,1,4]=>[3,1,4,5,2]=>2
[5,+,-,1,4]=>[2,1,4,5,3]=>2
[5,-,-,1,4]=>[1,4,5,2,3]=>2
[5,+,+,+,1]=>[2,3,4,1,5]=>2
[5,-,+,+,1]=>[3,4,1,5,2]=>2
[5,+,-,+,1]=>[2,4,1,5,3]=>2
[5,+,+,-,1]=>[2,3,1,5,4]=>2
[5,-,-,+,1]=>[4,1,5,2,3]=>2
[5,-,+,-,1]=>[3,1,5,2,4]=>2
[5,+,-,-,1]=>[2,1,5,3,4]=>2
[5,-,-,-,1]=>[1,5,2,3,4]=>2
[5,+,4,1,3]=>[2,1,3,5,4]=>1
[5,-,4,1,3]=>[1,3,5,2,4]=>2
[5,+,4,3,1]=>[2,3,1,5,4]=>2
[5,-,4,3,1]=>[3,1,5,2,4]=>2
[5,3,1,2,4]=>[1,2,4,5,3]=>2
[5,3,1,+,2]=>[1,4,2,5,3]=>2
[5,3,1,-,2]=>[1,2,5,3,4]=>2
[5,3,2,1,4]=>[2,1,4,5,3]=>2
[5,3,2,+,1]=>[2,4,1,5,3]=>2
[5,3,2,-,1]=>[2,1,5,3,4]=>2
[5,3,4,1,2]=>[1,2,5,3,4]=>2
[5,3,4,2,1]=>[2,1,5,3,4]=>2
[5,4,1,2,3]=>[1,2,3,5,4]=>1
[5,4,1,3,2]=>[1,3,2,5,4]=>1
[5,4,2,1,3]=>[2,1,3,5,4]=>1
[5,4,2,3,1]=>[2,3,1,5,4]=>2
[5,4,+,1,2]=>[3,1,2,5,4]=>2
[5,4,-,1,2]=>[1,2,5,4,3]=>2
[5,4,+,2,1]=>[3,2,1,5,4]=>2
[5,4,-,2,1]=>[2,1,5,4,3]=>2
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Description
The maximal modular displacement of a permutation.
This is $\max_{1\leq i \leq n} \left(\min(\pi(i)-i\pmod n, i-\pi(i)\pmod n)\right)$ for a permutation $\pi$ of $\{1,\dots,n\}$.
This is $\max_{1\leq i \leq n} \left(\min(\pi(i)-i\pmod n, i-\pi(i)\pmod n)\right)$ for a permutation $\pi$ of $\{1,\dots,n\}$.
Map
lower permutation
Description
The lower bound in the Grassmann interval corresponding to the decorated permutation.
Let $I$ be the anti-exceedance set of a decorated permutation $w$. Let $v$ be the $k$-Grassmannian permutation determined by $v[k] = w^{-1}(I)$ and let $u$ be the permutation satisfying $u = wv$. Then $[u, v]$ is the Grassmann interval corresponding to $w$.
This map returns $u$.
Let $I$ be the anti-exceedance set of a decorated permutation $w$. Let $v$ be the $k$-Grassmannian permutation determined by $v[k] = w^{-1}(I)$ and let $u$ be the permutation satisfying $u = wv$. Then $[u, v]$ is the Grassmann interval corresponding to $w$.
This map returns $u$.
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