Identifier
- St000317: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>0
[2,1]=>0
[1,2,3]=>0
[1,3,2]=>0
[2,1,3]=>0
[2,3,1]=>0
[3,1,2]=>1
[3,2,1]=>0
[1,2,3,4]=>0
[1,2,4,3]=>0
[1,3,2,4]=>0
[1,3,4,2]=>0
[1,4,2,3]=>1
[1,4,3,2]=>0
[2,1,3,4]=>0
[2,1,4,3]=>0
[2,3,1,4]=>0
[2,3,4,1]=>0
[2,4,1,3]=>1
[2,4,3,1]=>0
[3,1,2,4]=>1
[3,1,4,2]=>1
[3,2,1,4]=>0
[3,2,4,1]=>0
[3,4,1,2]=>0
[3,4,2,1]=>1
[4,1,2,3]=>2
[4,1,3,2]=>1
[4,2,1,3]=>1
[4,2,3,1]=>0
[4,3,1,2]=>1
[4,3,2,1]=>0
[1,2,3,4,5]=>0
[1,2,3,5,4]=>0
[1,2,4,3,5]=>0
[1,2,4,5,3]=>0
[1,2,5,3,4]=>1
[1,2,5,4,3]=>0
[1,3,2,4,5]=>0
[1,3,2,5,4]=>0
[1,3,4,2,5]=>0
[1,3,4,5,2]=>0
[1,3,5,2,4]=>1
[1,3,5,4,2]=>0
[1,4,2,3,5]=>1
[1,4,2,5,3]=>1
[1,4,3,2,5]=>0
[1,4,3,5,2]=>0
[1,4,5,2,3]=>0
[1,4,5,3,2]=>1
[1,5,2,3,4]=>2
[1,5,2,4,3]=>1
[1,5,3,2,4]=>1
[1,5,3,4,2]=>0
[1,5,4,2,3]=>1
[1,5,4,3,2]=>0
[2,1,3,4,5]=>0
[2,1,3,5,4]=>0
[2,1,4,3,5]=>0
[2,1,4,5,3]=>0
[2,1,5,3,4]=>1
[2,1,5,4,3]=>0
[2,3,1,4,5]=>0
[2,3,1,5,4]=>0
[2,3,4,1,5]=>0
[2,3,4,5,1]=>0
[2,3,5,1,4]=>1
[2,3,5,4,1]=>0
[2,4,1,3,5]=>1
[2,4,1,5,3]=>1
[2,4,3,1,5]=>0
[2,4,3,5,1]=>0
[2,4,5,1,3]=>0
[2,4,5,3,1]=>1
[2,5,1,3,4]=>2
[2,5,1,4,3]=>1
[2,5,3,1,4]=>1
[2,5,3,4,1]=>0
[2,5,4,1,3]=>1
[2,5,4,3,1]=>0
[3,1,2,4,5]=>1
[3,1,2,5,4]=>1
[3,1,4,2,5]=>1
[3,1,4,5,2]=>1
[3,1,5,2,4]=>2
[3,1,5,4,2]=>1
[3,2,1,4,5]=>0
[3,2,1,5,4]=>0
[3,2,4,1,5]=>0
[3,2,4,5,1]=>0
[3,2,5,1,4]=>1
[3,2,5,4,1]=>0
[3,4,1,2,5]=>0
[3,4,1,5,2]=>0
[3,4,2,1,5]=>1
[3,4,2,5,1]=>1
[3,4,5,1,2]=>1
[3,4,5,2,1]=>0
[3,5,1,2,4]=>1
[3,5,1,4,2]=>0
[3,5,2,1,4]=>2
[3,5,2,4,1]=>1
[3,5,4,1,2]=>0
[3,5,4,2,1]=>1
[4,1,2,3,5]=>2
[4,1,2,5,3]=>2
[4,1,3,2,5]=>1
[4,1,3,5,2]=>1
[4,1,5,2,3]=>1
[4,1,5,3,2]=>2
[4,2,1,3,5]=>1
[4,2,1,5,3]=>1
[4,2,3,1,5]=>0
[4,2,3,5,1]=>0
[4,2,5,1,3]=>0
[4,2,5,3,1]=>1
[4,3,1,2,5]=>1
[4,3,1,5,2]=>1
[4,3,2,1,5]=>0
[4,3,2,5,1]=>0
[4,3,5,1,2]=>0
[4,3,5,2,1]=>1
[4,5,1,2,3]=>2
[4,5,1,3,2]=>1
[4,5,2,1,3]=>1
[4,5,2,3,1]=>2
[4,5,3,1,2]=>0
[4,5,3,2,1]=>1
[5,1,2,3,4]=>3
[5,1,2,4,3]=>2
[5,1,3,2,4]=>2
[5,1,3,4,2]=>1
