- FindStat

edit this statistic or download as text // json

Identifier

St000690: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1,2]=>1
[2,1]=>1
[1,2,3]=>1
[1,3,2]=>3
[2,1,3]=>3
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>3
[1,2,3,4]=>1
[1,2,4,3]=>6
[1,3,2,4]=>6
[1,3,4,2]=>8
[1,4,2,3]=>8
[1,4,3,2]=>6
[2,1,3,4]=>6
[2,1,4,3]=>3
[2,3,1,4]=>8
[2,3,4,1]=>6
[2,4,1,3]=>6
[2,4,3,1]=>8
[3,1,2,4]=>8
[3,1,4,2]=>6
[3,2,1,4]=>6
[3,2,4,1]=>8
[3,4,1,2]=>3
[3,4,2,1]=>6
[4,1,2,3]=>6
[4,1,3,2]=>8
[4,2,1,3]=>8
[4,2,3,1]=>6
[4,3,1,2]=>6
[4,3,2,1]=>3
[1,2,3,4,5]=>1
[1,2,3,5,4]=>10
[1,2,4,3,5]=>10
[1,2,4,5,3]=>20
[1,2,5,3,4]=>20
[1,2,5,4,3]=>10
[1,3,2,4,5]=>10
[1,3,2,5,4]=>15
[1,3,4,2,5]=>20
[1,3,4,5,2]=>30
[1,3,5,2,4]=>30
[1,3,5,4,2]=>20
[1,4,2,3,5]=>20
[1,4,2,5,3]=>30
[1,4,3,2,5]=>10
[1,4,3,5,2]=>20
[1,4,5,2,3]=>15
[1,4,5,3,2]=>30
[1,5,2,3,4]=>30
[1,5,2,4,3]=>20
[1,5,3,2,4]=>20
[1,5,3,4,2]=>10
[1,5,4,2,3]=>30
[1,5,4,3,2]=>15
[2,1,3,4,5]=>10
[2,1,3,5,4]=>15
[2,1,4,3,5]=>15
[2,1,4,5,3]=>20
[2,1,5,3,4]=>20
[2,1,5,4,3]=>15
[2,3,1,4,5]=>20
[2,3,1,5,4]=>20
[2,3,4,1,5]=>30
[2,3,4,5,1]=>24
[2,3,5,1,4]=>24
[2,3,5,4,1]=>30
[2,4,1,3,5]=>30
[2,4,1,5,3]=>24
[2,4,3,1,5]=>20
[2,4,3,5,1]=>30
[2,4,5,1,3]=>20
[2,4,5,3,1]=>24
[2,5,1,3,4]=>24
[2,5,1,4,3]=>30
[2,5,3,1,4]=>30
[2,5,3,4,1]=>20
[2,5,4,1,3]=>24
[2,5,4,3,1]=>20
[3,1,2,4,5]=>20
[3,1,2,5,4]=>20
[3,1,4,2,5]=>30
[3,1,4,5,2]=>24
[3,1,5,2,4]=>24
[3,1,5,4,2]=>30
[3,2,1,4,5]=>10
[3,2,1,5,4]=>15
[3,2,4,1,5]=>20
[3,2,4,5,1]=>30
[3,2,5,1,4]=>30
[3,2,5,4,1]=>20
[3,4,1,2,5]=>15
[3,4,1,5,2]=>20
[3,4,2,1,5]=>30
[3,4,2,5,1]=>24
[3,4,5,1,2]=>24
[3,4,5,2,1]=>20
[3,5,1,2,4]=>20
[3,5,1,4,2]=>15
[3,5,2,1,4]=>24
[3,5,2,4,1]=>30
[3,5,4,1,2]=>20
[3,5,4,2,1]=>24
[4,1,2,3,5]=>30
[4,1,2,5,3]=>24
[4,1,3,2,5]=>20
[4,1,3,5,2]=>30
[4,1,5,2,3]=>20
[4,1,5,3,2]=>24
[4,2,1,3,5]=>20
[4,2,1,5,3]=>30
[4,2,3,1,5]=>10
[4,2,3,5,1]=>20
[4,2,5,1,3]=>15
[4,2,5,3,1]=>30
[4,3,1,2,5]=>30
[4,3,1,5,2]=>24
[4,3,2,1,5]=>15
[4,3,2,5,1]=>20
[4,3,5,1,2]=>20
[4,3,5,2,1]=>24
[4,5,1,2,3]=>24
[4,5,1,3,2]=>20
[4,5,2,1,3]=>20
[4,5,2,3,1]=>24
[4,5,3,1,2]=>15
[4,5,3,2,1]=>30
