edit this statistic or download as text // json
Identifier
Values
=>
[]=>0 [1]=>0 [1,2]=>0 [2,1]=>1 [1,2,3]=>0 [1,3,2]=>1 [2,1,3]=>1 [2,3,1]=>1 [3,1,2]=>1 [3,2,1]=>2 [1,2,3,4]=>0 [1,2,4,3]=>1 [1,3,2,4]=>1 [1,3,4,2]=>1 [1,4,2,3]=>1 [1,4,3,2]=>2 [2,1,3,4]=>1 [2,1,4,3]=>2 [2,3,1,4]=>1 [2,3,4,1]=>1 [2,4,1,3]=>1 [2,4,3,1]=>2 [3,1,2,4]=>1 [3,1,4,2]=>2 [3,2,1,4]=>2 [3,2,4,1]=>2 [3,4,1,2]=>1 [3,4,2,1]=>2 [4,1,2,3]=>1 [4,1,3,2]=>2 [4,2,1,3]=>2 [4,2,3,1]=>2 [4,3,1,2]=>2 [4,3,2,1]=>3 [1,2,3,4,5]=>0 [1,2,3,5,4]=>1 [1,2,4,3,5]=>1 [1,2,4,5,3]=>1 [1,2,5,3,4]=>1 [1,2,5,4,3]=>2 [1,3,2,4,5]=>1 [1,3,2,5,4]=>2 [1,3,4,2,5]=>1 [1,3,4,5,2]=>1 [1,3,5,2,4]=>1 [1,3,5,4,2]=>2 [1,4,2,3,5]=>1 [1,4,2,5,3]=>2 [1,4,3,2,5]=>2 [1,4,3,5,2]=>2 [1,4,5,2,3]=>1 [1,4,5,3,2]=>2 [1,5,2,3,4]=>1 [1,5,2,4,3]=>2 [1,5,3,2,4]=>2 [1,5,3,4,2]=>2 [1,5,4,2,3]=>2 [1,5,4,3,2]=>3 [2,1,3,4,5]=>1 [2,1,3,5,4]=>2 [2,1,4,3,5]=>2 [2,1,4,5,3]=>2 [2,1,5,3,4]=>2 [2,1,5,4,3]=>3 [2,3,1,4,5]=>1 [2,3,1,5,4]=>2 [2,3,4,1,5]=>1 [2,3,4,5,1]=>1 [2,3,5,1,4]=>1 [2,3,5,4,1]=>2 [2,4,1,3,5]=>1 [2,4,1,5,3]=>2 [2,4,3,1,5]=>2 [2,4,3,5,1]=>2 [2,4,5,1,3]=>1 [2,4,5,3,1]=>2 [2,5,1,3,4]=>1 [2,5,1,4,3]=>2 [2,5,3,1,4]=>2 [2,5,3,4,1]=>2 [2,5,4,1,3]=>2 [2,5,4,3,1]=>3 [3,1,2,4,5]=>1 [3,1,2,5,4]=>2 [3,1,4,2,5]=>2 [3,1,4,5,2]=>2 [3,1,5,2,4]=>2 [3,1,5,4,2]=>3 [3,2,1,4,5]=>2 [3,2,1,5,4]=>3 [3,2,4,1,5]=>2 [3,2,4,5,1]=>2 [3,2,5,1,4]=>2 [3,2,5,4,1]=>3 [3,4,1,2,5]=>1 [3,4,1,5,2]=>2 [3,4,2,1,5]=>2 [3,4,2,5,1]=>2 [3,4,5,1,2]=>1 [3,4,5,2,1]=>2 [3,5,1,2,4]=>1 [3,5,1,4,2]=>2 [3,5,2,1,4]=>2 [3,5,2,4,1]=>2 [3,5,4,1,2]=>2 [3,5,4,2,1]=>3 [4,1,2,3,5]=>1 [4,1,2,5,3]=>2 [4,1,3,2,5]=>2 [4,1,3,5,2]=>2 [4,1,5,2,3]=>2 [4,1,5,3,2]=>3 [4,2,1,3,5]=>2 [4,2,1,5,3]=>3 [4,2,3,1,5]=>2 [4,2,3,5,1]=>2 [4,2,5,1,3]=>2 [4,2,5,3,1]=>3 [4,3,1,2,5]=>2 [4,3,1,5,2]=>3 [4,3,2,1,5]=>3 [4,3,2,5,1]=>3 [4,3,5,1,2]=>2 [4,3,5,2,1]=>3 [4,5,1,2,3]=>1 [4,5,1,3,2]=>2 [4,5,2,1,3]=>2 [4,5,2,3,1]=>2 [4,5,3,1,2]=>2 [4,5,3,2,1]=>3 [5,1,2,3,4]=>1 [5,1,2,4,3]=>2 [5,1,3,2,4]=>2 [5,1,3,4,2]=>2 [5,1,4,2,3]=>2 [5,1,4,3,2]=>3 [5,2,1,3,4]=>2 [5,2,1,4,3]=>3 [5,2,3,1,4]=>2 [5,2,3,4,1]=>2 [5,2,4,1,3]=>2 [5,2,4,3,1]=>3 [5,3,1,2,4]=>2 [5,3,1,4,2]=>3 [5,3,2,1,4]=>3 [5,3,2,4,1]=>3 [5,3,4,1,2]=>2 [5,3,4,2,1]=>3 [5,4,1,2,3]=>2 [5,4,1,3,2]=>3 [5,4,2,1,3]=>3 [5,4,2,3,1]=>3 [5,4,3,1,2]=>3 [5,4,3,2,1]=>4 [1,2,3,4,5,6]=>0 [1,2,3,4,6,5]=>1 [1,2,3,5,4,6]=>1 [1,2,3,5,6,4]=>1 [1,2,3,6,4,5]=>1 [1,2,3,6,5,4]=>2 [1,2,4,3,5,6]=>1 [1,2,4,3,6,5]=>2 [1,2,4,5,3,6]=>1 [1,2,4,5,6,3]=>1 [1,2,4,6,3,5]=>1 [1,2,4,6,5,3]=>2 [1,2,5,3,4,6]=>1 [1,2,5,3,6,4]=>2 [1,2,5,4,3,6]=>2 [1,2,5,4,6,3]=>2 [1,2,5,6,3,4]=>1 [1,2,5,6,4,3]=>2 [1,2,6,3,4,5]=>1 [1,2,6,3,5,4]=>2 [1,2,6,4,3,5]=>2 [1,2,6,4,5,3]=>2 [1,2,6,5,3,4]=>2 [1,2,6,5,4,3]=>3 [1,3,2,4,5,6]=>1 [1,3,2,4,6,5]=>2 [1,3,2,5,4,6]=>2 [1,3,2,5,6,4]=>2 [1,3,2,6,4,5]=>2 [1,3,2,6,5,4]=>3 [1,3,4,2,5,6]=>1 [1,3,4,2,6,5]=>2 [1,3,4,5,2,6]=>1 [1,3,4,5,6,2]=>1 [1,3,4,6,2,5]=>1 [1,3,4,6,5,2]=>2 [1,3,5,2,4,6]=>1 [1,3,5,2,6,4]=>2 [1,3,5,4,2,6]=>2 [1,3,5,4,6,2]=>2 [1,3,5,6,2,4]=>1 [1,3,5,6,4,2]=>2 [1,3,6,2,4,5]=>1 [1,3,6,2,5,4]=>2 [1,3,6,4,2,5]=>2 [1,3,6,4,5,2]=>2 [1,3,6,5,2,4]=>2 [1,3,6,5,4,2]=>3 [1,4,2,3,5,6]=>1 [1,4,2,3,6,5]=>2 [1,4,2,5,3,6]=>2 [1,4,2,5,6,3]=>2 [1,4,2,6,3,5]=>2 [1,4,2,6,5,3]=>3 [1,4,3,2,5,6]=>2 [1,4,3,2,6,5]=>3 [1,4,3,5,2,6]=>2 [1,4,3,5,6,2]=>2 [1,4,3,6,2,5]=>2 [1,4,3,6,5,2]=>3 [1,4,5,2,3,6]=>1 [1,4,5,2,6,3]=>2 [1,4,5,3,2,6]=>2 [1,4,5,3,6,2]=>2 [1,4,5,6,2,3]=>1 [1,4,5,6,3,2]=>2 [1,4,6,2,3,5]=>1 [1,4,6,2,5,3]=>2 [1,4,6,3,2,5]=>2 [1,4,6,3,5,2]=>2 [1,4,6,5,2,3]=>2 [1,4,6,5,3,2]=>3 [1,5,2,3,4,6]=>1 [1,5,2,3,6,4]=>2 [1,5,2,4,3,6]=>2 [1,5,2,4,6,3]=>2 [1,5,2,6,3,4]=>2 [1,5,2,6,4,3]=>3 [1,5,3,2,4,6]=>2 [1,5,3,2,6,4]=>3 [1,5,3,4,2,6]=>2 [1,5,3,4,6,2]=>2 [1,5,3,6,2,4]=>2 [1,5,3,6,4,2]=>3 [1,5,4,2,3,6]=>2 [1,5,4,2,6,3]=>3 [1,5,4,3,2,6]=>3 [1,5,4,3,6,2]=>3 [1,5,4,6,2,3]=>2 [1,5,4,6,3,2]=>3 [1,5,6,2,3,4]=>1 [1,5,6,2,4,3]=>2 [1,5,6,3,2,4]=>2 [1,5,6,3,4,2]=>2 [1,5,6,4,2,3]=>2 [1,5,6,4,3,2]=>3 [1,6,2,3,4,5]=>1 [1,6,2,3,5,4]=>2 [1,6,2,4,3,5]=>2 [1,6,2,4,5,3]=>2 [1,6,2,5,3,4]=>2 [1,6,2,5,4,3]=>3 [1,6,3,2,4,5]=>2 [1,6,3,2,5,4]=>3 [1,6,3,4,2,5]=>2 [1,6,3,4,5,2]=>2 [1,6,3,5,2,4]=>2 [1,6,3,5,4,2]=>3 [1,6,4,2,3,5]=>2 [1,6,4,2,5,3]=>3 [1,6,4,3,2,5]=>3 [1,6,4,3,5,2]=>3 [1,6,4,5,2,3]=>2 [1,6,4,5,3,2]=>3 [1,6,5,2,3,4]=>2 [1,6,5,2,4,3]=>3 [1,6,5,3,2,4]=>3 [1,6,5,3,4,2]=>3 [1,6,5,4,2,3]=>3 [1,6,5,4,3,2]=>4 [2,1,3,4,5,6]=>1 [2,1,3,4,6,5]=>2 [2,1,3,5,4,6]=>2 [2,1,3,5,6,4]=>2 [2,1,3,6,4,5]=>2 [2,1,3,6,5,4]=>3 [2,1,4,3,5,6]=>2 [2,1,4,3,6,5]=>3 [2,1,4,5,3,6]=>2 [2,1,4,5,6,3]=>2 [2,1,4,6,3,5]=>2 [2,1,4,6,5,3]=>3 [2,1,5,3,4,6]=>2 [2,1,5,3,6,4]=>3 [2,1,5,4,3,6]=>3 [2,1,5,4,6,3]=>3 [2,1,5,6,3,4]=>2 [2,1,5,6,4,3]=>3 [2,1,6,3,4,5]=>2 [2,1,6,3,5,4]=>3 [2,1,6,4,3,5]=>3 [2,1,6,4,5,3]=>3 [2,1,6,5,3,4]=>3 [2,1,6,5,4,3]=>4 [2,3,1,4,5,6]=>1 [2,3,1,4,6,5]=>2 [2,3,1,5,4,6]=>2 [2,3,1,5,6,4]=>2 [2,3,1,6,4,5]=>2 [2,3,1,6,5,4]=>3 [2,3,4,1,5,6]=>1 [2,3,4,1,6,5]=>2 [2,3,4,5,1,6]=>1 [2,3,4,5,6,1]=>1 [2,3,4,6,1,5]=>1 [2,3,4,6,5,1]=>2 [2,3,5,1,4,6]=>1 [2,3,5,1,6,4]=>2 [2,3,5,4,1,6]=>2 [2,3,5,4,6,1]=>2 [2,3,5,6,1,4]=>1 [2,3,5,6,4,1]=>2 [2,3,6,1,4,5]=>1 [2,3,6,1,5,4]=>2 [2,3,6,4,1,5]=>2 [2,3,6,4,5,1]=>2 [2,3,6,5,1,4]=>2 [2,3,6,5,4,1]=>3 [2,4,1,3,5,6]=>1 [2,4,1,3,6,5]=>2 [2,4,1,5,3,6]=>2 [2,4,1,5,6,3]=>2 [2,4,1,6,3,5]=>2 [2,4,1,6,5,3]=>3 [2,4,3,1,5,6]=>2 [2,4,3,1,6,5]=>3 [2,4,3,5,1,6]=>2 [2,4,3,5,6,1]=>2 [2,4,3,6,1,5]=>2 [2,4,3,6,5,1]=>3 [2,4,5,1,3,6]=>1 [2,4,5,1,6,3]=>2 [2,4,5,3,1,6]=>2 [2,4,5,3,6,1]=>2 [2,4,5,6,1,3]=>1 [2,4,5,6,3,1]=>2 [2,4,6,1,3,5]=>1 [2,4,6,1,5,3]=>2 [2,4,6,3,1,5]=>2 [2,4,6,3,5,1]=>2 [2,4,6,5,1,3]=>2 [2,4,6,5,3,1]=>3 [2,5,1,3,4,6]=>1 [2,5,1,3,6,4]=>2 [2,5,1,4,3,6]=>2 [2,5,1,4,6,3]=>2 [2,5,1,6,3,4]=>2 [2,5,1,6,4,3]=>3 [2,5,3,1,4,6]=>2 [2,5,3,1,6,4]=>3 [2,5,3,4,1,6]=>2 [2,5,3,4,6,1]=>2 [2,5,3,6,1,4]=>2 [2,5,3,6,4,1]=>3 [2,5,4,1,3,6]=>2 [2,5,4,1,6,3]=>3 [2,5,4,3,1,6]=>3 [2,5,4,3,6,1]=>3 [2,5,4,6,1,3]=>2 [2,5,4,6,3,1]=>3 [2,5,6,1,3,4]=>1 [2,5,6,1,4,3]=>2 [2,5,6,3,1,4]=>2 [2,5,6,3,4,1]=>2 [2,5,6,4,1,3]=>2 [2,5,6,4,3,1]=>3 [2,6,1,3,4,5]=>1 [2,6,1,3,5,4]=>2 [2,6,1,4,3,5]=>2 [2,6,1,4,5,3]=>2 [2,6,1,5,3,4]=>2 [2,6,1,5,4,3]=>3 [2,6,3,1,4,5]=>2 [2,6,3,1,5,4]=>3 [2,6,3,4,1,5]=>2 [2,6,3,4,5,1]=>2 [2,6,3,5,1,4]=>2 [2,6,3,5,4,1]=>3 [2,6,4,1,3,5]=>2 [2,6,4,1,5,3]=>3 [2,6,4,3,1,5]=>3 [2,6,4,3,5,1]=>3 [2,6,4,5,1,3]=>2 [2,6,4,5,3,1]=>3 [2,6,5,1,3,4]=>2 [2,6,5,1,4,3]=>3 [2,6,5,3,1,4]=>3 [2,6,5,3,4,1]=>3 [2,6,5,4,1,3]=>3 [2,6,5,4,3,1]=>4 [3,1,2,4,5,6]=>1 [3,1,2,4,6,5]=>2 [3,1,2,5,4,6]=>2 [3,1,2,5,6,4]=>2 [3,1,2,6,4,5]=>2 [3,1,2,6,5,4]=>3 [3,1,4,2,5,6]=>2 [3,1,4,2,6,5]=>3 [3,1,4,5,2,6]=>2 [3,1,4,5,6,2]=>2 [3,1,4,6,2,5]=>2 [3,1,4,6,5,2]=>3 [3,1,5,2,4,6]=>2 [3,1,5,2,6,4]=>3 [3,1,5,4,2,6]=>3 [3,1,5,4,6,2]=>3 [3,1,5,6,2,4]=>2 [3,1,5,6,4,2]=>3 [3,1,6,2,4,5]=>2 [3,1,6,2,5,4]=>3 [3,1,6,4,2,5]=>3 [3,1,6,4,5,2]=>3 [3,1,6,5,2,4]=>3 [3,1,6,5,4,2]=>4 [3,2,1,4,5,6]=>2 [3,2,1,4,6,5]=>3 [3,2,1,5,4,6]=>3 [3,2,1,5,6,4]=>3 [3,2,1,6,4,5]=>3 [3,2,1,6,5,4]=>4 [3,2,4,1,5,6]=>2 [3,2,4,1,6,5]=>3 [3,2,4,5,1,6]=>2 [3,2,4,5,6,1]=>2 [3,2,4,6,1,5]=>2 [3,2,4,6,5,1]=>3 [3,2,5,1,4,6]=>2 [3,2,5,1,6,4]=>3 [3,2,5,4,1,6]=>3 [3,2,5,4,6,1]=>3 [3,2,5,6,1,4]=>2 [3,2,5,6,4,1]=>3 [3,2,6,1,4,5]=>2 [3,2,6,1,5,4]=>3 [3,2,6,4,1,5]=>3 [3,2,6,4,5,1]=>3 [3,2,6,5,1,4]=>3 [3,2,6,5,4,1]=>4 [3,4,1,2,5,6]=>1 [3,4,1,2,6,5]=>2 [3,4,1,5,2,6]=>2 [3,4,1,5,6,2]=>2 [3,4,1,6,2,5]=>2 [3,4,1,6,5,2]=>3 [3,4,2,1,5,6]=>2 [3,4,2,1,6,5]=>3 [3,4,2,5,1,6]=>2 [3,4,2,5,6,1]=>2 [3,4,2,6,1,5]=>2 [3,4,2,6,5,1]=>3 [3,4,5,1,2,6]=>1 [3,4,5,1,6,2]=>2 [3,4,5,2,1,6]=>2 [3,4,5,2,6,1]=>2 [3,4,5,6,1,2]=>1 [3,4,5,6,2,1]=>2 [3,4,6,1,2,5]=>1 [3,4,6,1,5,2]=>2 [3,4,6,2,1,5]=>2 [3,4,6,2,5,1]=>2 [3,4,6,5,1,2]=>2 [3,4,6,5,2,1]=>3 [3,5,1,2,4,6]=>1 [3,5,1,2,6,4]=>2 [3,5,1,4,2,6]=>2 [3,5,1,4,6,2]=>2 [3,5,1,6,2,4]=>2 [3,5,1,6,4,2]=>3 [3,5,2,1,4,6]=>2 [3,5,2,1,6,4]=>3 [3,5,2,4,1,6]=>2 [3,5,2,4,6,1]=>2 [3,5,2,6,1,4]=>2 [3,5,2,6,4,1]=>3 [3,5,4,1,2,6]=>2 [3,5,4,1,6,2]=>3 [3,5,4,2,1,6]=>3 [3,5,4,2,6,1]=>3 [3,5,4,6,1,2]=>2 [3,5,4,6,2,1]=>3 [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]=>2 [3,5,6,4,1,2]=>2 [3,5,6,4,2,1]=>3 [3,6,1,2,4,5]=>1 [3,6,1,2,5,4]=>2 [3,6,1,4,2,5]=>2 [3,6,1,4,5,2]=>2 [3,6,1,5,2,4]=>2 [3,6,1,5,4,2]=>3 [3,6,2,1,4,5]=>2 [3,6,2,1,5,4]=>3 [3,6,2,4,1,5]=>2 [3,6,2,4,5,1]=>2 [3,6,2,5,1,4]=>2 [3,6,2,5,4,1]=>3 [3,6,4,1,2,5]=>2 [3,6,4,1,5,2]=>3 [3,6,4,2,1,5]=>3 [3,6,4,2,5,1]=>3 [3,6,4,5,1,2]=>2 [3,6,4,5,2,1]=>3 [3,6,5,1,2,4]=>2 [3,6,5,1,4,2]=>3 [3,6,5,2,1,4]=>3 [3,6,5,2,4,1]=>3 [3,6,5,4,1,2]=>3 [3,6,5,4,2,1]=>4 [4,1,2,3,5,6]=>1 [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]=>2 [4,1,2,6,5,3]=>3 [4,1,3,2,5,6]=>2 [4,1,3,2,6,5]=>3 [4,1,3,5,2,6]=>2 [4,1,3,5,6,2]=>2 [4,1,3,6,2,5]=>2 [4,1,3,6,5,2]=>3 [4,1,5,2,3,6]=>2 [4,1,5,2,6,3]=>3 [4,1,5,3,2,6]=>3 [4,1,5,3,6,2]=>3 [4,1,5,6,2,3]=>2 [4,1,5,6,3,2]=>3 [4,1,6,2,3,5]=>2 [4,1,6,2,5,3]=>3 [4,1,6,3,2,5]=>3 [4,1,6,3,5,2]=>3 [4,1,6,5,2,3]=>3 [4,1,6,5,3,2]=>4 [4,2,1,3,5,6]=>2 [4,2,1,3,6,5]=>3 [4,2,1,5,3,6]=>3 [4,2,1,5,6,3]=>3 [4,2,1,6,3,5]=>3 [4,2,1,6,5,3]=>4 [4,2,3,1,5,6]=>2 [4,2,3,1,6,5]=>3 [4,2,3,5,1,6]=>2 [4,2,3,5,6,1]=>2 [4,2,3,6,1,5]=>2 [4,2,3,6,5,1]=>3 [4,2,5,1,3,6]=>2 [4,2,5,1,6,3]=>3 [4,2,5,3,1,6]=>3 [4,2,5,3,6,1]=>3 [4,2,5,6,1,3]=>2 [4,2,5,6,3,1]=>3 [4,2,6,1,3,5]=>2 [4,2,6,1,5,3]=>3 [4,2,6,3,1,5]=>3 [4,2,6,3,5,1]=>3 [4,2,6,5,1,3]=>3 [4,2,6,5,3,1]=>4 [4,3,1,2,5,6]=>2 [4,3,1,2,6,5]=>3 [4,3,1,5,2,6]=>3 [4,3,1,5,6,2]=>3 [4,3,1,6,2,5]=>3 [4,3,1,6,5,2]=>4 [4,3,2,1,5,6]=>3 [4,3,2,1,6,5]=>4 [4,3,2,5,1,6]=>3 [4,3,2,5,6,1]=>3 [4,3,2,6,1,5]=>3 [4,3,2,6,5,1]=>4 [4,3,5,1,2,6]=>2 [4,3,5,1,6,2]=>3 [4,3,5,2,1,6]=>3 [4,3,5,2,6,1]=>3 [4,3,5,6,1,2]=>2 [4,3,5,6,2,1]=>3 [4,3,6,1,2,5]=>2 [4,3,6,1,5,2]=>3 [4,3,6,2,1,5]=>3 [4,3,6,2,5,1]=>3 [4,3,6,5,1,2]=>3 [4,3,6,5,2,1]=>4 [4,5,1,2,3,6]=>1 [4,5,1,2,6,3]=>2 [4,5,1,3,2,6]=>2 [4,5,1,3,6,2]=>2 [4,5,1,6,2,3]=>2 [4,5,1,6,3,2]=>3 [4,5,2,1,3,6]=>2 [4,5,2,1,6,3]=>3 [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]=>3 [4,5,3,1,2,6]=>2 [4,5,3,1,6,2]=>3 [4,5,3,2,1,6]=>3 [4,5,3,2,6,1]=>3 [4,5,3,6,1,2]=>2 [4,5,3,6,2,1]=>3 [4,5,6,1,2,3]=>1 [4,5,6,1,3,2]=>2 [4,5,6,2,1,3]=>2 [4,5,6,2,3,1]=>2 [4,5,6,3,1,2]=>2 [4,5,6,3,2,1]=>3 [4,6,1,2,3,5]=>1 [4,6,1,2,5,3]=>2 [4,6,1,3,2,5]=>2 [4,6,1,3,5,2]=>2 [4,6,1,5,2,3]=>2 [4,6,1,5,3,2]=>3 [4,6,2,1,3,5]=>2 [4,6,2,1,5,3]=>3 [4,6,2,3,1,5]=>2 [4,6,2,3,5,1]=>2 [4,6,2,5,1,3]=>2 [4,6,2,5,3,1]=>3 [4,6,3,1,2,5]=>2 [4,6,3,1,5,2]=>3 [4,6,3,2,1,5]=>3 [4,6,3,2,5,1]=>3 [4,6,3,5,1,2]=>2 [4,6,3,5,2,1]=>3 [4,6,5,1,2,3]=>2 [4,6,5,1,3,2]=>3 [4,6,5,2,1,3]=>3 [4,6,5,2,3,1]=>3 [4,6,5,3,1,2]=>3 [4,6,5,3,2,1]=>4 [5,1,2,3,4,6]=>1 [5,1,2,3,6,4]=>2 [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]=>3 [5,1,3,4,2,6]=>2 [5,1,3,4,6,2]=>2 [5,1,3,6,2,4]=>2 [5,1,3,6,4,2]=>3 [5,1,4,2,3,6]=>2 [5,1,4,2,6,3]=>3 [5,1,4,3,2,6]=>3 [5,1,4,3,6,2]=>3 [5,1,4,6,2,3]=>2 [5,1,4,6,3,2]=>3 [5,1,6,2,3,4]=>2 [5,1,6,2,4,3]=>3 [5,1,6,3,2,4]=>3 [5,1,6,3,4,2]=>3 [5,1,6,4,2,3]=>3 [5,1,6,4,3,2]=>4 [5,2,1,3,4,6]=>2 [5,2,1,3,6,4]=>3 [5,2,1,4,3,6]=>3 [5,2,1,4,6,3]=>3 [5,2,1,6,3,4]=>3 [5,2,1,6,4,3]=>4 [5,2,3,1,4,6]=>2 [5,2,3,1,6,4]=>3 [5,2,3,4,1,6]=>2 [5,2,3,4,6,1]=>2 [5,2,3,6,1,4]=>2 [5,2,3,6,4,1]=>3 [5,2,4,1,3,6]=>2 [5,2,4,1,6,3]=>3 [5,2,4,3,1,6]=>3 [5,2,4,3,6,1]=>3 [5,2,4,6,1,3]=>2 [5,2,4,6,3,1]=>3 [5,2,6,1,3,4]=>2 [5,2,6,1,4,3]=>3 [5,2,6,3,1,4]=>3 [5,2,6,3,4,1]=>3 [5,2,6,4,1,3]=>3 [5,2,6,4,3,1]=>4 [5,3,1,2,4,6]=>2 [5,3,1,2,6,4]=>3 [5,3,1,4,2,6]=>3 [5,3,1,4,6,2]=>3 [5,3,1,6,2,4]=>3 [5,3,1,6,4,2]=>4 [5,3,2,1,4,6]=>3 [5,3,2,1,6,4]=>4 [5,3,2,4,1,6]=>3 [5,3,2,4,6,1]=>3 [5,3,2,6,1,4]=>3 [5,3,2,6,4,1]=>4 [5,3,4,1,2,6]=>2 [5,3,4,1,6,2]=>3 [5,3,4,2,1,6]=>3 [5,3,4,2,6,1]=>3 [5,3,4,6,1,2]=>2 [5,3,4,6,2,1]=>3 [5,3,6,1,2,4]=>2 [5,3,6,1,4,2]=>3 [5,3,6,2,1,4]=>3 [5,3,6,2,4,1]=>3 [5,3,6,4,1,2]=>3 [5,3,6,4,2,1]=>4 [5,4,1,2,3,6]=>2 [5,4,1,2,6,3]=>3 [5,4,1,3,2,6]=>3 [5,4,1,3,6,2]=>3 [5,4,1,6,2,3]=>3 [5,4,1,6,3,2]=>4 [5,4,2,1,3,6]=>3 [5,4,2,1,6,3]=>4 [5,4,2,3,1,6]=>3 [5,4,2,3,6,1]=>3 [5,4,2,6,1,3]=>3 [5,4,2,6,3,1]=>4 [5,4,3,1,2,6]=>3 [5,4,3,1,6,2]=>4 [5,4,3,2,1,6]=>4 [5,4,3,2,6,1]=>4 [5,4,3,6,1,2]=>3 [5,4,3,6,2,1]=>4 [5,4,6,1,2,3]=>2 [5,4,6,1,3,2]=>3 [5,4,6,2,1,3]=>3 [5,4,6,2,3,1]=>3 [5,4,6,3,1,2]=>3 [5,4,6,3,2,1]=>4 [5,6,1,2,3,4]=>1 [5,6,1,2,4,3]=>2 [5,6,1,3,2,4]=>2 [5,6,1,3,4,2]=>2 [5,6,1,4,2,3]=>2 [5,6,1,4,3,2]=>3 [5,6,2,1,3,4]=>2 [5,6,2,1,4,3]=>3 [5,6,2,3,1,4]=>2 [5,6,2,3,4,1]=>2 [5,6,2,4,1,3]=>2 [5,6,2,4,3,1]=>3 [5,6,3,1,2,4]=>2 [5,6,3,1,4,2]=>3 [5,6,3,2,1,4]=>3 [5,6,3,2,4,1]=>3 [5,6,3,4,1,2]=>2 [5,6,3,4,2,1]=>3 [5,6,4,1,2,3]=>2 [5,6,4,1,3,2]=>3 [5,6,4,2,1,3]=>3 [5,6,4,2,3,1]=>3 [5,6,4,3,1,2]=>3 [5,6,4,3,2,1]=>4 [6,1,2,3,4,5]=>1 [6,1,2,3,5,4]=>2 [6,1,2,4,3,5]=>2 [6,1,2,4,5,3]=>2 [6,1,2,5,3,4]=>2 [6,1,2,5,4,3]=>3 [6,1,3,2,4,5]=>2 [6,1,3,2,5,4]=>3 [6,1,3,4,2,5]=>2 [6,1,3,4,5,2]=>2 [6,1,3,5,2,4]=>2 [6,1,3,5,4,2]=>3 [6,1,4,2,3,5]=>2 [6,1,4,2,5,3]=>3 [6,1,4,3,2,5]=>3 [6,1,4,3,5,2]=>3 [6,1,4,5,2,3]=>2 [6,1,4,5,3,2]=>3 [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]=>3 [6,1,5,4,2,3]=>3 [6,1,5,4,3,2]=>4 [6,2,1,3,4,5]=>2 [6,2,1,3,5,4]=>3 [6,2,1,4,3,5]=>3 [6,2,1,4,5,3]=>3 [6,2,1,5,3,4]=>3 [6,2,1,5,4,3]=>4 [6,2,3,1,4,5]=>2 [6,2,3,1,5,4]=>3 [6,2,3,4,1,5]=>2 [6,2,3,4,5,1]=>2 [6,2,3,5,1,4]=>2 [6,2,3,5,4,1]=>3 [6,2,4,1,3,5]=>2 [6,2,4,1,5,3]=>3 [6,2,4,3,1,5]=>3 [6,2,4,3,5,1]=>3 [6,2,4,5,1,3]=>2 [6,2,4,5,3,1]=>3 [6,2,5,1,3,4]=>2 [6,2,5,1,4,3]=>3 [6,2,5,3,1,4]=>3 [6,2,5,3,4,1]=>3 [6,2,5,4,1,3]=>3 [6,2,5,4,3,1]=>4 [6,3,1,2,4,5]=>2 [6,3,1,2,5,4]=>3 [6,3,1,4,2,5]=>3 [6,3,1,4,5,2]=>3 [6,3,1,5,2,4]=>3 [6,3,1,5,4,2]=>4 [6,3,2,1,4,5]=>3 [6,3,2,1,5,4]=>4 [6,3,2,4,1,5]=>3 [6,3,2,4,5,1]=>3 [6,3,2,5,1,4]=>3 [6,3,2,5,4,1]=>4 [6,3,4,1,2,5]=>2 [6,3,4,1,5,2]=>3 [6,3,4,2,1,5]=>3 [6,3,4,2,5,1]=>3 [6,3,4,5,1,2]=>2 [6,3,4,5,2,1]=>3 [6,3,5,1,2,4]=>2 [6,3,5,1,4,2]=>3 [6,3,5,2,1,4]=>3 [6,3,5,2,4,1]=>3 [6,3,5,4,1,2]=>3 [6,3,5,4,2,1]=>4 [6,4,1,2,3,5]=>2 [6,4,1,2,5,3]=>3 [6,4,1,3,2,5]=>3 [6,4,1,3,5,2]=>3 [6,4,1,5,2,3]=>3 [6,4,1,5,3,2]=>4 [6,4,2,1,3,5]=>3 [6,4,2,1,5,3]=>4 [6,4,2,3,1,5]=>3 [6,4,2,3,5,1]=>3 [6,4,2,5,1,3]=>3 [6,4,2,5,3,1]=>4 [6,4,3,1,2,5]=>3 [6,4,3,1,5,2]=>4 [6,4,3,2,1,5]=>4 [6,4,3,2,5,1]=>4 [6,4,3,5,1,2]=>3 [6,4,3,5,2,1]=>4 [6,4,5,1,2,3]=>2 [6,4,5,1,3,2]=>3 [6,4,5,2,1,3]=>3 [6,4,5,2,3,1]=>3 [6,4,5,3,1,2]=>3 [6,4,5,3,2,1]=>4 [6,5,1,2,3,4]=>2 [6,5,1,2,4,3]=>3 [6,5,1,3,2,4]=>3 [6,5,1,3,4,2]=>3 [6,5,1,4,2,3]=>3 [6,5,1,4,3,2]=>4 [6,5,2,1,3,4]=>3 [6,5,2,1,4,3]=>4 [6,5,2,3,1,4]=>3 [6,5,2,3,4,1]=>3 [6,5,2,4,1,3]=>3 [6,5,2,4,3,1]=>4 [6,5,3,1,2,4]=>3 [6,5,3,1,4,2]=>4 [6,5,3,2,1,4]=>4 [6,5,3,2,4,1]=>4 [6,5,3,4,1,2]=>3 [6,5,3,4,2,1]=>4 [6,5,4,1,2,3]=>3 [6,5,4,1,3,2]=>4 [6,5,4,2,1,3]=>4 [6,5,4,2,3,1]=>4 [6,5,4,3,1,2]=>4 [6,5,4,3,2,1]=>5
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The number of descents of a permutation.
This can be described as an occurrence of the vincular mesh pattern ([2,1], {(1,0),(1,1),(1,2)}), i.e., the middle column is shaded, see [3].
References
[1] /Permutations/Descents
[2] Triangle of Eulerian numbers T(n,k) (n>=1, 1 <= k <= n) read by rows. OEIS:A008292
[3] Brändén, P., Claesson, A. Mesh patterns and the expansion of permutation statistics as sums of permutation patterns arXiv:1102.4226
Code
def statistic(x):
    return x.number_of_descents()
Created
Oct 11, 2011 at 19:06 by Christian Stump
Updated
May 10, 2019 at 17:11 by Henning Ulfarsson