[5,1,4,2,3]=>2
[5,1,4,3,2]=>1
[5,2,1,3,4]=>2
[5,2,1,4,3]=>1
[5,2,3,1,4]=>1
[5,2,3,4,1]=>0
[5,2,4,1,3]=>1
[5,2,4,3,1]=>0
[5,3,1,2,4]=>2
[5,3,1,4,2]=>1
[5,3,2,1,4]=>1
[5,3,2,4,1]=>0
[5,3,4,1,2]=>1
[5,3,4,2,1]=>0
[5,4,1,2,3]=>1
[5,4,1,3,2]=>2
[5,4,2,1,3]=>2
[5,4,2,3,1]=>1
[5,4,3,1,2]=>1
[5,4,3,2,1]=>0
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>0
[1,2,3,5,4,6]=>0
[1,2,3,5,6,4]=>0
[1,2,3,6,4,5]=>1
[1,2,3,6,5,4]=>0
[1,2,4,3,5,6]=>0
[1,2,4,3,6,5]=>0
[1,2,4,5,3,6]=>0
[1,2,4,5,6,3]=>0
[1,2,4,6,3,5]=>1
[1,2,4,6,5,3]=>0
[1,2,5,3,4,6]=>1
[1,2,5,3,6,4]=>1
[1,2,5,4,3,6]=>0
[1,2,5,4,6,3]=>0
[1,2,5,6,3,4]=>0
[1,2,5,6,4,3]=>1
[1,2,6,3,4,5]=>2
[1,2,6,3,5,4]=>1
[1,2,6,4,3,5]=>1
[1,2,6,4,5,3]=>0
[1,2,6,5,3,4]=>1
[1,2,6,5,4,3]=>0
[1,3,2,4,5,6]=>0
[1,3,2,4,6,5]=>0
[1,3,2,5,4,6]=>0
[1,3,2,5,6,4]=>0
[1,3,2,6,4,5]=>1
[1,3,2,6,5,4]=>0
[1,3,4,2,5,6]=>0
[1,3,4,2,6,5]=>0
[1,3,4,5,2,6]=>0
[1,3,4,5,6,2]=>0
[1,3,4,6,2,5]=>1
[1,3,4,6,5,2]=>0
[1,3,5,2,4,6]=>1
[1,3,5,2,6,4]=>1
[1,3,5,4,2,6]=>0
[1,3,5,4,6,2]=>0
[1,3,5,6,2,4]=>0
[1,3,5,6,4,2]=>1
[1,3,6,2,4,5]=>2
[1,3,6,2,5,4]=>1
[1,3,6,4,2,5]=>1
[1,3,6,4,5,2]=>0
[1,3,6,5,2,4]=>1
[1,3,6,5,4,2]=>0
[1,4,2,3,5,6]=>1
[1,4,2,3,6,5]=>1
[1,4,2,5,3,6]=>1
[1,4,2,5,6,3]=>1
[1,4,2,6,3,5]=>2
[1,4,2,6,5,3]=>1
[1,4,3,2,5,6]=>0
[1,4,3,2,6,5]=>0
[1,4,3,5,2,6]=>0
[1,4,3,5,6,2]=>0
[1,4,3,6,2,5]=>1
[1,4,3,6,5,2]=>0
[1,4,5,2,3,6]=>0
[1,4,5,2,6,3]=>0
[1,4,5,3,2,6]=>1
[1,4,5,3,6,2]=>1
[1,4,5,6,2,3]=>1
[1,4,5,6,3,2]=>0
[1,4,6,2,3,5]=>1
[1,4,6,2,5,3]=>0
[1,4,6,3,2,5]=>2
[1,4,6,3,5,2]=>1
[1,4,6,5,2,3]=>0
[1,4,6,5,3,2]=>1
[1,5,2,3,4,6]=>2
[1,5,2,3,6,4]=>2
[1,5,2,4,3,6]=>1
[1,5,2,4,6,3]=>1
[1,5,2,6,3,4]=>1
[1,5,2,6,4,3]=>2
[1,5,3,2,4,6]=>1
[1,5,3,2,6,4]=>1
[1,5,3,4,2,6]=>0
[1,5,3,4,6,2]=>0
[1,5,3,6,2,4]=>0
[1,5,3,6,4,2]=>1
[1,5,4,2,3,6]=>1
[1,5,4,2,6,3]=>1
[1,5,4,3,2,6]=>0
[1,5,4,3,6,2]=>0
[1,5,4,6,2,3]=>0
[1,5,4,6,3,2]=>1
[1,5,6,2,3,4]=>2
[1,5,6,2,4,3]=>1
[1,5,6,3,2,4]=>1
[1,5,6,3,4,2]=>2
[1,5,6,4,2,3]=>0
[1,5,6,4,3,2]=>1