[5,1,2,3,4]=>24
[5,1,2,4,3]=>30
[5,1,3,2,4]=>30
[5,1,3,4,2]=>20
[5,1,4,2,3]=>24
[5,1,4,3,2]=>20
[5,2,1,3,4]=>30
[5,2,1,4,3]=>20
[5,2,3,1,4]=>20
[5,2,3,4,1]=>10
[5,2,4,1,3]=>30
[5,2,4,3,1]=>15
[5,3,1,2,4]=>24
[5,3,1,4,2]=>30
[5,3,2,1,4]=>20
[5,3,2,4,1]=>15
[5,3,4,1,2]=>24
[5,3,4,2,1]=>20
[5,4,1,2,3]=>20
[5,4,1,3,2]=>24
[5,4,2,1,3]=>24
[5,4,2,3,1]=>20
[5,4,3,1,2]=>30
[5,4,3,2,1]=>15
[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>15
[1,2,3,5,4,6]=>15
[1,2,3,5,6,4]=>40
[1,2,3,6,4,5]=>40
[1,2,3,6,5,4]=>15
[1,2,4,3,5,6]=>15
[1,2,4,3,6,5]=>45
[1,2,4,5,3,6]=>40
[1,2,4,5,6,3]=>90
[1,2,4,6,3,5]=>90
[1,2,4,6,5,3]=>40
[1,2,5,3,4,6]=>40
[1,2,5,3,6,4]=>90
[1,2,5,4,3,6]=>15
[1,2,5,4,6,3]=>40
[1,2,5,6,3,4]=>45
[1,2,5,6,4,3]=>90
[1,2,6,3,4,5]=>90
[1,2,6,3,5,4]=>40
[1,2,6,4,3,5]=>40
[1,2,6,4,5,3]=>15
[1,2,6,5,3,4]=>90
[1,2,6,5,4,3]=>45
[1,3,2,4,5,6]=>15
[1,3,2,4,6,5]=>45
[1,3,2,5,4,6]=>45
[1,3,2,5,6,4]=>120
[1,3,2,6,4,5]=>120
[1,3,2,6,5,4]=>45
[1,3,4,2,5,6]=>40
[1,3,4,2,6,5]=>120
[1,3,4,5,2,6]=>90
[1,3,4,5,6,2]=>144
[1,3,4,6,2,5]=>144
[1,3,4,6,5,2]=>90
[1,3,5,2,4,6]=>90
[1,3,5,2,6,4]=>144
[1,3,5,4,2,6]=>40
[1,3,5,4,6,2]=>90
[1,3,5,6,2,4]=>120
[1,3,5,6,4,2]=>144
[1,3,6,2,4,5]=>144
[1,3,6,2,5,4]=>90
[1,3,6,4,2,5]=>90
[1,3,6,4,5,2]=>40
[1,3,6,5,2,4]=>144
[1,3,6,5,4,2]=>120
[1,4,2,3,5,6]=>40
[1,4,2,3,6,5]=>120
[1,4,2,5,3,6]=>90
[1,4,2,5,6,3]=>144
[1,4,2,6,3,5]=>144
[1,4,2,6,5,3]=>90
[1,4,3,2,5,6]=>15
[1,4,3,2,6,5]=>45
[1,4,3,5,2,6]=>40
[1,4,3,5,6,2]=>90
[1,4,3,6,2,5]=>90
[1,4,3,6,5,2]=>40
[1,4,5,2,3,6]=>45
[1,4,5,2,6,3]=>120
[1,4,5,3,2,6]=>90
[1,4,5,3,6,2]=>144
[1,4,5,6,2,3]=>144
[1,4,5,6,3,2]=>120
[1,4,6,2,3,5]=>120
[1,4,6,2,5,3]=>45
[1,4,6,3,2,5]=>144
[1,4,6,3,5,2]=>90
[1,4,6,5,2,3]=>120
[1,4,6,5,3,2]=>144
[1,5,2,3,4,6]=>90
[1,5,2,3,6,4]=>144
[1,5,2,4,3,6]=>40
[1,5,2,4,6,3]=>90
[1,5,2,6,3,4]=>120
[1,5,2,6,4,3]=>144
[1,5,3,2,4,6]=>40
[1,5,3,2,6,4]=>90
[1,5,3,4,2,6]=>15
[1,5,3,4,6,2]=>40
[1,5,3,6,2,4]=>45
[1,5,3,6,4,2]=>90
[1,5,4,2,3,6]=>90
[1,5,4,2,6,3]=>144
[1,5,4,3,2,6]=>45
[1,5,4,3,6,2]=>120
[1,5,4,6,2,3]=>120
[1,5,4,6,3,2]=>144
[1,5,6,2,3,4]=>144
[1,5,6,2,4,3]=>120
