edit this statistic or download as text // json
Identifier
Values
=>
[1,2]=>2 [2,1]=>2 [1,2,3]=>6 [1,3,2]=>6 [2,1,3]=>6 [2,3,1]=>6 [3,1,2]=>6 [3,2,1]=>6 [1,2,3,4]=>24 [1,2,4,3]=>24 [1,3,2,4]=>24 [1,3,4,2]=>24 [1,4,2,3]=>24 [1,4,3,2]=>24 [2,1,3,4]=>24 [2,1,4,3]=>24 [2,3,1,4]=>24 [2,3,4,1]=>24 [2,4,1,3]=>25 [2,4,3,1]=>24 [3,1,2,4]=>24 [3,1,4,2]=>25 [3,2,1,4]=>24 [3,2,4,1]=>24 [3,4,1,2]=>24 [3,4,2,1]=>24 [4,1,2,3]=>24 [4,1,3,2]=>24 [4,2,1,3]=>24 [4,2,3,1]=>24 [4,3,1,2]=>24 [4,3,2,1]=>24 [1,2,3,4,5]=>120 [1,2,3,5,4]=>120 [1,2,4,3,5]=>120 [1,2,4,5,3]=>120 [1,2,5,3,4]=>120 [1,2,5,4,3]=>120 [1,3,2,4,5]=>120 [1,3,2,5,4]=>120 [1,3,4,2,5]=>120 [1,3,4,5,2]=>120 [1,3,5,2,4]=>125 [1,3,5,4,2]=>120 [1,4,2,3,5]=>120 [1,4,2,5,3]=>125 [1,4,3,2,5]=>120 [1,4,3,5,2]=>120 [1,4,5,2,3]=>120 [1,4,5,3,2]=>120 [1,5,2,3,4]=>120 [1,5,2,4,3]=>120 [1,5,3,2,4]=>120 [1,5,3,4,2]=>120 [1,5,4,2,3]=>120 [1,5,4,3,2]=>120 [2,1,3,4,5]=>120 [2,1,3,5,4]=>120 [2,1,4,3,5]=>120 [2,1,4,5,3]=>120 [2,1,5,3,4]=>120 [2,1,5,4,3]=>120 [2,3,1,4,5]=>120 [2,3,1,5,4]=>120 [2,3,4,1,5]=>120 [2,3,4,5,1]=>120 [2,3,5,1,4]=>126 [2,3,5,4,1]=>120 [2,4,1,3,5]=>125 [2,4,1,5,3]=>128 [2,4,3,1,5]=>120 [2,4,3,5,1]=>120 [2,4,5,1,3]=>126 [2,4,5,3,1]=>120 [2,5,1,3,4]=>126 [2,5,1,4,3]=>126 [2,5,3,1,4]=>121 [2,5,3,4,1]=>120 [2,5,4,1,3]=>126 [2,5,4,3,1]=>120 [3,1,2,4,5]=>120 [3,1,2,5,4]=>120 [3,1,4,2,5]=>125 [3,1,4,5,2]=>126 [3,1,5,2,4]=>128 [3,1,5,4,2]=>126 [3,2,1,4,5]=>120 [3,2,1,5,4]=>120 [3,2,4,1,5]=>120 [3,2,4,5,1]=>120 [3,2,5,1,4]=>126 [3,2,5,4,1]=>120 [3,4,1,2,5]=>120 [3,4,1,5,2]=>126 [3,4,2,1,5]=>120 [3,4,2,5,1]=>120 [3,4,5,1,2]=>120 [3,4,5,2,1]=>120 [3,5,1,2,4]=>126 [3,5,1,4,2]=>128 [3,5,2,1,4]=>126 [3,5,2,4,1]=>125 [3,5,4,1,2]=>120 [3,5,4,2,1]=>120 [4,1,2,3,5]=>120 [4,1,2,5,3]=>126 [4,1,3,2,5]=>120 [4,1,3,5,2]=>121 [4,1,5,2,3]=>126 [4,1,5,3,2]=>126 [4,2,1,3,5]=>120 [4,2,1,5,3]=>126 [4,2,3,1,5]=>120 [4,2,3,5,1]=>120 [4,2,5,1,3]=>128 [4,2,5,3,1]=>125 [4,3,1,2,5]=>120 [4,3,1,5,2]=>126 [4,3,2,1,5]=>120 [4,3,2,5,1]=>120 [4,3,5,1,2]=>120 [4,3,5,2,1]=>120 [4,5,1,2,3]=>120 [4,5,1,3,2]=>120 [4,5,2,1,3]=>120 [4,5,2,3,1]=>120 [4,5,3,1,2]=>120 [4,5,3,2,1]=>120 [5,1,2,3,4]=>120 [5,1,2,4,3]=>120 [5,1,3,2,4]=>120 [5,1,3,4,2]=>120 [5,1,4,2,3]=>120 [5,1,4,3,2]=>120 [5,2,1,3,4]=>120 [5,2,1,4,3]=>120 [5,2,3,1,4]=>120 [5,2,3,4,1]=>120 [5,2,4,1,3]=>125 [5,2,4,3,1]=>120 [5,3,1,2,4]=>120 [5,3,1,4,2]=>125 [5,3,2,1,4]=>120 [5,3,2,4,1]=>120 [5,3,4,1,2]=>120 [5,3,4,2,1]=>120 [5,4,1,2,3]=>120 [5,4,1,3,2]=>120 [5,4,2,1,3]=>120 [5,4,2,3,1]=>120 [5,4,3,1,2]=>120 [5,4,3,2,1]=>120 [1,2,3,4,5,6]=>720 [1,2,3,4,6,5]=>720 [1,2,3,5,4,6]=>720 [1,2,3,5,6,4]=>720 [1,2,3,6,4,5]=>720 [1,2,3,6,5,4]=>720 [1,2,4,3,5,6]=>720 [1,2,4,3,6,5]=>720 [1,2,4,5,3,6]=>720 [1,2,4,5,6,3]=>720 [1,2,4,6,3,5]=>750 [1,2,4,6,5,3]=>720 [1,2,5,3,4,6]=>720 [1,2,5,3,6,4]=>750 [1,2,5,4,3,6]=>720 [1,2,5,4,6,3]=>720 [1,2,5,6,3,4]=>720 [1,2,5,6,4,3]=>720 [1,2,6,3,4,5]=>720 [1,2,6,3,5,4]=>720 [1,2,6,4,3,5]=>720 [1,2,6,4,5,3]=>720 [1,2,6,5,3,4]=>720 [1,2,6,5,4,3]=>720 [1,3,2,4,5,6]=>720 [1,3,2,4,6,5]=>720 [1,3,2,5,4,6]=>720 [1,3,2,5,6,4]=>720 [1,3,2,6,4,5]=>720 [1,3,2,6,5,4]=>720 [1,3,4,2,5,6]=>720 [1,3,4,2,6,5]=>720 [1,3,4,5,2,6]=>720 [1,3,4,5,6,2]=>720 [1,3,4,6,2,5]=>756 [1,3,4,6,5,2]=>720 [1,3,5,2,4,6]=>750 [1,3,5,2,6,4]=>768 [1,3,5,4,2,6]=>720 [1,3,5,4,6,2]=>720 [1,3,5,6,2,4]=>756 [1,3,5,6,4,2]=>720 [1,3,6,2,4,5]=>756 [1,3,6,2,5,4]=>756 [1,3,6,4,2,5]=>726 [1,3,6,4,5,2]=>720 [1,3,6,5,2,4]=>756 [1,3,6,5,4,2]=>720 [1,4,2,3,5,6]=>720 [1,4,2,3,6,5]=>720 [1,4,2,5,3,6]=>750 [1,4,2,5,6,3]=>756 [1,4,2,6,3,5]=>768 [1,4,2,6,5,3]=>756 [1,4,3,2,5,6]=>720 [1,4,3,2,6,5]=>720 [1,4,3,5,2,6]=>720 [1,4,3,5,6,2]=>720 [1,4,3,6,2,5]=>756 [1,4,3,6,5,2]=>720 [1,4,5,2,3,6]=>720 [1,4,5,2,6,3]=>756 [1,4,5,3,2,6]=>720 [1,4,5,3,6,2]=>720 [1,4,5,6,2,3]=>720 [1,4,5,6,3,2]=>720 [1,4,6,2,3,5]=>756 [1,4,6,2,5,3]=>768 [1,4,6,3,2,5]=>756 [1,4,6,3,5,2]=>750 [1,4,6,5,2,3]=>720 [1,4,6,5,3,2]=>720 [1,5,2,3,4,6]=>720 [1,5,2,3,6,4]=>756 [1,5,2,4,3,6]=>720 [1,5,2,4,6,3]=>726 [1,5,2,6,3,4]=>756 [1,5,2,6,4,3]=>756 [1,5,3,2,4,6]=>720 [1,5,3,2,6,4]=>756 [1,5,3,4,2,6]=>720 [1,5,3,4,6,2]=>720 [1,5,3,6,2,4]=>768 [1,5,3,6,4,2]=>750 [1,5,4,2,3,6]=>720 [1,5,4,2,6,3]=>756 [1,5,4,3,2,6]=>720 [1,5,4,3,6,2]=>720 [1,5,4,6,2,3]=>720 [1,5,4,6,3,2]=>720 [1,5,6,2,3,4]=>720 [1,5,6,2,4,3]=>720 [1,5,6,3,2,4]=>720 [1,5,6,3,4,2]=>720 [1,5,6,4,2,3]=>720 [1,5,6,4,3,2]=>720 [1,6,2,3,4,5]=>720 [1,6,2,3,5,4]=>720 [1,6,2,4,3,5]=>720 [1,6,2,4,5,3]=>720 [1,6,2,5,3,4]=>720 [1,6,2,5,4,3]=>720 [1,6,3,2,4,5]=>720 [1,6,3,2,5,4]=>720 [1,6,3,4,2,5]=>720 [1,6,3,4,5,2]=>720 [1,6,3,5,2,4]=>750 [1,6,3,5,4,2]=>720 [1,6,4,2,3,5]=>720 [1,6,4,2,5,3]=>750 [1,6,4,3,2,5]=>720 [1,6,4,3,5,2]=>720 [1,6,4,5,2,3]=>720 [1,6,4,5,3,2]=>720 [1,6,5,2,3,4]=>720 [1,6,5,2,4,3]=>720 [1,6,5,3,2,4]=>720 [1,6,5,3,4,2]=>720 [1,6,5,4,2,3]=>720 [1,6,5,4,3,2]=>720 [2,1,3,4,5,6]=>720 [2,1,3,4,6,5]=>720 [2,1,3,5,4,6]=>720 [2,1,3,5,6,4]=>720 [2,1,3,6,4,5]=>720 [2,1,3,6,5,4]=>720 [2,1,4,3,5,6]=>720 [2,1,4,3,6,5]=>720 [2,1,4,5,3,6]=>720 [2,1,4,5,6,3]=>720 [2,1,4,6,3,5]=>750 [2,1,4,6,5,3]=>720 [2,1,5,3,4,6]=>720 [2,1,5,3,6,4]=>750 [2,1,5,4,3,6]=>720 [2,1,5,4,6,3]=>720 [2,1,5,6,3,4]=>720 [2,1,5,6,4,3]=>720 [2,1,6,3,4,5]=>720 [2,1,6,3,5,4]=>720 [2,1,6,4,3,5]=>720 [2,1,6,4,5,3]=>720 [2,1,6,5,3,4]=>720 [2,1,6,5,4,3]=>720 [2,3,1,4,5,6]=>720 [2,3,1,4,6,5]=>720 [2,3,1,5,4,6]=>720 [2,3,1,5,6,4]=>720 [2,3,1,6,4,5]=>720 [2,3,1,6,5,4]=>720 [2,3,4,1,5,6]=>720 [2,3,4,1,6,5]=>720 [2,3,4,5,1,6]=>720 [2,3,4,5,6,1]=>720 [2,3,4,6,1,5]=>756 [2,3,4,6,5,1]=>720 [2,3,5,1,4,6]=>756 [2,3,5,1,6,4]=>770 [2,3,5,4,1,6]=>720 [2,3,5,4,6,1]=>720 [2,3,5,6,1,4]=>768 [2,3,5,6,4,1]=>720 [2,3,6,1,4,5]=>760 [2,3,6,1,5,4]=>760 [2,3,6,4,1,5]=>728 [2,3,6,4,5,1]=>720 [2,3,6,5,1,4]=>768 [2,3,6,5,4,1]=>720 [2,4,1,3,5,6]=>750 [2,4,1,3,6,5]=>750 [2,4,1,5,3,6]=>768 [2,4,1,5,6,3]=>770 [2,4,1,6,3,5]=>793 [2,4,1,6,5,3]=>770 [2,4,3,1,5,6]=>720 [2,4,3,1,6,5]=>720 [2,4,3,5,1,6]=>720 [2,4,3,5,6,1]=>720 [2,4,3,6,1,5]=>756 [2,4,3,6,5,1]=>720 [2,4,5,1,3,6]=>756 [2,4,5,1,6,3]=>780 [2,4,5,3,1,6]=>720 [2,4,5,3,6,1]=>720 [2,4,5,6,1,3]=>756 [2,4,5,6,3,1]=>720 [2,4,6,1,3,5]=>798 [2,4,6,1,5,3]=>792 [2,4,6,3,1,5]=>759 [2,4,6,3,5,1]=>750 [2,4,6,5,1,3]=>756 [2,4,6,5,3,1]=>720 [2,5,1,3,4,6]=>756 [2,5,1,3,6,4]=>792 [2,5,1,4,3,6]=>756 [2,5,1,4,6,3]=>760 [2,5,1,6,3,4]=>780 [2,5,1,6,4,3]=>780 [2,5,3,1,4,6]=>726 [2,5,3,1,6,4]=>760 [2,5,3,4,1,6]=>720 [2,5,3,4,6,1]=>720 [2,5,3,6,1,4]=>777 [2,5,3,6,4,1]=>750 [2,5,4,1,3,6]=>756 [2,5,4,1,6,3]=>780 [2,5,4,3,1,6]=>720 [2,5,4,3,6,1]=>720 [2,5,4,6,1,3]=>756 [2,5,4,6,3,1]=>720 [2,5,6,1,3,4]=>768 [2,5,6,1,4,3]=>768 [2,5,6,3,1,4]=>728 [2,5,6,3,4,1]=>720 [2,5,6,4,1,3]=>756 [2,5,6,4,3,1]=>720 [2,6,1,3,4,5]=>756 [2,6,1,3,5,4]=>756 [2,6,1,4,3,5]=>756 [2,6,1,4,5,3]=>756 [2,6,1,5,3,4]=>756 [2,6,1,5,4,3]=>756 [2,6,3,1,4,5]=>728 [2,6,3,1,5,4]=>728 [2,6,3,4,1,5]=>722 [2,6,3,4,5,1]=>720 [2,6,3,5,1,4]=>759 [2,6,3,5,4,1]=>720 [2,6,4,1,3,5]=>759 [2,6,4,1,5,3]=>777 [2,6,4,3,1,5]=>722 [2,6,4,3,5,1]=>720 [2,6,4,5,1,3]=>756 [2,6,4,5,3,1]=>720 [2,6,5,1,3,4]=>768 [2,6,5,1,4,3]=>768 [2,6,5,3,1,4]=>728 [2,6,5,3,4,1]=>720 [2,6,5,4,1,3]=>756 [2,6,5,4,3,1]=>720 [3,1,2,4,5,6]=>720 [3,1,2,4,6,5]=>720 [3,1,2,5,4,6]=>720 [3,1,2,5,6,4]=>720 [3,1,2,6,4,5]=>720 [3,1,2,6,5,4]=>720 [3,1,4,2,5,6]=>750 [3,1,4,2,6,5]=>750 [3,1,4,5,2,6]=>756 [3,1,4,5,6,2]=>756 [3,1,4,6,2,5]=>792 [3,1,4,6,5,2]=>756 [3,1,5,2,4,6]=>768 [3,1,5,2,6,4]=>793 [3,1,5,4,2,6]=>756 [3,1,5,4,6,2]=>756 [3,1,5,6,2,4]=>780 [3,1,5,6,4,2]=>756 [3,1,6,2,4,5]=>770 [3,1,6,2,5,4]=>770 [3,1,6,4,2,5]=>760 [3,1,6,4,5,2]=>756 [3,1,6,5,2,4]=>780 [3,1,6,5,4,2]=>756 [3,2,1,4,5,6]=>720 [3,2,1,4,6,5]=>720 [3,2,1,5,4,6]=>720 [3,2,1,5,6,4]=>720 [3,2,1,6,4,5]=>720 [3,2,1,6,5,4]=>720 [3,2,4,1,5,6]=>720 [3,2,4,1,6,5]=>720 [3,2,4,5,1,6]=>720 [3,2,4,5,6,1]=>720 [3,2,4,6,1,5]=>756 [3,2,4,6,5,1]=>720 [3,2,5,1,4,6]=>756 [3,2,5,1,6,4]=>770 [3,2,5,4,1,6]=>720 [3,2,5,4,6,1]=>720 [3,2,5,6,1,4]=>768 [3,2,5,6,4,1]=>720 [3,2,6,1,4,5]=>760 [3,2,6,1,5,4]=>760 [3,2,6,4,1,5]=>728 [3,2,6,4,5,1]=>720 [3,2,6,5,1,4]=>768 [3,2,6,5,4,1]=>720 [3,4,1,2,5,6]=>720 [3,4,1,2,6,5]=>720 [3,4,1,5,2,6]=>756 [3,4,1,5,6,2]=>768 [3,4,1,6,2,5]=>780 [3,4,1,6,5,2]=>768 [3,4,2,1,5,6]=>720 [3,4,2,1,6,5]=>720 [3,4,2,5,1,6]=>720 [3,4,2,5,6,1]=>720 [3,4,2,6,1,5]=>756 [3,4,2,6,5,1]=>720 [3,4,5,1,2,6]=>720 [3,4,5,1,6,2]=>756 [3,4,5,2,1,6]=>720 [3,4,5,2,6,1]=>720 [3,4,5,6,1,2]=>720 [3,4,5,6,2,1]=>720 [3,4,6,1,2,5]=>768 [3,4,6,1,5,2]=>780 [3,4,6,2,1,5]=>768 [3,4,6,2,5,1]=>756 [3,4,6,5,1,2]=>720 [3,4,6,5,2,1]=>720 [3,5,1,2,4,6]=>756 [3,5,1,2,6,4]=>780 [3,5,1,4,2,6]=>768 [3,5,1,4,6,2]=>777 [3,5,1,6,2,4]=>792 [3,5,1,6,4,2]=>792 [3,5,2,1,4,6]=>756 [3,5,2,1,6,4]=>780 [3,5,2,4,1,6]=>750 [3,5,2,4,6,1]=>750 [3,5,2,6,1,4]=>792 [3,5,2,6,4,1]=>768 [3,5,4,1,2,6]=>720 [3,5,4,1,6,2]=>756 [3,5,4,2,1,6]=>720 [3,5,4,2,6,1]=>720 [3,5,4,6,1,2]=>720 [3,5,4,6,2,1]=>720 [3,5,6,1,2,4]=>760 [3,5,6,1,4,2]=>770 [3,5,6,2,1,4]=>760 [3,5,6,2,4,1]=>756 [3,5,6,4,1,2]=>720 [3,5,6,4,2,1]=>720 [3,6,1,2,4,5]=>768 [3,6,1,2,5,4]=>768 [3,6,1,4,2,5]=>777 [3,6,1,4,5,2]=>780 [3,6,1,5,2,4]=>792 [3,6,1,5,4,2]=>780 [3,6,2,1,4,5]=>768 [3,6,2,1,5,4]=>768 [3,6,2,4,1,5]=>759 [3,6,2,4,5,1]=>756 [3,6,2,5,1,4]=>798 [3,6,2,5,4,1]=>756 [3,6,4,1,2,5]=>728 [3,6,4,1,5,2]=>760 [3,6,4,2,1,5]=>728 [3,6,4,2,5,1]=>726 [3,6,4,5,1,2]=>720 [3,6,4,5,2,1]=>720 [3,6,5,1,2,4]=>760 [3,6,5,1,4,2]=>770 [3,6,5,2,1,4]=>760 [3,6,5,2,4,1]=>756 [3,6,5,4,1,2]=>720 [3,6,5,4,2,1]=>720 [4,1,2,3,5,6]=>720 [4,1,2,3,6,5]=>720 [4,1,2,5,3,6]=>756 [4,1,2,5,6,3]=>760 [4,1,2,6,3,5]=>770 [4,1,2,6,5,3]=>760 [4,1,3,2,5,6]=>720 [4,1,3,2,6,5]=>720 [4,1,3,5,2,6]=>726 [4,1,3,5,6,2]=>728 [4,1,3,6,2,5]=>760 [4,1,3,6,5,2]=>728 [4,1,5,2,3,6]=>756 [4,1,5,2,6,3]=>798 [4,1,5,3,2,6]=>756 [4,1,5,3,6,2]=>759 [4,1,5,6,2,3]=>768 [4,1,5,6,3,2]=>768 [4,1,6,2,3,5]=>780 [4,1,6,2,5,3]=>792 [4,1,6,3,2,5]=>780 [4,1,6,3,5,2]=>777 [4,1,6,5,2,3]=>768 [4,1,6,5,3,2]=>768 [4,2,1,3,5,6]=>720 [4,2,1,3,6,5]=>720 [4,2,1,5,3,6]=>756 [4,2,1,5,6,3]=>760 [4,2,1,6,3,5]=>770 [4,2,1,6,5,3]=>760 [4,2,3,1,5,6]=>720 [4,2,3,1,6,5]=>720 [4,2,3,5,1,6]=>720 [4,2,3,5,6,1]=>720 [4,2,3,6,1,5]=>756 [4,2,3,6,5,1]=>720 [4,2,5,1,3,6]=>768 [4,2,5,1,6,3]=>792 [4,2,5,3,1,6]=>750 [4,2,5,3,6,1]=>750 [4,2,5,6,1,3]=>780 [4,2,5,6,3,1]=>756 [4,2,6,1,3,5]=>792 [4,2,6,1,5,3]=>792 [4,2,6,3,1,5]=>777 [4,2,6,3,5,1]=>768 [4,2,6,5,1,3]=>780 [4,2,6,5,3,1]=>756 [4,3,1,2,5,6]=>720 [4,3,1,2,6,5]=>720 [4,3,1,5,2,6]=>756 [4,3,1,5,6,2]=>768 [4,3,1,6,2,5]=>780 [4,3,1,6,5,2]=>768 [4,3,2,1,5,6]=>720 [4,3,2,1,6,5]=>720 [4,3,2,5,1,6]=>720 [4,3,2,5,6,1]=>720 [4,3,2,6,1,5]=>756 [4,3,2,6,5,1]=>720 [4,3,5,1,2,6]=>720 [4,3,5,1,6,2]=>756 [4,3,5,2,1,6]=>720 [4,3,5,2,6,1]=>720 [4,3,5,6,1,2]=>720 [4,3,5,6,2,1]=>720 [4,3,6,1,2,5]=>768 [4,3,6,1,5,2]=>780 [4,3,6,2,1,5]=>768 [4,3,6,2,5,1]=>756 [4,3,6,5,1,2]=>720 [4,3,6,5,2,1]=>720 [4,5,1,2,3,6]=>720 [4,5,1,2,6,3]=>768 [4,5,1,3,2,6]=>720 [4,5,1,3,6,2]=>728 [4,5,1,6,2,3]=>760 [4,5,1,6,3,2]=>760 [4,5,2,1,3,6]=>720 [4,5,2,1,6,3]=>768 [4,5,2,3,1,6]=>720 [4,5,2,3,6,1]=>720 [4,5,2,6,1,3]=>770 [4,5,2,6,3,1]=>756 [4,5,3,1,2,6]=>720 [4,5,3,1,6,2]=>756 [4,5,3,2,1,6]=>720 [4,5,3,2,6,1]=>720 [4,5,3,6,1,2]=>720 [4,5,3,6,2,1]=>720 [4,5,6,1,2,3]=>720 [4,5,6,1,3,2]=>720 [4,5,6,2,1,3]=>720 [4,5,6,2,3,1]=>720 [4,5,6,3,1,2]=>720 [4,5,6,3,2,1]=>720 [4,6,1,2,3,5]=>756 [4,6,1,2,5,3]=>780 [4,6,1,3,2,5]=>756 [4,6,1,3,5,2]=>760 [4,6,1,5,2,3]=>770 [4,6,1,5,3,2]=>770 [4,6,2,1,3,5]=>756 [4,6,2,1,5,3]=>780 [4,6,2,3,1,5]=>756 [4,6,2,3,5,1]=>756 [4,6,2,5,1,3]=>793 [4,6,2,5,3,1]=>768 [4,6,3,1,2,5]=>756 [4,6,3,1,5,2]=>792 [4,6,3,2,1,5]=>756 [4,6,3,2,5,1]=>756 [4,6,3,5,1,2]=>750 [4,6,3,5,2,1]=>750 [4,6,5,1,2,3]=>720 [4,6,5,1,3,2]=>720 [4,6,5,2,1,3]=>720 [4,6,5,2,3,1]=>720 [4,6,5,3,1,2]=>720 [4,6,5,3,2,1]=>720 [5,1,2,3,4,6]=>720 [5,1,2,3,6,4]=>756 [5,1,2,4,3,6]=>720 [5,1,2,4,6,3]=>728 [5,1,2,6,3,4]=>768 [5,1,2,6,4,3]=>768 [5,1,3,2,4,6]=>720 [5,1,3,2,6,4]=>756 [5,1,3,4,2,6]=>720 [5,1,3,4,6,2]=>722 [5,1,3,6,2,4]=>777 [5,1,3,6,4,2]=>759 [5,1,4,2,3,6]=>720 [5,1,4,2,6,3]=>759 [5,1,4,3,2,6]=>720 [5,1,4,3,6,2]=>722 [5,1,4,6,2,3]=>728 [5,1,4,6,3,2]=>728 [5,1,6,2,3,4]=>756 [5,1,6,2,4,3]=>756 [5,1,6,3,2,4]=>756 [5,1,6,3,4,2]=>756 [5,1,6,4,2,3]=>756 [5,1,6,4,3,2]=>756 [5,2,1,3,4,6]=>720 [5,2,1,3,6,4]=>756 [5,2,1,4,3,6]=>720 [5,2,1,4,6,3]=>728 [5,2,1,6,3,4]=>768 [5,2,1,6,4,3]=>768 [5,2,3,1,4,6]=>720 [5,2,3,1,6,4]=>756 [5,2,3,4,1,6]=>720 [5,2,3,4,6,1]=>720 [5,2,3,6,1,4]=>780 [5,2,3,6,4,1]=>756 [5,2,4,1,3,6]=>750 [5,2,4,1,6,3]=>777 [5,2,4,3,1,6]=>720 [5,2,4,3,6,1]=>720 [5,2,4,6,1,3]=>760 [5,2,4,6,3,1]=>726 [5,2,6,1,3,4]=>780 [5,2,6,1,4,3]=>780 [5,2,6,3,1,4]=>760 [5,2,6,3,4,1]=>756 [5,2,6,4,1,3]=>792 [5,2,6,4,3,1]=>756 [5,3,1,2,4,6]=>720 [5,3,1,2,6,4]=>756 [5,3,1,4,2,6]=>750 [5,3,1,4,6,2]=>759 [5,3,1,6,2,4]=>792 [5,3,1,6,4,2]=>798 [5,3,2,1,4,6]=>720 [5,3,2,1,6,4]=>756 [5,3,2,4,1,6]=>720 [5,3,2,4,6,1]=>720 [5,3,2,6,1,4]=>780 [5,3,2,6,4,1]=>756 [5,3,4,1,2,6]=>720 [5,3,4,1,6,2]=>756 [5,3,4,2,1,6]=>720 [5,3,4,2,6,1]=>720 [5,3,4,6,1,2]=>720 [5,3,4,6,2,1]=>720 [5,3,6,1,2,4]=>770 [5,3,6,1,4,2]=>793 [5,3,6,2,1,4]=>770 [5,3,6,2,4,1]=>768 [5,3,6,4,1,2]=>750 [5,3,6,4,2,1]=>750 [5,4,1,2,3,6]=>720 [5,4,1,2,6,3]=>768 [5,4,1,3,2,6]=>720 [5,4,1,3,6,2]=>728 [5,4,1,6,2,3]=>760 [5,4,1,6,3,2]=>760 [5,4,2,1,3,6]=>720 [5,4,2,1,6,3]=>768 [5,4,2,3,1,6]=>720 [5,4,2,3,6,1]=>720 [5,4,2,6,1,3]=>770 [5,4,2,6,3,1]=>756 [5,4,3,1,2,6]=>720 [5,4,3,1,6,2]=>756 [5,4,3,2,1,6]=>720 [5,4,3,2,6,1]=>720 [5,4,3,6,1,2]=>720 [5,4,3,6,2,1]=>720 [5,4,6,1,2,3]=>720 [5,4,6,1,3,2]=>720 [5,4,6,2,1,3]=>720 [5,4,6,2,3,1]=>720 [5,4,6,3,1,2]=>720 [5,4,6,3,2,1]=>720 [5,6,1,2,3,4]=>720 [5,6,1,2,4,3]=>720 [5,6,1,3,2,4]=>720 [5,6,1,3,4,2]=>720 [5,6,1,4,2,3]=>720 [5,6,1,4,3,2]=>720 [5,6,2,1,3,4]=>720 [5,6,2,1,4,3]=>720 [5,6,2,3,1,4]=>720 [5,6,2,3,4,1]=>720 [5,6,2,4,1,3]=>750 [5,6,2,4,3,1]=>720 [5,6,3,1,2,4]=>720 [5,6,3,1,4,2]=>750 [5,6,3,2,1,4]=>720 [5,6,3,2,4,1]=>720 [5,6,3,4,1,2]=>720 [5,6,3,4,2,1]=>720 [5,6,4,1,2,3]=>720 [5,6,4,1,3,2]=>720 [5,6,4,2,1,3]=>720 [5,6,4,2,3,1]=>720 [5,6,4,3,1,2]=>720 [5,6,4,3,2,1]=>720 [6,1,2,3,4,5]=>720 [6,1,2,3,5,4]=>720 [6,1,2,4,3,5]=>720 [6,1,2,4,5,3]=>720 [6,1,2,5,3,4]=>720 [6,1,2,5,4,3]=>720 [6,1,3,2,4,5]=>720 [6,1,3,2,5,4]=>720 [6,1,3,4,2,5]=>720 [6,1,3,4,5,2]=>720 [6,1,3,5,2,4]=>750 [6,1,3,5,4,2]=>720 [6,1,4,2,3,5]=>720 [6,1,4,2,5,3]=>750 [6,1,4,3,2,5]=>720 [6,1,4,3,5,2]=>720 [6,1,4,5,2,3]=>720 [6,1,4,5,3,2]=>720 [6,1,5,2,3,4]=>720 [6,1,5,2,4,3]=>720 [6,1,5,3,2,4]=>720 [6,1,5,3,4,2]=>720 [6,1,5,4,2,3]=>720 [6,1,5,4,3,2]=>720 [6,2,1,3,4,5]=>720 [6,2,1,3,5,4]=>720 [6,2,1,4,3,5]=>720 [6,2,1,4,5,3]=>720 [6,2,1,5,3,4]=>720 [6,2,1,5,4,3]=>720 [6,2,3,1,4,5]=>720 [6,2,3,1,5,4]=>720 [6,2,3,4,1,5]=>720 [6,2,3,4,5,1]=>720 [6,2,3,5,1,4]=>756 [6,2,3,5,4,1]=>720 [6,2,4,1,3,5]=>750 [6,2,4,1,5,3]=>768 [6,2,4,3,1,5]=>720 [6,2,4,3,5,1]=>720 [6,2,4,5,1,3]=>756 [6,2,4,5,3,1]=>720 [6,2,5,1,3,4]=>756 [6,2,5,1,4,3]=>756 [6,2,5,3,1,4]=>726 [6,2,5,3,4,1]=>720 [6,2,5,4,1,3]=>756 [6,2,5,4,3,1]=>720 [6,3,1,2,4,5]=>720 [6,3,1,2,5,4]=>720 [6,3,1,4,2,5]=>750 [6,3,1,4,5,2]=>756 [6,3,1,5,2,4]=>768 [6,3,1,5,4,2]=>756 [6,3,2,1,4,5]=>720 [6,3,2,1,5,4]=>720 [6,3,2,4,1,5]=>720 [6,3,2,4,5,1]=>720 [6,3,2,5,1,4]=>756 [6,3,2,5,4,1]=>720 [6,3,4,1,2,5]=>720 [6,3,4,1,5,2]=>756 [6,3,4,2,1,5]=>720 [6,3,4,2,5,1]=>720 [6,3,4,5,1,2]=>720 [6,3,4,5,2,1]=>720 [6,3,5,1,2,4]=>756 [6,3,5,1,4,2]=>768 [6,3,5,2,1,4]=>756 [6,3,5,2,4,1]=>750 [6,3,5,4,1,2]=>720 [6,3,5,4,2,1]=>720 [6,4,1,2,3,5]=>720 [6,4,1,2,5,3]=>756 [6,4,1,3,2,5]=>720 [6,4,1,3,5,2]=>726 [6,4,1,5,2,3]=>756 [6,4,1,5,3,2]=>756 [6,4,2,1,3,5]=>720 [6,4,2,1,5,3]=>756 [6,4,2,3,1,5]=>720 [6,4,2,3,5,1]=>720 [6,4,2,5,1,3]=>768 [6,4,2,5,3,1]=>750 [6,4,3,1,2,5]=>720 [6,4,3,1,5,2]=>756 [6,4,3,2,1,5]=>720 [6,4,3,2,5,1]=>720 [6,4,3,5,1,2]=>720 [6,4,3,5,2,1]=>720 [6,4,5,1,2,3]=>720 [6,4,5,1,3,2]=>720 [6,4,5,2,1,3]=>720 [6,4,5,2,3,1]=>720 [6,4,5,3,1,2]=>720 [6,4,5,3,2,1]=>720 [6,5,1,2,3,4]=>720 [6,5,1,2,4,3]=>720 [6,5,1,3,2,4]=>720 [6,5,1,3,4,2]=>720 [6,5,1,4,2,3]=>720 [6,5,1,4,3,2]=>720 [6,5,2,1,3,4]=>720 [6,5,2,1,4,3]=>720 [6,5,2,3,1,4]=>720 [6,5,2,3,4,1]=>720 [6,5,2,4,1,3]=>750 [6,5,2,4,3,1]=>720 [6,5,3,1,2,4]=>720 [6,5,3,1,4,2]=>750 [6,5,3,2,1,4]=>720 [6,5,3,2,4,1]=>720 [6,5,3,4,1,2]=>720 [6,5,3,4,2,1]=>720 [6,5,4,1,2,3]=>720 [6,5,4,1,3,2]=>720 [6,5,4,2,1,3]=>720 [6,5,4,2,3,1]=>720 [6,5,4,3,1,2]=>720 [6,5,4,3,2,1]=>720 [1,2,3,4,5,6,7]=>5040
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Description
The product of the cardinalities of the lower order ideal and upper order ideal generated by a permutation in weak order.
Let $a(\pi)$ denote this statistic, then $a(\pi)$ is the product of [1] and [2]. A result of Sidorenko [3] implies that $a(\pi) \geq n!$ when $\pi$ is a permutation of $n$, with equality if and only if $\pi$ avoids the patterns $2413$ and $3142$. See [4] for a combinatorial proof and refinement. Upper bounds for $a(\pi)$ are given in [5].
References
[1] St000100oMp00065oMp00064
[2] St000100oMp00065
[3] Sidorenko, A. Inequalities for the number of linear extensions DOI:10.1007/BF00571183
[4] Gaetz, C., Gao, Y. Separable elements and splittings of Weyl groups arXiv:1911.11172
[5] Bollobás, Béla, Brightwell, G., Sidorenko, A. Geometrical Techniques for Estimating Numbers of Linear Extensions DOI:10.1006/eujc.1999.0299
Code
def statistic(pi):
    a1=pi.permutation_poset().linear_extensions().cardinality()
    a2=pi.reverse().permutation_poset().linear_extensions().cardinality()
    return a1*a2
Created
Jul 09, 2020 at 14:21 by Christian Gaetz
Updated
Mar 12, 2026 at 17:44 by Nupur Jain