[1,6,2,3,4,5]=>3
[1,6,2,3,5,4]=>2
[1,6,2,4,3,5]=>2
[1,6,2,4,5,3]=>1
[1,6,2,5,3,4]=>2
[1,6,2,5,4,3]=>1
[1,6,3,2,4,5]=>2
[1,6,3,2,5,4]=>1
[1,6,3,4,2,5]=>1
[1,6,3,4,5,2]=>0
[1,6,3,5,2,4]=>1
[1,6,3,5,4,2]=>0
[1,6,4,2,3,5]=>2
[1,6,4,2,5,3]=>1
[1,6,4,3,2,5]=>1
[1,6,4,3,5,2]=>0
[1,6,4,5,2,3]=>1
[1,6,4,5,3,2]=>0
[1,6,5,2,3,4]=>1
[1,6,5,2,4,3]=>2
[1,6,5,3,2,4]=>2
[1,6,5,3,4,2]=>1
[1,6,5,4,2,3]=>1
[1,6,5,4,3,2]=>0
[2,1,3,4,5,6]=>0
[2,1,3,4,6,5]=>0
[2,1,3,5,4,6]=>0
[2,1,3,5,6,4]=>0
[2,1,3,6,4,5]=>1
[2,1,3,6,5,4]=>0
[2,1,4,3,5,6]=>0
[2,1,4,3,6,5]=>0
[2,1,4,5,3,6]=>0
[2,1,4,5,6,3]=>0
[2,1,4,6,3,5]=>1
[2,1,4,6,5,3]=>0
[2,1,5,3,4,6]=>1
[2,1,5,3,6,4]=>1
[2,1,5,4,3,6]=>0
[2,1,5,4,6,3]=>0
[2,1,5,6,3,4]=>0
[2,1,5,6,4,3]=>1
[2,1,6,3,4,5]=>2
[2,1,6,3,5,4]=>1
[2,1,6,4,3,5]=>1
[2,1,6,4,5,3]=>0
[2,1,6,5,3,4]=>1
[2,1,6,5,4,3]=>0
[2,3,1,4,5,6]=>0
[2,3,1,4,6,5]=>0
[2,3,1,5,4,6]=>0
[2,3,1,5,6,4]=>0
[2,3,1,6,4,5]=>1
[2,3,1,6,5,4]=>0
[2,3,4,1,5,6]=>0
[2,3,4,1,6,5]=>0
[2,3,4,5,1,6]=>0
[2,3,4,5,6,1]=>0
[2,3,4,6,1,5]=>1
[2,3,4,6,5,1]=>0
[2,3,5,1,4,6]=>1
[2,3,5,1,6,4]=>1
[2,3,5,4,1,6]=>0
[2,3,5,4,6,1]=>0
[2,3,5,6,1,4]=>0
[2,3,5,6,4,1]=>1
[2,3,6,1,4,5]=>2
[2,3,6,1,5,4]=>1
[2,3,6,4,1,5]=>1
[2,3,6,4,5,1]=>0
[2,3,6,5,1,4]=>1
[2,3,6,5,4,1]=>0
[2,4,1,3,5,6]=>1
[2,4,1,3,6,5]=>1
[2,4,1,5,3,6]=>1
[2,4,1,5,6,3]=>1
[2,4,1,6,3,5]=>2
[2,4,1,6,5,3]=>1
[2,4,3,1,5,6]=>0
[2,4,3,1,6,5]=>0
[2,4,3,5,1,6]=>0
[2,4,3,5,6,1]=>0
[2,4,3,6,1,5]=>1
[2,4,3,6,5,1]=>0
[2,4,5,1,3,6]=>0
[2,4,5,1,6,3]=>0
[2,4,5,3,1,6]=>1
[2,4,5,3,6,1]=>1
[2,4,5,6,1,3]=>1
[2,4,5,6,3,1]=>0
[2,4,6,1,3,5]=>1
[2,4,6,1,5,3]=>0
[2,4,6,3,1,5]=>2
[2,4,6,3,5,1]=>1
[2,4,6,5,1,3]=>0
[2,4,6,5,3,1]=>1
[2,5,1,3,4,6]=>2
[2,5,1,3,6,4]=>2
[2,5,1,4,3,6]=>1
[2,5,1,4,6,3]=>1
[2,5,1,6,3,4]=>1
[2,5,1,6,4,3]=>2
[2,5,3,1,4,6]=>1
[2,5,3,1,6,4]=>1
[2,5,3,4,1,6]=>0
[2,5,3,4,6,1]=>0
[2,5,3,6,1,4]=>0
[2,5,3,6,4,1]=>1
[2,5,4,1,3,6]=>1
[2,5,4,1,6,3]=>1
[2,5,4,3,1,6]=>0
[2,5,4,3,6,1]=>0
[2,5,4,6,1,3]=>0
[2,5,4,6,3,1]=>1
[2,5,6,1,3,4]=>2
[2,5,6,1,4,3]=>1