[1,5,6,3,2,4]=>120
[1,5,6,3,4,2]=>144
[1,5,6,4,2,3]=>45
[1,5,6,4,3,2]=>90
[1,6,2,3,4,5]=>144
[1,6,2,3,5,4]=>90
[1,6,2,4,3,5]=>90
[1,6,2,4,5,3]=>40
[1,6,2,5,3,4]=>144
[1,6,2,5,4,3]=>120
[1,6,3,2,4,5]=>90
[1,6,3,2,5,4]=>40
[1,6,3,4,2,5]=>40
[1,6,3,4,5,2]=>15
[1,6,3,5,2,4]=>90
[1,6,3,5,4,2]=>45
[1,6,4,2,3,5]=>144
[1,6,4,2,5,3]=>90
[1,6,4,3,2,5]=>120
[1,6,4,3,5,2]=>45
[1,6,4,5,2,3]=>144
[1,6,4,5,3,2]=>120
[1,6,5,2,3,4]=>120
[1,6,5,2,4,3]=>144
[1,6,5,3,2,4]=>144
[1,6,5,3,4,2]=>120
[1,6,5,4,2,3]=>90
[1,6,5,4,3,2]=>45
[2,1,3,4,5,6]=>15
[2,1,3,4,6,5]=>45
[2,1,3,5,4,6]=>45
[2,1,3,5,6,4]=>120
[2,1,3,6,4,5]=>120
[2,1,3,6,5,4]=>45
[2,1,4,3,5,6]=>45
[2,1,4,3,6,5]=>15
[2,1,4,5,3,6]=>120
[2,1,4,5,6,3]=>90
[2,1,4,6,3,5]=>90
[2,1,4,6,5,3]=>120
[2,1,5,3,4,6]=>120
[2,1,5,3,6,4]=>90
[2,1,5,4,3,6]=>45
[2,1,5,4,6,3]=>120
[2,1,5,6,3,4]=>15
[2,1,5,6,4,3]=>90
[2,1,6,3,4,5]=>90
[2,1,6,3,5,4]=>120
[2,1,6,4,3,5]=>120
[2,1,6,4,5,3]=>45
[2,1,6,5,3,4]=>90
[2,1,6,5,4,3]=>15
[2,3,1,4,5,6]=>40
[2,3,1,4,6,5]=>120
[2,3,1,5,4,6]=>120
[2,3,1,5,6,4]=>40
[2,3,1,6,4,5]=>40
[2,3,1,6,5,4]=>120
[2,3,4,1,5,6]=>90
[2,3,4,1,6,5]=>90
[2,3,4,5,1,6]=>144
[2,3,4,5,6,1]=>120
[2,3,4,6,1,5]=>120
[2,3,4,6,5,1]=>144
[2,3,5,1,4,6]=>144
[2,3,5,1,6,4]=>120
[2,3,5,4,1,6]=>90
[2,3,5,4,6,1]=>144
[2,3,5,6,1,4]=>90
[2,3,5,6,4,1]=>120
[2,3,6,1,4,5]=>120
[2,3,6,1,5,4]=>144
[2,3,6,4,1,5]=>144
[2,3,6,4,5,1]=>90
[2,3,6,5,1,4]=>120
[2,3,6,5,4,1]=>90
[2,4,1,3,5,6]=>90
[2,4,1,3,6,5]=>90
[2,4,1,5,3,6]=>144
[2,4,1,5,6,3]=>120
[2,4,1,6,3,5]=>120
[2,4,1,6,5,3]=>144
[2,4,3,1,5,6]=>40
[2,4,3,1,6,5]=>120
[2,4,3,5,1,6]=>90
[2,4,3,5,6,1]=>144
[2,4,3,6,1,5]=>144
[2,4,3,6,5,1]=>90
[2,4,5,1,3,6]=>120
[2,4,5,1,6,3]=>40
[2,4,5,3,1,6]=>144
[2,4,5,3,6,1]=>120
[2,4,5,6,1,3]=>120
[2,4,5,6,3,1]=>90
[2,4,6,1,3,5]=>40
[2,4,6,1,5,3]=>120
[2,4,6,3,1,5]=>120
[2,4,6,3,5,1]=>144
[2,4,6,5,1,3]=>90
[2,4,6,5,3,1]=>120
[2,5,1,3,4,6]=>144
[2,5,1,3,6,4]=>120
[2,5,1,4,3,6]=>90
[2,5,1,4,6,3]=>144
[2,5,1,6,3,4]=>90
[2,5,1,6,4,3]=>120
[2,5,3,1,4,6]=>90
[2,5,3,1,6,4]=>144
[2,5,3,4,1,6]=>40
[2,5,3,4,6,1]=>90
[2,5,3,6,1,4]=>120
[2,5,3,6,4,1]=>144
