Identifier
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 $1 \leq a < i$ 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
Dec 08, 2015 at 11:36 by Christian Stump