[2,5,6,3,1,4]=>1
[2,5,6,3,4,1]=>2
[2,5,6,4,1,3]=>0
[2,5,6,4,3,1]=>1
[2,6,1,3,4,5]=>3
[2,6,1,3,5,4]=>2
[2,6,1,4,3,5]=>2
[2,6,1,4,5,3]=>1
[2,6,1,5,3,4]=>2
[2,6,1,5,4,3]=>1
[2,6,3,1,4,5]=>2
[2,6,3,1,5,4]=>1
[2,6,3,4,1,5]=>1
[2,6,3,4,5,1]=>0
[2,6,3,5,1,4]=>1
[2,6,3,5,4,1]=>0
[2,6,4,1,3,5]=>2
[2,6,4,1,5,3]=>1
[2,6,4,3,1,5]=>1
[2,6,4,3,5,1]=>0
[2,6,4,5,1,3]=>1
[2,6,4,5,3,1]=>0
[2,6,5,1,3,4]=>1
[2,6,5,1,4,3]=>2
[2,6,5,3,1,4]=>2
[2,6,5,3,4,1]=>1
[2,6,5,4,1,3]=>1
[2,6,5,4,3,1]=>0
[3,1,2,4,5,6]=>1
[3,1,2,4,6,5]=>1
[3,1,2,5,4,6]=>1
[3,1,2,5,6,4]=>1
[3,1,2,6,4,5]=>2
[3,1,2,6,5,4]=>1
[3,1,4,2,5,6]=>1
[3,1,4,2,6,5]=>1
[3,1,4,5,2,6]=>1
[3,1,4,5,6,2]=>1
[3,1,4,6,2,5]=>2
[3,1,4,6,5,2]=>1
[3,1,5,2,4,6]=>2
[3,1,5,2,6,4]=>2
[3,1,5,4,2,6]=>1
[3,1,5,4,6,2]=>1
[3,1,5,6,2,4]=>1
[3,1,5,6,4,2]=>2
[3,1,6,2,4,5]=>3
[3,1,6,2,5,4]=>2
[3,1,6,4,2,5]=>2
[3,1,6,4,5,2]=>1
[3,1,6,5,2,4]=>2
[3,1,6,5,4,2]=>1
[3,2,1,4,5,6]=>0
[3,2,1,4,6,5]=>0
[3,2,1,5,4,6]=>0
[3,2,1,5,6,4]=>0
[3,2,1,6,4,5]=>1
[3,2,1,6,5,4]=>0
[3,2,4,1,5,6]=>0
[3,2,4,1,6,5]=>0
[3,2,4,5,1,6]=>0
[3,2,4,5,6,1]=>0
[3,2,4,6,1,5]=>1
[3,2,4,6,5,1]=>0
[3,2,5,1,4,6]=>1
[3,2,5,1,6,4]=>1
[3,2,5,4,1,6]=>0
[3,2,5,4,6,1]=>0
[3,2,5,6,1,4]=>0
[3,2,5,6,4,1]=>1
[3,2,6,1,4,5]=>2
[3,2,6,1,5,4]=>1
[3,2,6,4,1,5]=>1
[3,2,6,4,5,1]=>0
[3,2,6,5,1,4]=>1
[3,2,6,5,4,1]=>0
[3,4,1,2,5,6]=>0
[3,4,1,2,6,5]=>0
[3,4,1,5,2,6]=>0
[3,4,1,5,6,2]=>0
[3,4,1,6,2,5]=>1
[3,4,1,6,5,2]=>0
[3,4,2,1,5,6]=>1
[3,4,2,1,6,5]=>1
[3,4,2,5,1,6]=>1
[3,4,2,5,6,1]=>1
[3,4,2,6,1,5]=>2
[3,4,2,6,5,1]=>1
[3,4,5,1,2,6]=>1
[3,4,5,1,6,2]=>1
[3,4,5,2,1,6]=>0
[3,4,5,2,6,1]=>0
[3,4,5,6,1,2]=>0
[3,4,5,6,2,1]=>1
[3,4,6,1,2,5]=>2
[3,4,6,1,5,2]=>1
[3,4,6,2,1,5]=>1
[3,4,6,2,5,1]=>0
[3,4,6,5,1,2]=>1
[3,4,6,5,2,1]=>0
[3,5,1,2,4,6]=>1
[3,5,1,2,6,4]=>1
[3,5,1,4,2,6]=>0
[3,5,1,4,6,2]=>0
[3,5,1,6,2,4]=>0
[3,5,1,6,4,2]=>1
[3,5,2,1,4,6]=>2
[3,5,2,1,6,4]=>2
[3,5,2,4,1,6]=>1
[3,5,2,4,6,1]=>1
[3,5,2,6,1,4]=>1
[3,5,2,6,4,1]=>2
[3,5,4,1,2,6]=>0
[3,5,4,1,6,2]=>0
[3,5,4,2,1,6]=>1