[2,5,4,1,3,6]=>144
[2,5,4,1,6,3]=>120
[2,5,4,3,1,6]=>120
[2,5,4,3,6,1]=>90
[2,5,4,6,1,3]=>40
[2,5,4,6,3,1]=>120
[2,5,6,1,3,4]=>120
[2,5,6,1,4,3]=>90
[2,5,6,3,1,4]=>40
[2,5,6,3,4,1]=>120
[2,5,6,4,1,3]=>120
[2,5,6,4,3,1]=>144
[2,6,1,3,4,5]=>120
[2,6,1,3,5,4]=>144
[2,6,1,4,3,5]=>144
[2,6,1,4,5,3]=>90
[2,6,1,5,3,4]=>120
[2,6,1,5,4,3]=>90
[2,6,3,1,4,5]=>144
[2,6,3,1,5,4]=>90
[2,6,3,4,1,5]=>90
[2,6,3,4,5,1]=>40
[2,6,3,5,1,4]=>144
[2,6,3,5,4,1]=>120
[2,6,4,1,3,5]=>120
[2,6,4,1,5,3]=>144
[2,6,4,3,1,5]=>90
[2,6,4,3,5,1]=>120
[2,6,4,5,1,3]=>120
[2,6,4,5,3,1]=>40
[2,6,5,1,3,4]=>90
[2,6,5,1,4,3]=>120
[2,6,5,3,1,4]=>120
[2,6,5,3,4,1]=>40
[2,6,5,4,1,3]=>144
[2,6,5,4,3,1]=>120
[3,1,2,4,5,6]=>40
[3,1,2,4,6,5]=>120
[3,1,2,5,4,6]=>120
[3,1,2,5,6,4]=>40
[3,1,2,6,4,5]=>40
[3,1,2,6,5,4]=>120
[3,1,4,2,5,6]=>90
[3,1,4,2,6,5]=>90
[3,1,4,5,2,6]=>144
[3,1,4,5,6,2]=>120
[3,1,4,6,2,5]=>120
[3,1,4,6,5,2]=>144
[3,1,5,2,4,6]=>144
[3,1,5,2,6,4]=>120
[3,1,5,4,2,6]=>90
[3,1,5,4,6,2]=>144
[3,1,5,6,2,4]=>90
[3,1,5,6,4,2]=>120
[3,1,6,2,4,5]=>120
[3,1,6,2,5,4]=>144
[3,1,6,4,2,5]=>144
[3,1,6,4,5,2]=>90
[3,1,6,5,2,4]=>120
[3,1,6,5,4,2]=>90
[3,2,1,4,5,6]=>15
[3,2,1,4,6,5]=>45
[3,2,1,5,4,6]=>45
[3,2,1,5,6,4]=>120
[3,2,1,6,4,5]=>120
[3,2,1,6,5,4]=>45
[3,2,4,1,5,6]=>40
[3,2,4,1,6,5]=>120
[3,2,4,5,1,6]=>90
[3,2,4,5,6,1]=>144
[3,2,4,6,1,5]=>144
[3,2,4,6,5,1]=>90
[3,2,5,1,4,6]=>90
[3,2,5,1,6,4]=>144
[3,2,5,4,1,6]=>40
[3,2,5,4,6,1]=>90
[3,2,5,6,1,4]=>120
[3,2,5,6,4,1]=>144
[3,2,6,1,4,5]=>144
[3,2,6,1,5,4]=>90
[3,2,6,4,1,5]=>90
[3,2,6,4,5,1]=>40
[3,2,6,5,1,4]=>144
[3,2,6,5,4,1]=>120
[3,4,1,2,5,6]=>45
[3,4,1,2,6,5]=>15
[3,4,1,5,2,6]=>120
[3,4,1,5,6,2]=>90
[3,4,1,6,2,5]=>90
[3,4,1,6,5,2]=>120
[3,4,2,1,5,6]=>90
[3,4,2,1,6,5]=>90
[3,4,2,5,1,6]=>144
[3,4,2,5,6,1]=>120
[3,4,2,6,1,5]=>120
[3,4,2,6,5,1]=>144
[3,4,5,1,2,6]=>144
[3,4,5,1,6,2]=>120
[3,4,5,2,1,6]=>120
[3,4,5,2,6,1]=>90
[3,4,5,6,1,2]=>40
[3,4,5,6,2,1]=>120
[3,4,6,1,2,5]=>120
[3,4,6,1,5,2]=>144
[3,4,6,2,1,5]=>90
[3,4,6,2,5,1]=>120
[3,4,6,5,1,2]=>120
[3,4,6,5,2,1]=>40
[3,5,1,2,4,6]=>120
[3,5,1,2,6,4]=>90
[3,5,1,4,2,6]=>45
[3,5,1,4,6,2]=>120
[3,5,1,6,2,4]=>15
