edit this statistic or download as text // json
Identifier
Values
=>
[1,2]=>0 [2,1]=>0 [1,2,3]=>0 [1,3,2]=>0 [2,1,3]=>0 [2,3,1]=>1 [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]=>1 [1,4,2,3]=>1 [1,4,3,2]=>0 [2,1,3,4]=>0 [2,1,4,3]=>1 [2,3,1,4]=>1 [2,3,4,1]=>6 [2,4,1,3]=>6 [2,4,3,1]=>1 [3,1,2,4]=>1 [3,1,4,2]=>6 [3,2,1,4]=>0 [3,2,4,1]=>1 [3,4,1,2]=>1 [3,4,2,1]=>6 [4,1,2,3]=>6 [4,1,3,2]=>1 [4,2,1,3]=>1 [4,2,3,1]=>0 [4,3,1,2]=>6 [4,3,2,1]=>1 [1,2,3,4,5]=>0 [1,2,3,5,4]=>0 [1,2,4,3,5]=>0 [1,2,4,5,3]=>1 [1,2,5,3,4]=>1 [1,2,5,4,3]=>0 [1,3,2,4,5]=>0 [1,3,2,5,4]=>1 [1,3,4,2,5]=>1 [1,3,4,5,2]=>6 [1,3,5,2,4]=>6 [1,3,5,4,2]=>1 [1,4,2,3,5]=>1 [1,4,2,5,3]=>6 [1,4,3,2,5]=>0 [1,4,3,5,2]=>1 [1,4,5,2,3]=>1 [1,4,5,3,2]=>6 [1,5,2,3,4]=>6 [1,5,2,4,3]=>1 [1,5,3,2,4]=>1 [1,5,3,4,2]=>0 [1,5,4,2,3]=>6 [1,5,4,3,2]=>1 [2,1,3,4,5]=>0 [2,1,3,5,4]=>1 [2,1,4,3,5]=>1 [2,1,4,5,3]=>4 [2,1,5,3,4]=>4 [2,1,5,4,3]=>1 [2,3,1,4,5]=>1 [2,3,1,5,4]=>4 [2,3,4,1,5]=>6 [2,3,4,5,1]=>20 [2,3,5,1,4]=>20 [2,3,5,4,1]=>6 [2,4,1,3,5]=>6 [2,4,1,5,3]=>20 [2,4,3,1,5]=>1 [2,4,3,5,1]=>6 [2,4,5,1,3]=>4 [2,4,5,3,1]=>20 [2,5,1,3,4]=>20 [2,5,1,4,3]=>6 [2,5,3,1,4]=>6 [2,5,3,4,1]=>1 [2,5,4,1,3]=>20 [2,5,4,3,1]=>4 [3,1,2,4,5]=>1 [3,1,2,5,4]=>4 [3,1,4,2,5]=>6 [3,1,4,5,2]=>20 [3,1,5,2,4]=>20 [3,1,5,4,2]=>6 [3,2,1,4,5]=>0 [3,2,1,5,4]=>1 [3,2,4,1,5]=>1 [3,2,4,5,1]=>6 [3,2,5,1,4]=>6 [3,2,5,4,1]=>1 [3,4,1,2,5]=>1 [3,4,1,5,2]=>4 [3,4,2,1,5]=>6 [3,4,2,5,1]=>20 [3,4,5,1,2]=>20 [3,4,5,2,1]=>4 [3,5,1,2,4]=>4 [3,5,1,4,2]=>1 [3,5,2,1,4]=>20 [3,5,2,4,1]=>6 [3,5,4,1,2]=>4 [3,5,4,2,1]=>20 [4,1,2,3,5]=>6 [4,1,2,5,3]=>20 [4,1,3,2,5]=>1 [4,1,3,5,2]=>6 [4,1,5,2,3]=>4 [4,1,5,3,2]=>20 [4,2,1,3,5]=>1 [4,2,1,5,3]=>6 [4,2,3,1,5]=>0 [4,2,3,5,1]=>1 [4,2,5,1,3]=>1 [4,2,5,3,1]=>6 [4,3,1,2,5]=>6 [4,3,1,5,2]=>20 [4,3,2,1,5]=>1 [4,3,2,5,1]=>4 [4,3,5,1,2]=>4 [4,3,5,2,1]=>20 [4,5,1,2,3]=>20 [4,5,1,3,2]=>4 [4,5,2,1,3]=>4 [4,5,2,3,1]=>20 [4,5,3,1,2]=>1 [4,5,3,2,1]=>6 [5,1,2,3,4]=>20 [5,1,2,4,3]=>6 [5,1,3,2,4]=>6 [5,1,3,4,2]=>1 [5,1,4,2,3]=>20 [5,1,4,3,2]=>4 [5,2,1,3,4]=>6 [5,2,1,4,3]=>1 [5,2,3,1,4]=>1 [5,2,3,4,1]=>0 [5,2,4,1,3]=>6 [5,2,4,3,1]=>1 [5,3,1,2,4]=>20 [5,3,1,4,2]=>6 [5,3,2,1,4]=>4 [5,3,2,4,1]=>1 [5,3,4,1,2]=>20 [5,3,4,2,1]=>4 [5,4,1,2,3]=>4 [5,4,1,3,2]=>20 [5,4,2,1,3]=>20 [5,4,2,3,1]=>4 [5,4,3,1,2]=>6 [5,4,3,2,1]=>1 [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]=>1 [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]=>1 [1,2,4,5,3,6]=>1 [1,2,4,5,6,3]=>6 [1,2,4,6,3,5]=>6 [1,2,4,6,5,3]=>1 [1,2,5,3,4,6]=>1 [1,2,5,3,6,4]=>6 [1,2,5,4,3,6]=>0 [1,2,5,4,6,3]=>1 [1,2,5,6,3,4]=>1 [1,2,5,6,4,3]=>6 [1,2,6,3,4,5]=>6 [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]=>6 [1,2,6,5,4,3]=>1 [1,3,2,4,5,6]=>0 [1,3,2,4,6,5]=>1 [1,3,2,5,4,6]=>1 [1,3,2,5,6,4]=>4 [1,3,2,6,4,5]=>4 [1,3,2,6,5,4]=>1 [1,3,4,2,5,6]=>1 [1,3,4,2,6,5]=>4 [1,3,4,5,2,6]=>6 [1,3,4,5,6,2]=>20 [1,3,4,6,2,5]=>20 [1,3,4,6,5,2]=>6 [1,3,5,2,4,6]=>6 [1,3,5,2,6,4]=>20 [1,3,5,4,2,6]=>1 [1,3,5,4,6,2]=>6 [1,3,5,6,2,4]=>4 [1,3,5,6,4,2]=>20 [1,3,6,2,4,5]=>20 [1,3,6,2,5,4]=>6 [1,3,6,4,2,5]=>6 [1,3,6,4,5,2]=>1 [1,3,6,5,2,4]=>20 [1,3,6,5,4,2]=>4 [1,4,2,3,5,6]=>1 [1,4,2,3,6,5]=>4 [1,4,2,5,3,6]=>6 [1,4,2,5,6,3]=>20 [1,4,2,6,3,5]=>20 [1,4,2,6,5,3]=>6 [1,4,3,2,5,6]=>0 [1,4,3,2,6,5]=>1 [1,4,3,5,2,6]=>1 [1,4,3,5,6,2]=>6 [1,4,3,6,2,5]=>6 [1,4,3,6,5,2]=>1 [1,4,5,2,3,6]=>1 [1,4,5,2,6,3]=>4 [1,4,5,3,2,6]=>6 [1,4,5,3,6,2]=>20 [1,4,5,6,2,3]=>20 [1,4,5,6,3,2]=>4 [1,4,6,2,3,5]=>4 [1,4,6,2,5,3]=>1 [1,4,6,3,2,5]=>20 [1,4,6,3,5,2]=>6 [1,4,6,5,2,3]=>4 [1,4,6,5,3,2]=>20 [1,5,2,3,4,6]=>6 [1,5,2,3,6,4]=>20 [1,5,2,4,3,6]=>1 [1,5,2,4,6,3]=>6 [1,5,2,6,3,4]=>4 [1,5,2,6,4,3]=>20 [1,5,3,2,4,6]=>1 [1,5,3,2,6,4]=>6 [1,5,3,4,2,6]=>0 [1,5,3,4,6,2]=>1 [1,5,3,6,2,4]=>1 [1,5,3,6,4,2]=>6 [1,5,4,2,3,6]=>6 [1,5,4,2,6,3]=>20 [1,5,4,3,2,6]=>1 [1,5,4,3,6,2]=>4 [1,5,4,6,2,3]=>4 [1,5,4,6,3,2]=>20 [1,5,6,2,3,4]=>20 [1,5,6,2,4,3]=>4 [1,5,6,3,2,4]=>4 [1,5,6,3,4,2]=>20 [1,5,6,4,2,3]=>1 [1,5,6,4,3,2]=>6 [1,6,2,3,4,5]=>20 [1,6,2,3,5,4]=>6 [1,6,2,4,3,5]=>6 [1,6,2,4,5,3]=>1 [1,6,2,5,3,4]=>20 [1,6,2,5,4,3]=>4 [1,6,3,2,4,5]=>6 [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]=>6 [1,6,3,5,4,2]=>1 [1,6,4,2,3,5]=>20 [1,6,4,2,5,3]=>6 [1,6,4,3,2,5]=>4 [1,6,4,3,5,2]=>1 [1,6,4,5,2,3]=>20 [1,6,4,5,3,2]=>4 [1,6,5,2,3,4]=>4 [1,6,5,2,4,3]=>20 [1,6,5,3,2,4]=>20 [1,6,5,3,4,2]=>4 [1,6,5,4,2,3]=>6 [1,6,5,4,3,2]=>1 [2,1,3,4,5,6]=>0 [2,1,3,4,6,5]=>1 [2,1,3,5,4,6]=>1 [2,1,3,5,6,4]=>4 [2,1,3,6,4,5]=>4 [2,1,3,6,5,4]=>1 [2,1,4,3,5,6]=>1 [2,1,4,3,6,5]=>3 [2,1,4,5,3,6]=>4 [2,1,4,5,6,3]=>12 [2,1,4,6,3,5]=>12 [2,1,4,6,5,3]=>4 [2,1,5,3,4,6]=>4 [2,1,5,3,6,4]=>12 [2,1,5,4,3,6]=>1 [2,1,5,4,6,3]=>4 [2,1,5,6,3,4]=>3 [2,1,5,6,4,3]=>12 [2,1,6,3,4,5]=>12 [2,1,6,3,5,4]=>4 [2,1,6,4,3,5]=>4 [2,1,6,4,5,3]=>1 [2,1,6,5,3,4]=>12 [2,1,6,5,4,3]=>3 [2,3,1,4,5,6]=>1 [2,3,1,4,6,5]=>4 [2,3,1,5,4,6]=>4 [2,3,1,5,6,4]=>11 [2,3,1,6,4,5]=>11 [2,3,1,6,5,4]=>4 [2,3,4,1,5,6]=>6 [2,3,4,1,6,5]=>12 [2,3,4,5,1,6]=>20 [2,3,4,5,6,1]=>50 [2,3,4,6,1,5]=>50 [2,3,4,6,5,1]=>20 [2,3,5,1,4,6]=>20 [2,3,5,1,6,4]=>50 [2,3,5,4,1,6]=>6 [2,3,5,4,6,1]=>20 [2,3,5,6,1,4]=>12 [2,3,5,6,4,1]=>50 [2,3,6,1,4,5]=>50 [2,3,6,1,5,4]=>20 [2,3,6,4,1,5]=>20 [2,3,6,4,5,1]=>6 [2,3,6,5,1,4]=>50 [2,3,6,5,4,1]=>12 [2,4,1,3,5,6]=>6 [2,4,1,3,6,5]=>12 [2,4,1,5,3,6]=>20 [2,4,1,5,6,3]=>50 [2,4,1,6,3,5]=>50 [2,4,1,6,5,3]=>20 [2,4,3,1,5,6]=>1 [2,4,3,1,6,5]=>4 [2,4,3,5,1,6]=>6 [2,4,3,5,6,1]=>20 [2,4,3,6,1,5]=>20 [2,4,3,6,5,1]=>6 [2,4,5,1,3,6]=>4 [2,4,5,1,6,3]=>11 [2,4,5,3,1,6]=>20 [2,4,5,3,6,1]=>50 [2,4,5,6,1,3]=>50 [2,4,5,6,3,1]=>12 [2,4,6,1,3,5]=>11 [2,4,6,1,5,3]=>4 [2,4,6,3,1,5]=>50 [2,4,6,3,5,1]=>20 [2,4,6,5,1,3]=>12 [2,4,6,5,3,1]=>50 [2,5,1,3,4,6]=>20 [2,5,1,3,6,4]=>50 [2,5,1,4,3,6]=>6 [2,5,1,4,6,3]=>20 [2,5,1,6,3,4]=>12 [2,5,1,6,4,3]=>50 [2,5,3,1,4,6]=>6 [2,5,3,1,6,4]=>20 [2,5,3,4,1,6]=>1 [2,5,3,4,6,1]=>6 [2,5,3,6,1,4]=>4 [2,5,3,6,4,1]=>20 [2,5,4,1,3,6]=>20 [2,5,4,1,6,3]=>50 [2,5,4,3,1,6]=>4 [2,5,4,3,6,1]=>12 [2,5,4,6,1,3]=>11 [2,5,4,6,3,1]=>50 [2,5,6,1,3,4]=>50 [2,5,6,1,4,3]=>12 [2,5,6,3,1,4]=>11 [2,5,6,3,4,1]=>50 [2,5,6,4,1,3]=>4 [2,5,6,4,3,1]=>20 [2,6,1,3,4,5]=>50 [2,6,1,3,5,4]=>20 [2,6,1,4,3,5]=>20 [2,6,1,4,5,3]=>6 [2,6,1,5,3,4]=>50 [2,6,1,5,4,3]=>12 [2,6,3,1,4,5]=>20 [2,6,3,1,5,4]=>6 [2,6,3,4,1,5]=>6 [2,6,3,4,5,1]=>1 [2,6,3,5,1,4]=>20 [2,6,3,5,4,1]=>4 [2,6,4,1,3,5]=>50 [2,6,4,1,5,3]=>20 [2,6,4,3,1,5]=>12 [2,6,4,3,5,1]=>4 [2,6,4,5,1,3]=>50 [2,6,4,5,3,1]=>11 [2,6,5,1,3,4]=>12 [2,6,5,1,4,3]=>50 [2,6,5,3,1,4]=>50 [2,6,5,3,4,1]=>11 [2,6,5,4,1,3]=>20 [2,6,5,4,3,1]=>4 [3,1,2,4,5,6]=>1 [3,1,2,4,6,5]=>4 [3,1,2,5,4,6]=>4 [3,1,2,5,6,4]=>11 [3,1,2,6,4,5]=>11 [3,1,2,6,5,4]=>4 [3,1,4,2,5,6]=>6 [3,1,4,2,6,5]=>12 [3,1,4,5,2,6]=>20 [3,1,4,5,6,2]=>50 [3,1,4,6,2,5]=>50 [3,1,4,6,5,2]=>20 [3,1,5,2,4,6]=>20 [3,1,5,2,6,4]=>50 [3,1,5,4,2,6]=>6 [3,1,5,4,6,2]=>20 [3,1,5,6,2,4]=>12 [3,1,5,6,4,2]=>50 [3,1,6,2,4,5]=>50 [3,1,6,2,5,4]=>20 [3,1,6,4,2,5]=>20 [3,1,6,4,5,2]=>6 [3,1,6,5,2,4]=>50 [3,1,6,5,4,2]=>12 [3,2,1,4,5,6]=>0 [3,2,1,4,6,5]=>1 [3,2,1,5,4,6]=>1 [3,2,1,5,6,4]=>4 [3,2,1,6,4,5]=>4 [3,2,1,6,5,4]=>1 [3,2,4,1,5,6]=>1 [3,2,4,1,6,5]=>4 [3,2,4,5,1,6]=>6 [3,2,4,5,6,1]=>20 [3,2,4,6,1,5]=>20 [3,2,4,6,5,1]=>6 [3,2,5,1,4,6]=>6 [3,2,5,1,6,4]=>20 [3,2,5,4,1,6]=>1 [3,2,5,4,6,1]=>6 [3,2,5,6,1,4]=>4 [3,2,5,6,4,1]=>20 [3,2,6,1,4,5]=>20 [3,2,6,1,5,4]=>6 [3,2,6,4,1,5]=>6 [3,2,6,4,5,1]=>1 [3,2,6,5,1,4]=>20 [3,2,6,5,4,1]=>4 [3,4,1,2,5,6]=>1 [3,4,1,2,6,5]=>3 [3,4,1,5,2,6]=>4 [3,4,1,5,6,2]=>12 [3,4,1,6,2,5]=>12 [3,4,1,6,5,2]=>4 [3,4,2,1,5,6]=>6 [3,4,2,1,6,5]=>12 [3,4,2,5,1,6]=>20 [3,4,2,5,6,1]=>50 [3,4,2,6,1,5]=>50 [3,4,2,6,5,1]=>20 [3,4,5,1,2,6]=>20 [3,4,5,1,6,2]=>50 [3,4,5,2,1,6]=>4 [3,4,5,2,6,1]=>12 [3,4,5,6,1,2]=>11 [3,4,5,6,2,1]=>50 [3,4,6,1,2,5]=>50 [3,4,6,1,5,2]=>20 [3,4,6,2,1,5]=>12 [3,4,6,2,5,1]=>4 [3,4,6,5,1,2]=>50 [3,4,6,5,2,1]=>11 [3,5,1,2,4,6]=>4 [3,5,1,2,6,4]=>12 [3,5,1,4,2,6]=>1 [3,5,1,4,6,2]=>4 [3,5,1,6,2,4]=>3 [3,5,1,6,4,2]=>12 [3,5,2,1,4,6]=>20 [3,5,2,1,6,4]=>50 [3,5,2,4,1,6]=>6 [3,5,2,4,6,1]=>20 [3,5,2,6,1,4]=>12 [3,5,2,6,4,1]=>50 [3,5,4,1,2,6]=>4 [3,5,4,1,6,2]=>11 [3,5,4,2,1,6]=>20 [3,5,4,2,6,1]=>50 [3,5,4,6,1,2]=>50 [3,5,4,6,2,1]=>12 [3,5,6,1,2,4]=>12 [3,5,6,1,4,2]=>50 [3,5,6,2,1,4]=>50 [3,5,6,2,4,1]=>11 [3,5,6,4,1,2]=>20 [3,5,6,4,2,1]=>4 [3,6,1,2,4,5]=>12 [3,6,1,2,5,4]=>4 [3,6,1,4,2,5]=>4 [3,6,1,4,5,2]=>1 [3,6,1,5,2,4]=>12 [3,6,1,5,4,2]=>3 [3,6,2,1,4,5]=>50 [3,6,2,1,5,4]=>20 [3,6,2,4,1,5]=>20 [3,6,2,4,5,1]=>6 [3,6,2,5,1,4]=>50 [3,6,2,5,4,1]=>12 [3,6,4,1,2,5]=>11 [3,6,4,1,5,2]=>4 [3,6,4,2,1,5]=>50 [3,6,4,2,5,1]=>20 [3,6,4,5,1,2]=>12 [3,6,4,5,2,1]=>50 [3,6,5,1,2,4]=>50 [3,6,5,1,4,2]=>12 [3,6,5,2,1,4]=>11 [3,6,5,2,4,1]=>50 [3,6,5,4,1,2]=>4 [3,6,5,4,2,1]=>20 [4,1,2,3,5,6]=>6 [4,1,2,3,6,5]=>12 [4,1,2,5,3,6]=>20 [4,1,2,5,6,3]=>50 [4,1,2,6,3,5]=>50 [4,1,2,6,5,3]=>20 [4,1,3,2,5,6]=>1 [4,1,3,2,6,5]=>4 [4,1,3,5,2,6]=>6 [4,1,3,5,6,2]=>20 [4,1,3,6,2,5]=>20 [4,1,3,6,5,2]=>6 [4,1,5,2,3,6]=>4 [4,1,5,2,6,3]=>11 [4,1,5,3,2,6]=>20 [4,1,5,3,6,2]=>50 [4,1,5,6,2,3]=>50 [4,1,5,6,3,2]=>12 [4,1,6,2,3,5]=>11 [4,1,6,2,5,3]=>4 [4,1,6,3,2,5]=>50 [4,1,6,3,5,2]=>20 [4,1,6,5,2,3]=>12 [4,1,6,5,3,2]=>50 [4,2,1,3,5,6]=>1 [4,2,1,3,6,5]=>4 [4,2,1,5,3,6]=>6 [4,2,1,5,6,3]=>20 [4,2,1,6,3,5]=>20 [4,2,1,6,5,3]=>6 [4,2,3,1,5,6]=>0 [4,2,3,1,6,5]=>1 [4,2,3,5,1,6]=>1 [4,2,3,5,6,1]=>6 [4,2,3,6,1,5]=>6 [4,2,3,6,5,1]=>1 [4,2,5,1,3,6]=>1 [4,2,5,1,6,3]=>4 [4,2,5,3,1,6]=>6 [4,2,5,3,6,1]=>20 [4,2,5,6,1,3]=>20 [4,2,5,6,3,1]=>4 [4,2,6,1,3,5]=>4 [4,2,6,1,5,3]=>1 [4,2,6,3,1,5]=>20 [4,2,6,3,5,1]=>6 [4,2,6,5,1,3]=>4 [4,2,6,5,3,1]=>20 [4,3,1,2,5,6]=>6 [4,3,1,2,6,5]=>12 [4,3,1,5,2,6]=>20 [4,3,1,5,6,2]=>50 [4,3,1,6,2,5]=>50 [4,3,1,6,5,2]=>20 [4,3,2,1,5,6]=>1 [4,3,2,1,6,5]=>3 [4,3,2,5,1,6]=>4 [4,3,2,5,6,1]=>12 [4,3,2,6,1,5]=>12 [4,3,2,6,5,1]=>4 [4,3,5,1,2,6]=>4 [4,3,5,1,6,2]=>12 [4,3,5,2,1,6]=>20 [4,3,5,2,6,1]=>50 [4,3,5,6,1,2]=>50 [4,3,5,6,2,1]=>11 [4,3,6,1,2,5]=>12 [4,3,6,1,5,2]=>4 [4,3,6,2,1,5]=>50 [4,3,6,2,5,1]=>20 [4,3,6,5,1,2]=>11 [4,3,6,5,2,1]=>50 [4,5,1,2,3,6]=>20 [4,5,1,2,6,3]=>50 [4,5,1,3,2,6]=>4 [4,5,1,3,6,2]=>11 [4,5,1,6,2,3]=>12 [4,5,1,6,3,2]=>50 [4,5,2,1,3,6]=>4 [4,5,2,1,6,3]=>12 [4,5,2,3,1,6]=>20 [4,5,2,3,6,1]=>50 [4,5,2,6,1,3]=>50 [4,5,2,6,3,1]=>11 [4,5,3,1,2,6]=>1 [4,5,3,1,6,2]=>4 [4,5,3,2,1,6]=>6 [4,5,3,2,6,1]=>20 [4,5,3,6,1,2]=>20 [4,5,3,6,2,1]=>4 [4,5,6,1,2,3]=>3 [4,5,6,1,3,2]=>12 [4,5,6,2,1,3]=>12 [4,5,6,2,3,1]=>50 [4,5,6,3,1,2]=>50 [4,5,6,3,2,1]=>12 [4,6,1,2,3,5]=>50 [4,6,1,2,5,3]=>20 [4,6,1,3,2,5]=>11 [4,6,1,3,5,2]=>4 [4,6,1,5,2,3]=>50 [4,6,1,5,3,2]=>12 [4,6,2,1,3,5]=>12 [4,6,2,1,5,3]=>4 [4,6,2,3,1,5]=>50 [4,6,2,3,5,1]=>20 [4,6,2,5,1,3]=>11 [4,6,2,5,3,1]=>50 [4,6,3,1,2,5]=>4 [4,6,3,1,5,2]=>1 [4,6,3,2,1,5]=>20 [4,6,3,2,5,1]=>6 [4,6,3,5,1,2]=>4 [4,6,3,5,2,1]=>20 [4,6,5,1,2,3]=>12 [4,6,5,1,3,2]=>3 [4,6,5,2,1,3]=>50 [4,6,5,2,3,1]=>12 [4,6,5,3,1,2]=>12 [4,6,5,3,2,1]=>50 [5,1,2,3,4,6]=>20 [5,1,2,3,6,4]=>50 [5,1,2,4,3,6]=>6 [5,1,2,4,6,3]=>20 [5,1,2,6,3,4]=>12 [5,1,2,6,4,3]=>50 [5,1,3,2,4,6]=>6 [5,1,3,2,6,4]=>20 [5,1,3,4,2,6]=>1 [5,1,3,4,6,2]=>6 [5,1,3,6,2,4]=>4 [5,1,3,6,4,2]=>20 [5,1,4,2,3,6]=>20 [5,1,4,2,6,3]=>50 [5,1,4,3,2,6]=>4 [5,1,4,3,6,2]=>12 [5,1,4,6,2,3]=>11 [5,1,4,6,3,2]=>50 [5,1,6,2,3,4]=>50 [5,1,6,2,4,3]=>12 [5,1,6,3,2,4]=>11 [5,1,6,3,4,2]=>50 [5,1,6,4,2,3]=>4 [5,1,6,4,3,2]=>20 [5,2,1,3,4,6]=>6 [5,2,1,3,6,4]=>20 [5,2,1,4,3,6]=>1 [5,2,1,4,6,3]=>6 [5,2,1,6,3,4]=>4 [5,2,1,6,4,3]=>20 [5,2,3,1,4,6]=>1 [5,2,3,1,6,4]=>6 [5,2,3,4,1,6]=>0 [5,2,3,4,6,1]=>1 [5,2,3,6,1,4]=>1 [5,2,3,6,4,1]=>6 [5,2,4,1,3,6]=>6 [5,2,4,1,6,3]=>20 [5,2,4,3,1,6]=>1 [5,2,4,3,6,1]=>4 [5,2,4,6,1,3]=>4 [5,2,4,6,3,1]=>20 [5,2,6,1,3,4]=>20 [5,2,6,1,4,3]=>4 [5,2,6,3,1,4]=>4 [5,2,6,3,4,1]=>20 [5,2,6,4,1,3]=>1 [5,2,6,4,3,1]=>6 [5,3,1,2,4,6]=>20 [5,3,1,2,6,4]=>50 [5,3,1,4,2,6]=>6 [5,3,1,4,6,2]=>20 [5,3,1,6,2,4]=>12 [5,3,1,6,4,2]=>50 [5,3,2,1,4,6]=>4 [5,3,2,1,6,4]=>12 [5,3,2,4,1,6]=>1 [5,3,2,4,6,1]=>4 [5,3,2,6,1,4]=>3 [5,3,2,6,4,1]=>12 [5,3,4,1,2,6]=>20 [5,3,4,1,6,2]=>50 [5,3,4,2,1,6]=>4 [5,3,4,2,6,1]=>11 [5,3,4,6,1,2]=>12 [5,3,4,6,2,1]=>50 [5,3,6,1,2,4]=>50 [5,3,6,1,4,2]=>11 [5,3,6,2,1,4]=>12 [5,3,6,2,4,1]=>50 [5,3,6,4,1,2]=>4 [5,3,6,4,2,1]=>20 [5,4,1,2,3,6]=>4 [5,4,1,2,6,3]=>12 [5,4,1,3,2,6]=>20 [5,4,1,3,6,2]=>50 [5,4,1,6,2,3]=>50 [5,4,1,6,3,2]=>11 [5,4,2,1,3,6]=>20 [5,4,2,1,6,3]=>50 [5,4,2,3,1,6]=>4 [5,4,2,3,6,1]=>11 [5,4,2,6,1,3]=>12 [5,4,2,6,3,1]=>50 [5,4,3,1,2,6]=>6 [5,4,3,1,6,2]=>20 [5,4,3,2,1,6]=>1 [5,4,3,2,6,1]=>4 [5,4,3,6,1,2]=>4 [5,4,3,6,2,1]=>20 [5,4,6,1,2,3]=>12 [5,4,6,1,3,2]=>50 [5,4,6,2,1,3]=>3 [5,4,6,2,3,1]=>12 [5,4,6,3,1,2]=>12 [5,4,6,3,2,1]=>50 [5,6,1,2,3,4]=>11 [5,6,1,2,4,3]=>50 [5,6,1,3,2,4]=>50 [5,6,1,3,4,2]=>12 [5,6,1,4,2,3]=>20 [5,6,1,4,3,2]=>4 [5,6,2,1,3,4]=>50 [5,6,2,1,4,3]=>11 [5,6,2,3,1,4]=>12 [5,6,2,3,4,1]=>50 [5,6,2,4,1,3]=>4 [5,6,2,4,3,1]=>20 [5,6,3,1,2,4]=>20 [5,6,3,1,4,2]=>4 [5,6,3,2,1,4]=>4 [5,6,3,2,4,1]=>20 [5,6,3,4,1,2]=>1 [5,6,3,4,2,1]=>6 [5,6,4,1,2,3]=>50 [5,6,4,1,3,2]=>12 [5,6,4,2,1,3]=>12 [5,6,4,2,3,1]=>50 [5,6,4,3,1,2]=>3 [5,6,4,3,2,1]=>12 [6,1,2,3,4,5]=>50 [6,1,2,3,5,4]=>20 [6,1,2,4,3,5]=>20 [6,1,2,4,5,3]=>6 [6,1,2,5,3,4]=>50 [6,1,2,5,4,3]=>12 [6,1,3,2,4,5]=>20 [6,1,3,2,5,4]=>6 [6,1,3,4,2,5]=>6 [6,1,3,4,5,2]=>1 [6,1,3,5,2,4]=>20 [6,1,3,5,4,2]=>4 [6,1,4,2,3,5]=>50 [6,1,4,2,5,3]=>20 [6,1,4,3,2,5]=>12 [6,1,4,3,5,2]=>4 [6,1,4,5,2,3]=>50 [6,1,4,5,3,2]=>11 [6,1,5,2,3,4]=>12 [6,1,5,2,4,3]=>50 [6,1,5,3,2,4]=>50 [6,1,5,3,4,2]=>11 [6,1,5,4,2,3]=>20 [6,1,5,4,3,2]=>4 [6,2,1,3,4,5]=>20 [6,2,1,3,5,4]=>6 [6,2,1,4,3,5]=>6 [6,2,1,4,5,3]=>1 [6,2,1,5,3,4]=>20 [6,2,1,5,4,3]=>4 [6,2,3,1,4,5]=>6 [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]=>6 [6,2,3,5,4,1]=>1 [6,2,4,1,3,5]=>20 [6,2,4,1,5,3]=>6 [6,2,4,3,1,5]=>4 [6,2,4,3,5,1]=>1 [6,2,4,5,1,3]=>20 [6,2,4,5,3,1]=>4 [6,2,5,1,3,4]=>4 [6,2,5,1,4,3]=>20 [6,2,5,3,1,4]=>20 [6,2,5,3,4,1]=>4 [6,2,5,4,1,3]=>6 [6,2,5,4,3,1]=>1 [6,3,1,2,4,5]=>50 [6,3,1,2,5,4]=>20 [6,3,1,4,2,5]=>20 [6,3,1,4,5,2]=>6 [6,3,1,5,2,4]=>50 [6,3,1,5,4,2]=>12 [6,3,2,1,4,5]=>12 [6,3,2,1,5,4]=>4 [6,3,2,4,1,5]=>4 [6,3,2,4,5,1]=>1 [6,3,2,5,1,4]=>12 [6,3,2,5,4,1]=>3 [6,3,4,1,2,5]=>50 [6,3,4,1,5,2]=>20 [6,3,4,2,1,5]=>11 [6,3,4,2,5,1]=>4 [6,3,4,5,1,2]=>50 [6,3,4,5,2,1]=>12 [6,3,5,1,2,4]=>11 [6,3,5,1,4,2]=>50 [6,3,5,2,1,4]=>50 [6,3,5,2,4,1]=>12 [6,3,5,4,1,2]=>20 [6,3,5,4,2,1]=>4 [6,4,1,2,3,5]=>12 [6,4,1,2,5,3]=>4 [6,4,1,3,2,5]=>50 [6,4,1,3,5,2]=>20 [6,4,1,5,2,3]=>11 [6,4,1,5,3,2]=>50 [6,4,2,1,3,5]=>50 [6,4,2,1,5,3]=>20 [6,4,2,3,1,5]=>11 [6,4,2,3,5,1]=>4 [6,4,2,5,1,3]=>50 [6,4,2,5,3,1]=>12 [6,4,3,1,2,5]=>20 [6,4,3,1,5,2]=>6 [6,4,3,2,1,5]=>4 [6,4,3,2,5,1]=>1 [6,4,3,5,1,2]=>20 [6,4,3,5,2,1]=>4 [6,4,5,1,2,3]=>50 [6,4,5,1,3,2]=>12 [6,4,5,2,1,3]=>12 [6,4,5,2,3,1]=>3 [6,4,5,3,1,2]=>50 [6,4,5,3,2,1]=>12 [6,5,1,2,3,4]=>50 [6,5,1,2,4,3]=>11 [6,5,1,3,2,4]=>12 [6,5,1,3,4,2]=>50 [6,5,1,4,2,3]=>4 [6,5,1,4,3,2]=>20 [6,5,2,1,3,4]=>11 [6,5,2,1,4,3]=>50 [6,5,2,3,1,4]=>50 [6,5,2,3,4,1]=>12 [6,5,2,4,1,3]=>20 [6,5,2,4,3,1]=>4 [6,5,3,1,2,4]=>4 [6,5,3,1,4,2]=>20 [6,5,3,2,1,4]=>20 [6,5,3,2,4,1]=>4 [6,5,3,4,1,2]=>6 [6,5,3,4,2,1]=>1 [6,5,4,1,2,3]=>12 [6,5,4,1,3,2]=>50 [6,5,4,2,1,3]=>50 [6,5,4,2,3,1]=>12 [6,5,4,3,1,2]=>12 [6,5,4,3,2,1]=>3
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Description
The factorization defect of a permutation.
The factorization poset of a permutation $\sigma$ is the principal order ideal generated by $\sigma$ in the absolute order. In particular, the maximal chains in the factorization poset of $\sigma$ are in bijection with the reduced factorizations of $\sigma$ into transpositions. The factorization defect of $\sigma$ is the number of rank-2 elements in its factorization poset.
This is the statistic "d" defined in [1, Section 6.1], where it was called the minimal size of a feedback arc set in the cycle graph. The fact that this equals the number of rank-2 elements in the factorization poset follows from [1, Proposition 6.3] together with the shellability of the factorization poset.
References
[1] Mühle, H., Ripoll, V. Connectivity Properties of Factorization Posets in Generated Groups DOI:10.1007/s11083-019-09496-1
Code
def narayana_number(n,k):
    return 1/n*binomial(n,k)*binomial(n,k-1)

def defect_stat(pi):
    c = tuple(p.cycle_type())
    return sum([narayana_number(c[T[0]],2)*narayana_number(c[T[1]],2) for T in Subsets(range(len(c)),2)]) + sum([narayana_number(t,3) for t in c])

Created
Jul 07, 2021 at 10:23 by Henri Mühle
Updated
Jul 07, 2021 at 10:23 by Henri Mühle