[3,5,4,2,6,1]=>1
[3,5,4,6,1,2]=>1
[3,5,4,6,2,1]=>0
[3,5,6,1,2,4]=>1
[3,5,6,1,4,2]=>2
[3,5,6,2,1,4]=>2
[3,5,6,2,4,1]=>1
[3,5,6,4,1,2]=>1
[3,5,6,4,2,1]=>0
[3,6,1,2,4,5]=>2
[3,6,1,2,5,4]=>1
[3,6,1,4,2,5]=>1
[3,6,1,4,5,2]=>0
[3,6,1,5,2,4]=>1
[3,6,1,5,4,2]=>0
[3,6,2,1,4,5]=>3
[3,6,2,1,5,4]=>2
[3,6,2,4,1,5]=>2
[3,6,2,4,5,1]=>1
[3,6,2,5,1,4]=>2
[3,6,2,5,4,1]=>1
[3,6,4,1,2,5]=>1
[3,6,4,1,5,2]=>0
[3,6,4,2,1,5]=>2
[3,6,4,2,5,1]=>1
[3,6,4,5,1,2]=>0
[3,6,4,5,2,1]=>1
[3,6,5,1,2,4]=>2
[3,6,5,1,4,2]=>1
[3,6,5,2,1,4]=>1
[3,6,5,2,4,1]=>2
[3,6,5,4,1,2]=>0
[3,6,5,4,2,1]=>1
[4,1,2,3,5,6]=>2
[4,1,2,3,6,5]=>2
[4,1,2,5,3,6]=>2
[4,1,2,5,6,3]=>2
[4,1,2,6,3,5]=>3
[4,1,2,6,5,3]=>2
[4,1,3,2,5,6]=>1
[4,1,3,2,6,5]=>1
[4,1,3,5,2,6]=>1
[4,1,3,5,6,2]=>1
[4,1,3,6,2,5]=>2
[4,1,3,6,5,2]=>1
[4,1,5,2,3,6]=>1
[4,1,5,2,6,3]=>1
[4,1,5,3,2,6]=>2
[4,1,5,3,6,2]=>2
[4,1,5,6,2,3]=>2
[4,1,5,6,3,2]=>1
[4,1,6,2,3,5]=>2
[4,1,6,2,5,3]=>1
[4,1,6,3,2,5]=>3
[4,1,6,3,5,2]=>2
[4,1,6,5,2,3]=>1
[4,1,6,5,3,2]=>2
[4,2,1,3,5,6]=>1
[4,2,1,3,6,5]=>1
[4,2,1,5,3,6]=>1
[4,2,1,5,6,3]=>1
[4,2,1,6,3,5]=>2
[4,2,1,6,5,3]=>1
[4,2,3,1,5,6]=>0
[4,2,3,1,6,5]=>0
[4,2,3,5,1,6]=>0
[4,2,3,5,6,1]=>0
[4,2,3,6,1,5]=>1
[4,2,3,6,5,1]=>0
[4,2,5,1,3,6]=>0
[4,2,5,1,6,3]=>0
[4,2,5,3,1,6]=>1
[4,2,5,3,6,1]=>1
[4,2,5,6,1,3]=>1
[4,2,5,6,3,1]=>0
[4,2,6,1,3,5]=>1
[4,2,6,1,5,3]=>0
[4,2,6,3,1,5]=>2
[4,2,6,3,5,1]=>1
[4,2,6,5,1,3]=>0
[4,2,6,5,3,1]=>1
[4,3,1,2,5,6]=>1
[4,3,1,2,6,5]=>1
[4,3,1,5,2,6]=>1
[4,3,1,5,6,2]=>1
[4,3,1,6,2,5]=>2
[4,3,1,6,5,2]=>1
[4,3,2,1,5,6]=>0
[4,3,2,1,6,5]=>0
[4,3,2,5,1,6]=>0
[4,3,2,5,6,1]=>0
[4,3,2,6,1,5]=>1
[4,3,2,6,5,1]=>0
[4,3,5,1,2,6]=>0
[4,3,5,1,6,2]=>0
[4,3,5,2,1,6]=>1
[4,3,5,2,6,1]=>1
[4,3,5,6,1,2]=>1
[4,3,5,6,2,1]=>0
[4,3,6,1,2,5]=>1
[4,3,6,1,5,2]=>0
[4,3,6,2,1,5]=>2
[4,3,6,2,5,1]=>1
[4,3,6,5,1,2]=>0
[4,3,6,5,2,1]=>1
[4,5,1,2,3,6]=>2
[4,5,1,2,6,3]=>2
[4,5,1,3,2,6]=>1
[4,5,1,3,6,2]=>1
[4,5,1,6,2,3]=>1
[4,5,1,6,3,2]=>2
[4,5,2,1,3,6]=>1
[4,5,2,1,6,3]=>1
[4,5,2,3,1,6]=>2
[4,5,2,3,6,1]=>2
[4,5,2,6,1,3]=>2