[3,5,1,6,4,2]=>90
[3,5,2,1,4,6]=>144
[3,5,2,1,6,4]=>120
[3,5,2,4,1,6]=>90
[3,5,2,4,6,1]=>144
[3,5,2,6,1,4]=>90
[3,5,2,6,4,1]=>120
[3,5,4,1,2,6]=>120
[3,5,4,1,6,2]=>40
[3,5,4,2,1,6]=>144
[3,5,4,2,6,1]=>120
[3,5,4,6,1,2]=>120
[3,5,4,6,2,1]=>90
[3,5,6,1,2,4]=>90
[3,5,6,1,4,2]=>120
[3,5,6,2,1,4]=>120
[3,5,6,2,4,1]=>40
[3,5,6,4,1,2]=>144
[3,5,6,4,2,1]=>120
[3,6,1,2,4,5]=>90
[3,6,1,2,5,4]=>120
[3,6,1,4,2,5]=>120
[3,6,1,4,5,2]=>45
[3,6,1,5,2,4]=>90
[3,6,1,5,4,2]=>15
[3,6,2,1,4,5]=>120
[3,6,2,1,5,4]=>144
[3,6,2,4,1,5]=>144
[3,6,2,4,5,1]=>90
[3,6,2,5,1,4]=>120
[3,6,2,5,4,1]=>90
[3,6,4,1,2,5]=>40
[3,6,4,1,5,2]=>120
[3,6,4,2,1,5]=>120
[3,6,4,2,5,1]=>144
[3,6,4,5,1,2]=>90
[3,6,4,5,2,1]=>120
[3,6,5,1,2,4]=>120
[3,6,5,1,4,2]=>90
[3,6,5,2,1,4]=>40
[3,6,5,2,4,1]=>120
[3,6,5,4,1,2]=>120
[3,6,5,4,2,1]=>144
[4,1,2,3,5,6]=>90
[4,1,2,3,6,5]=>90
[4,1,2,5,3,6]=>144
[4,1,2,5,6,3]=>120
[4,1,2,6,3,5]=>120
[4,1,2,6,5,3]=>144
[4,1,3,2,5,6]=>40
[4,1,3,2,6,5]=>120
[4,1,3,5,2,6]=>90
[4,1,3,5,6,2]=>144
[4,1,3,6,2,5]=>144
[4,1,3,6,5,2]=>90
[4,1,5,2,3,6]=>120
[4,1,5,2,6,3]=>40
[4,1,5,3,2,6]=>144
[4,1,5,3,6,2]=>120
[4,1,5,6,2,3]=>120
[4,1,5,6,3,2]=>90
[4,1,6,2,3,5]=>40
[4,1,6,2,5,3]=>120
[4,1,6,3,2,5]=>120
[4,1,6,3,5,2]=>144
[4,1,6,5,2,3]=>90
[4,1,6,5,3,2]=>120
[4,2,1,3,5,6]=>40
[4,2,1,3,6,5]=>120
[4,2,1,5,3,6]=>90
[4,2,1,5,6,3]=>144
[4,2,1,6,3,5]=>144
[4,2,1,6,5,3]=>90
[4,2,3,1,5,6]=>15
[4,2,3,1,6,5]=>45
[4,2,3,5,1,6]=>40
[4,2,3,5,6,1]=>90
[4,2,3,6,1,5]=>90
[4,2,3,6,5,1]=>40
[4,2,5,1,3,6]=>45
[4,2,5,1,6,3]=>120
[4,2,5,3,1,6]=>90
[4,2,5,3,6,1]=>144
[4,2,5,6,1,3]=>144
[4,2,5,6,3,1]=>120
[4,2,6,1,3,5]=>120
[4,2,6,1,5,3]=>45
[4,2,6,3,1,5]=>144
[4,2,6,3,5,1]=>90
[4,2,6,5,1,3]=>120
[4,2,6,5,3,1]=>144
[4,3,1,2,5,6]=>90
[4,3,1,2,6,5]=>90
[4,3,1,5,2,6]=>144
[4,3,1,5,6,2]=>120
[4,3,1,6,2,5]=>120
[4,3,1,6,5,2]=>144
[4,3,2,1,5,6]=>45
[4,3,2,1,6,5]=>15
[4,3,2,5,1,6]=>120
[4,3,2,5,6,1]=>90
[4,3,2,6,1,5]=>90
[4,3,2,6,5,1]=>120
[4,3,5,1,2,6]=>120
[4,3,5,1,6,2]=>90
[4,3,5,2,1,6]=>144
[4,3,5,2,6,1]=>120
[4,3,5,6,1,2]=>120
[4,3,5,6,2,1]=>40
[4,3,6,1,2,5]=>90
[4,3,6,1,5,2]=>120
[4,3,6,2,1,5]=>120