[4,5,2,6,3,1]=>1
[4,5,3,1,2,6]=>0
[4,5,3,1,6,2]=>0
[4,5,3,2,1,6]=>1
[4,5,3,2,6,1]=>1
[4,5,3,6,1,2]=>1
[4,5,3,6,2,1]=>0
[4,5,6,1,2,3]=>0
[4,5,6,1,3,2]=>1
[4,5,6,2,1,3]=>1
[4,5,6,2,3,1]=>2
[4,5,6,3,1,2]=>2
[4,5,6,3,2,1]=>1
[4,6,1,2,3,5]=>3
[4,6,1,2,5,3]=>2
[4,6,1,3,2,5]=>2
[4,6,1,3,5,2]=>1
[4,6,1,5,2,3]=>2
[4,6,1,5,3,2]=>1
[4,6,2,1,3,5]=>2
[4,6,2,1,5,3]=>1
[4,6,2,3,1,5]=>3
[4,6,2,3,5,1]=>2
[4,6,2,5,1,3]=>1
[4,6,2,5,3,1]=>2
[4,6,3,1,2,5]=>1
[4,6,3,1,5,2]=>0
[4,6,3,2,1,5]=>2
[4,6,3,2,5,1]=>1
[4,6,3,5,1,2]=>0
[4,6,3,5,2,1]=>1
[4,6,5,1,2,3]=>1
[4,6,5,1,3,2]=>0
[4,6,5,2,1,3]=>2
[4,6,5,2,3,1]=>1
[4,6,5,3,1,2]=>1
[4,6,5,3,2,1]=>2
[5,1,2,3,4,6]=>3
[5,1,2,3,6,4]=>3
[5,1,2,4,3,6]=>2
[5,1,2,4,6,3]=>2
[5,1,2,6,3,4]=>2
[5,1,2,6,4,3]=>3
[5,1,3,2,4,6]=>2
[5,1,3,2,6,4]=>2
[5,1,3,4,2,6]=>1
[5,1,3,4,6,2]=>1
[5,1,3,6,2,4]=>1
[5,1,3,6,4,2]=>2
[5,1,4,2,3,6]=>2
[5,1,4,2,6,3]=>2
[5,1,4,3,2,6]=>1
[5,1,4,3,6,2]=>1
[5,1,4,6,2,3]=>1
[5,1,4,6,3,2]=>2
[5,1,6,2,3,4]=>3
[5,1,6,2,4,3]=>2
[5,1,6,3,2,4]=>2
[5,1,6,3,4,2]=>3
[5,1,6,4,2,3]=>1
[5,1,6,4,3,2]=>2
[5,2,1,3,4,6]=>2
[5,2,1,3,6,4]=>2
[5,2,1,4,3,6]=>1
[5,2,1,4,6,3]=>1
[5,2,1,6,3,4]=>1
[5,2,1,6,4,3]=>2
[5,2,3,1,4,6]=>1
[5,2,3,1,6,4]=>1
[5,2,3,4,1,6]=>0
[5,2,3,4,6,1]=>0
[5,2,3,6,1,4]=>0
[5,2,3,6,4,1]=>1
[5,2,4,1,3,6]=>1
[5,2,4,1,6,3]=>1
[5,2,4,3,1,6]=>0
[5,2,4,3,6,1]=>0
[5,2,4,6,1,3]=>0
[5,2,4,6,3,1]=>1
[5,2,6,1,3,4]=>2
[5,2,6,1,4,3]=>1
[5,2,6,3,1,4]=>1
[5,2,6,3,4,1]=>2
[5,2,6,4,1,3]=>0
[5,2,6,4,3,1]=>1
[5,3,1,2,4,6]=>2
[5,3,1,2,6,4]=>2
[5,3,1,4,2,6]=>1
[5,3,1,4,6,2]=>1
[5,3,1,6,2,4]=>1
[5,3,1,6,4,2]=>2
[5,3,2,1,4,6]=>1
[5,3,2,1,6,4]=>1
[5,3,2,4,1,6]=>0
[5,3,2,4,6,1]=>0
[5,3,2,6,1,4]=>0
[5,3,2,6,4,1]=>1
[5,3,4,1,2,6]=>1
[5,3,4,1,6,2]=>1
[5,3,4,2,1,6]=>0
[5,3,4,2,6,1]=>0
[5,3,4,6,1,2]=>0
[5,3,4,6,2,1]=>1
[5,3,6,1,2,4]=>2
[5,3,6,1,4,2]=>1
[5,3,6,2,1,4]=>1
[5,3,6,2,4,1]=>2
[5,3,6,4,1,2]=>0
[5,3,6,4,2,1]=>1
[5,4,1,2,3,6]=>1
[5,4,1,2,6,3]=>1
[5,4,1,3,2,6]=>2
[5,4,1,3,6,2]=>2
[5,4,1,6,2,3]=>2
[5,4,1,6,3,2]=>1
[5,4,2,1,3,6]=>2
[5,4,2,1,6,3]=>2
[5,4,2,3,1,6]=>1
[5,4,2,3,6,1]=>1
[5,4,2,6,1,3]=>1
[5,4,2,6,3,1]=>2
[5,4,3,1,2,6]=>1
[5,4,3,1,6,2]=>1
[5,4,3,2,1,6]=>0
[5,4,3,2,6,1]=>0
[5,4,3,6,1,2]=>0
[5,4,3,6,2,1]=>1
[5,4,6,1,2,3]=>1
[5,4,6,1,3,2]=>2
[5,4,6,2,1,3]=>0
[5,4,6,2,3,1]=>1
[5,4,6,3,1,2]=>1
[5,4,6,3,2,1]=>2
[5,6,1,2,3,4]=>2
[5,6,1,2,4,3]=>3
[5,6,1,3,2,4]=>3
[5,6,1,3,4,2]=>2
[5,6,1,4,2,3]=>2
[5,6,1,4,3,2]=>1
[5,6,2,1,3,4]=>3
[5,6,2,1,4,3]=>2
[5,6,2,3,1,4]=>2
[5,6,2,3,4,1]=>3
[5,6,2,4,1,3]=>1
[5,6,2,4,3,1]=>2
[5,6,3,1,2,4]=>2
[5,6,3,1,4,2]=>1
[5,6,3,2,1,4]=>1
[5,6,3,2,4,1]=>2
[5,6,3,4,1,2]=>0
[5,6,3,4,2,1]=>1
[5,6,4,1,2,3]=>2
[5,6,4,1,3,2]=>1
[5,6,4,2,1,3]=>1
[5,6,4,2,3,1]=>2
[5,6,4,3,1,2]=>0
[5,6,4,3,2,1]=>1
[6,1,2,3,4,5]=>4
[6,1,2,3,5,4]=>3
[6,1,2,4,3,5]=>3
[6,1,2,4,5,3]=>2
[6,1,2,5,3,4]=>3
[6,1,2,5,4,3]=>2
[6,1,3,2,4,5]=>3
[6,1,3,2,5,4]=>2
[6,1,3,4,2,5]=>2
[6,1,3,4,5,2]=>1
[6,1,3,5,2,4]=>2
[6,1,3,5,4,2]=>1
[6,1,4,2,3,5]=>3
[6,1,4,2,5,3]=>2
[6,1,4,3,2,5]=>2
[6,1,4,3,5,2]=>1
[6,1,4,5,2,3]=>2
[6,1,4,5,3,2]=>1
[6,1,5,2,3,4]=>2
[6,1,5,2,4,3]=>3
[6,1,5,3,2,4]=>3
[6,1,5,3,4,2]=>2
[6,1,5,4,2,3]=>2
[6,1,5,4,3,2]=>1
[6,2,1,3,4,5]=>3
[6,2,1,3,5,4]=>2
[6,2,1,4,3,5]=>2
[6,2,1,4,5,3]=>1
[6,2,1,5,3,4]=>2
[6,2,1,5,4,3]=>1
[6,2,3,1,4,5]=>2
[6,2,3,1,5,4]=>1
[6,2,3,4,1,5]=>1
[6,2,3,4,5,1]=>0
[6,2,3,5,1,4]=>1
[6,2,3,5,4,1]=>0
[6,2,4,1,3,5]=>2
[6,2,4,1,5,3]=>1
[6,2,4,3,1,5]=>1
[6,2,4,3,5,1]=>0
[6,2,4,5,1,3]=>1
[6,2,4,5,3,1]=>0
[6,2,5,1,3,4]=>1
[6,2,5,1,4,3]=>2
[6,2,5,3,1,4]=>2
[6,2,5,3,4,1]=>1
[6,2,5,4,1,3]=>1
[6,2,5,4,3,1]=>0
[6,3,1,2,4,5]=>3
[6,3,1,2,5,4]=>2
[6,3,1,4,2,5]=>2
[6,3,1,4,5,2]=>1
[6,3,1,5,2,4]=>2
[6,3,1,5,4,2]=>1
[6,3,2,1,4,5]=>2
[6,3,2,1,5,4]=>1
[6,3,2,4,1,5]=>1
[6,3,2,4,5,1]=>0
[6,3,2,5,1,4]=>1
[6,3,2,5,4,1]=>0
[6,3,4,1,2,5]=>2
[6,3,4,1,5,2]=>1
[6,3,4,2,1,5]=>1
[6,3,4,2,5,1]=>0
[6,3,4,5,1,2]=>1
[6,3,4,5,2,1]=>0
[6,3,5,1,2,4]=>1
[6,3,5,1,4,2]=>2
[6,3,5,2,1,4]=>2
[6,3,5,2,4,1]=>1
[6,3,5,4,1,2]=>1
[6,3,5,4,2,1]=>0
[6,4,1,2,3,5]=>2
[6,4,1,2,5,3]=>1