[4,3,6,2,5,1]=>144
[4,3,6,5,1,2]=>40
[4,3,6,5,2,1]=>120
[4,5,1,2,3,6]=>144
[4,5,1,2,6,3]=>120
[4,5,1,3,2,6]=>120
[4,5,1,3,6,2]=>40
[4,5,1,6,2,3]=>90
[4,5,1,6,3,2]=>120
[4,5,2,1,3,6]=>120
[4,5,2,1,6,3]=>90
[4,5,2,3,1,6]=>144
[4,5,2,3,6,1]=>120
[4,5,2,6,1,3]=>120
[4,5,2,6,3,1]=>40
[4,5,3,1,2,6]=>45
[4,5,3,1,6,2]=>120
[4,5,3,2,1,6]=>90
[4,5,3,2,6,1]=>144
[4,5,3,6,1,2]=>144
[4,5,3,6,2,1]=>120
[4,5,6,1,2,3]=>15
[4,5,6,1,3,2]=>90
[4,5,6,2,1,3]=>90
[4,5,6,2,3,1]=>120
[4,5,6,3,1,2]=>120
[4,5,6,3,2,1]=>90
[4,6,1,2,3,5]=>120
[4,6,1,2,5,3]=>144
[4,6,1,3,2,5]=>40
[4,6,1,3,5,2]=>120
[4,6,1,5,2,3]=>120
[4,6,1,5,3,2]=>90
[4,6,2,1,3,5]=>90
[4,6,2,1,5,3]=>120
[4,6,2,3,1,5]=>120
[4,6,2,3,5,1]=>144
[4,6,2,5,1,3]=>40
[4,6,2,5,3,1]=>120
[4,6,3,1,2,5]=>120
[4,6,3,1,5,2]=>45
[4,6,3,2,1,5]=>144
[4,6,3,2,5,1]=>90
[4,6,3,5,1,2]=>120
[4,6,3,5,2,1]=>144
[4,6,5,1,2,3]=>90
[4,6,5,1,3,2]=>15
[4,6,5,2,1,3]=>120
[4,6,5,2,3,1]=>90
[4,6,5,3,1,2]=>90
[4,6,5,3,2,1]=>120
[5,1,2,3,4,6]=>144
[5,1,2,3,6,4]=>120
[5,1,2,4,3,6]=>90
[5,1,2,4,6,3]=>144
[5,1,2,6,3,4]=>90
[5,1,2,6,4,3]=>120
[5,1,3,2,4,6]=>90
[5,1,3,2,6,4]=>144
[5,1,3,4,2,6]=>40
[5,1,3,4,6,2]=>90
[5,1,3,6,2,4]=>120
[5,1,3,6,4,2]=>144
[5,1,4,2,3,6]=>144
[5,1,4,2,6,3]=>120
[5,1,4,3,2,6]=>120
[5,1,4,3,6,2]=>90
[5,1,4,6,2,3]=>40
[5,1,4,6,3,2]=>120
[5,1,6,2,3,4]=>120
[5,1,6,2,4,3]=>90
[5,1,6,3,2,4]=>40
[5,1,6,3,4,2]=>120
[5,1,6,4,2,3]=>120
[5,1,6,4,3,2]=>144
[5,2,1,3,4,6]=>90
[5,2,1,3,6,4]=>144
[5,2,1,4,3,6]=>40
[5,2,1,4,6,3]=>90
[5,2,1,6,3,4]=>120
[5,2,1,6,4,3]=>144
[5,2,3,1,4,6]=>40
[5,2,3,1,6,4]=>90
[5,2,3,4,1,6]=>15
[5,2,3,4,6,1]=>40
[5,2,3,6,1,4]=>45
[5,2,3,6,4,1]=>90
[5,2,4,1,3,6]=>90
[5,2,4,1,6,3]=>144
[5,2,4,3,1,6]=>45
[5,2,4,3,6,1]=>120
[5,2,4,6,1,3]=>120
[5,2,4,6,3,1]=>144
[5,2,6,1,3,4]=>144
[5,2,6,1,4,3]=>120
[5,2,6,3,1,4]=>120
[5,2,6,3,4,1]=>144
[5,2,6,4,1,3]=>45
[5,2,6,4,3,1]=>90
[5,3,1,2,4,6]=>144
[5,3,1,2,6,4]=>120
[5,3,1,4,2,6]=>90
[5,3,1,4,6,2]=>144
[5,3,1,6,2,4]=>90
[5,3,1,6,4,2]=>120
[5,3,2,1,4,6]=>120
[5,3,2,1,6,4]=>90
[5,3,2,4,1,6]=>45
[5,3,2,4,6,1]=>120
[5,3,2,6,1,4]=>15
[5,3,2,6,4,1]=>90
[5,3,4,1,2,6]=>144