[6,4,1,3,2,5]=>3
[6,4,1,3,5,2]=>2
[6,4,1,5,2,3]=>1
[6,4,1,5,3,2]=>2
[6,4,2,1,3,5]=>3
[6,4,2,1,5,3]=>2
[6,4,2,3,1,5]=>2
[6,4,2,3,5,1]=>1
[6,4,2,5,1,3]=>2
[6,4,2,5,3,1]=>1
[6,4,3,1,2,5]=>2
[6,4,3,1,5,2]=>1
[6,4,3,2,1,5]=>1
[6,4,3,2,5,1]=>0
[6,4,3,5,1,2]=>1
[6,4,3,5,2,1]=>0
[6,4,5,1,2,3]=>2
[6,4,5,1,3,2]=>1
[6,4,5,2,1,3]=>1
[6,4,5,2,3,1]=>0
[6,4,5,3,1,2]=>2
[6,4,5,3,2,1]=>1
[6,5,1,2,3,4]=>3
[6,5,1,2,4,3]=>2
[6,5,1,3,2,4]=>2
[6,5,1,3,4,2]=>3
[6,5,1,4,2,3]=>1
[6,5,1,4,3,2]=>2
[6,5,2,1,3,4]=>2
[6,5,2,1,4,3]=>3
[6,5,2,3,1,4]=>3
[6,5,2,3,4,1]=>2
[6,5,2,4,1,3]=>2
[6,5,2,4,3,1]=>1
[6,5,3,1,2,4]=>1
[6,5,3,1,4,2]=>2
[6,5,3,2,1,4]=>2
[6,5,3,2,4,1]=>1
[6,5,3,4,1,2]=>1
[6,5,3,4,2,1]=>0
[6,5,4,1,2,3]=>1
[6,5,4,1,3,2]=>2
[6,5,4,2,1,3]=>2
[6,5,4,2,3,1]=>1
[6,5,4,3,1,2]=>1
[6,5,4,3,2,1]=>0
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Description
The cycle descent number of a permutation.
Let $(i_1,\ldots,i_k)$ be a cycle of a permutation $\pi$ such that $i_1$ is its smallest element. A **cycle descent** of $(i_1,\ldots,i_k)$ is an $i_a$ for $1 \leq a < k$ such that $i_a > i_{a+1}$. The **cycle descent set** of $\pi$ is then the set of descents in all the cycles of $\pi$, and the **cycle descent number** is its cardinality.
Let $(i_1,\ldots,i_k)$ be a cycle of a permutation $\pi$ such that $i_1$ is its smallest element. A **cycle descent** of $(i_1,\ldots,i_k)$ is an $i_a$ for $1 \leq a < k$ such that $i_a > i_{a+1}$. The **cycle descent set** of $\pi$ is then the set of descents in all the cycles of $\pi$, and the **cycle descent number** is its cardinality.
References
[1] Ma, J., Ma, S., Yeh, Y.-N., Xu, Z. The cycle descent statistic on permutations arXiv:1512.01799
Code
def statistic(pi):
return sum( 1 for cycle in pi.cycle_tuples() for a in range(len(cycle)-1) if cycle[a] > cycle[a+1] )
Created
Dec 08, 2015 at 11:36 by Christian Stump
Updated
Aug 08, 2023 at 21:35 by Jessica Striker
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