[5,3,4,1,6,2]=>120
[5,3,4,2,1,6]=>120
[5,3,4,2,6,1]=>40
[5,3,4,6,1,2]=>90
[5,3,4,6,2,1]=>120
[5,3,6,1,2,4]=>120
[5,3,6,1,4,2]=>40
[5,3,6,2,1,4]=>90
[5,3,6,2,4,1]=>120
[5,3,6,4,1,2]=>120
[5,3,6,4,2,1]=>144
[5,4,1,2,3,6]=>120
[5,4,1,2,6,3]=>90
[5,4,1,3,2,6]=>144
[5,4,1,3,6,2]=>120
[5,4,1,6,2,3]=>120
[5,4,1,6,3,2]=>40
[5,4,2,1,3,6]=>144
[5,4,2,1,6,3]=>120
[5,4,2,3,1,6]=>120
[5,4,2,3,6,1]=>40
[5,4,2,6,1,3]=>90
[5,4,2,6,3,1]=>120
[5,4,3,1,2,6]=>90
[5,4,3,1,6,2]=>144
[5,4,3,2,1,6]=>45
[5,4,3,2,6,1]=>120
[5,4,3,6,1,2]=>120
[5,4,3,6,2,1]=>144
[5,4,6,1,2,3]=>90
[5,4,6,1,3,2]=>120
[5,4,6,2,1,3]=>15
[5,4,6,2,3,1]=>90
[5,4,6,3,1,2]=>90
[5,4,6,3,2,1]=>120
[5,6,1,2,3,4]=>40
[5,6,1,2,4,3]=>120
[5,6,1,3,2,4]=>120
[5,6,1,3,4,2]=>90
[5,6,1,4,2,3]=>144
[5,6,1,4,3,2]=>120
[5,6,2,1,3,4]=>120
[5,6,2,1,4,3]=>40
[5,6,2,3,1,4]=>90
[5,6,2,3,4,1]=>120
[5,6,2,4,1,3]=>120
[5,6,2,4,3,1]=>144
[5,6,3,1,2,4]=>144
[5,6,3,1,4,2]=>120
[5,6,3,2,1,4]=>120
[5,6,3,2,4,1]=>144
[5,6,3,4,1,2]=>45
[5,6,3,4,2,1]=>90
[5,6,4,1,2,3]=>120
[5,6,4,1,3,2]=>90
[5,6,4,2,1,3]=>90
[5,6,4,2,3,1]=>120
[5,6,4,3,1,2]=>15
[5,6,4,3,2,1]=>90
[6,1,2,3,4,5]=>120
[6,1,2,3,5,4]=>144
[6,1,2,4,3,5]=>144
[6,1,2,4,5,3]=>90
[6,1,2,5,3,4]=>120
[6,1,2,5,4,3]=>90
[6,1,3,2,4,5]=>144
[6,1,3,2,5,4]=>90
[6,1,3,4,2,5]=>90
[6,1,3,4,5,2]=>40
[6,1,3,5,2,4]=>144
[6,1,3,5,4,2]=>120
[6,1,4,2,3,5]=>120
[6,1,4,2,5,3]=>144
[6,1,4,3,2,5]=>90
[6,1,4,3,5,2]=>120
[6,1,4,5,2,3]=>120
[6,1,4,5,3,2]=>40
[6,1,5,2,3,4]=>90
[6,1,5,2,4,3]=>120
[6,1,5,3,2,4]=>120
[6,1,5,3,4,2]=>40
[6,1,5,4,2,3]=>144
[6,1,5,4,3,2]=>120
[6,2,1,3,4,5]=>144
[6,2,1,3,5,4]=>90
[6,2,1,4,3,5]=>90
[6,2,1,4,5,3]=>40
[6,2,1,5,3,4]=>144
[6,2,1,5,4,3]=>120
[6,2,3,1,4,5]=>90
[6,2,3,1,5,4]=>40
[6,2,3,4,1,5]=>40
[6,2,3,4,5,1]=>15
[6,2,3,5,1,4]=>90
[6,2,3,5,4,1]=>45
[6,2,4,1,3,5]=>144
[6,2,4,1,5,3]=>90
[6,2,4,3,1,5]=>120
[6,2,4,3,5,1]=>45
[6,2,4,5,1,3]=>144
[6,2,4,5,3,1]=>120
[6,2,5,1,3,4]=>120
[6,2,5,1,4,3]=>144
[6,2,5,3,1,4]=>144
[6,2,5,3,4,1]=>120
[6,2,5,4,1,3]=>90
[6,2,5,4,3,1]=>45
[6,3,1,2,4,5]=>120
[6,3,1,2,5,4]=>144
[6,3,1,4,2,5]=>144
[6,3,1,4,5,2]=>90
[6,3,1,5,2,4]=>120
[6,3,1,5,4,2]=>90
[6,3,2,1,4,5]=>90
[6,3,2,1,5,4]=>120
[6,3,2,4,1,5]=>120
[6,3,2,4,5,1]=>45
[6,3,2,5,1,4]=>90
[6,3,2,5,4,1]=>15
[6,3,4,1,2,5]=>120
[6,3,4,1,5,2]=>144
[6,3,4,2,1,5]=>40
[6,3,4,2,5,1]=>120
[6,3,4,5,1,2]=>120
[6,3,4,5,2,1]=>90
[6,3,5,1,2,4]=>40
[6,3,5,1,4,2]=>120
[6,3,5,2,1,4]=>120
[6,3,5,2,4,1]=>90
[6,3,5,4,1,2]=>144
[6,3,5,4,2,1]=>120
[6,4,1,2,3,5]=>90
[6,4,1,2,5,3]=>120
[6,4,1,3,2,5]=>120
[6,4,1,3,5,2]=>144
[6,4,1,5,2,3]=>40
[6,4,1,5,3,2]=>120
[6,4,2,1,3,5]=>120
[6,4,2,1,5,3]=>144
[6,4,2,3,1,5]=>40
[6,4,2,3,5,1]=>120
[6,4,2,5,1,3]=>120
[6,4,2,5,3,1]=>90
[6,4,3,1,2,5]=>144
[6,4,3,1,5,2]=>90
[6,4,3,2,1,5]=>120
[6,4,3,2,5,1]=>45
[6,4,3,5,1,2]=>144
[6,4,3,5,2,1]=>120
[6,4,5,1,2,3]=>120
[6,4,5,1,3,2]=>90
[6,4,5,2,1,3]=>90
[6,4,5,2,3,1]=>15
[6,4,5,3,1,2]=>120
[6,4,5,3,2,1]=>90
[6,5,1,2,3,4]=>120
[6,5,1,2,4,3]=>40
[6,5,1,3,2,4]=>90
[6,5,1,3,4,2]=>120
[6,5,1,4,2,3]=>120
[6,5,1,4,3,2]=>144
[6,5,2,1,3,4]=>40
[6,5,2,1,4,3]=>120
[6,5,2,3,1,4]=>120
[6,5,2,3,4,1]=>90
[6,5,2,4,1,3]=>144
[6,5,2,4,3,1]=>120
[6,5,3,1,2,4]=>120
[6,5,3,1,4,2]=>144
[6,5,3,2,1,4]=>144
[6,5,3,2,4,1]=>120
[6,5,3,4,1,2]=>90
[6,5,3,4,2,1]=>45
[6,5,4,1,2,3]=>90
[6,5,4,1,3,2]=>120
[6,5,4,2,1,3]=>120
[6,5,4,2,3,1]=>90
[6,5,4,3,1,2]=>90
[6,5,4,3,2,1]=>15
[1,2,3,4,5,6,7]=>1
[1,2,3,4,5,7,6]=>21
[1,2,3,4,6,5,7]=>21
[1,2,3,4,6,7,5]=>70
[1,2,3,4,7,5,6]=>70
[1,2,3,4,7,6,5]=>21
[1,2,3,5,4,6,7]=>21
[1,2,3,5,4,7,6]=>105
[1,2,3,5,6,4,7]=>70
[1,2,3,5,6,7,4]=>210
[1,2,3,5,7,4,6]=>210
[1,2,3,5,7,6,4]=>70
[1,2,3,6,4,5,7]=>70
[1,2,3,6,4,7,5]=>210
[1,2,3,6,5,4,7]=>21
[1,2,3,6,5,7,4]=>70
[1,2,3,6,7,4,5]=>105
[1,2,3,6,7,5,4]=>210
[1,2,3,7,4,5,6]=>210
[1,2,3,7,4,6,5]=>70
[1,2,3,7,5,4,6]=>70
[1,2,3,7,5,6,4]=>21
[1,2,3,7,6,4,5]=>210
[1,2,3,7,6,5,4]=>105
[1,2,4,3,5,6,7]=>21
[1,2,4,3,5,7,6]=>105
[1,2,4,3,6,5,7]=>105
[1,2,4,3,6,7,5]=>420
[1,2,4,3,7,5,6]=>420
[1,2,4,3,7,6,5]=>105
[1,2,4,5,3,6,7]=>70
[1,2,4,5,3,7,6]=>420
[1,2,4,5,6,3,7]=>210
[1,2,4,5,6,7,3]=>504
[1,2,4,5,7,3,6]=>504
[1,2,4,5,7,6,3]=>210
[1,2,4,6,3,5,7]=>210
[1,2,4,6,3,7,5]=>504
[1,2,4,6,5,3,7]=>70
[1,2,4,6,5,7,3]=>210
[1,2,4,6,7,3,5]=>420
[1,2,4,6,7,5,3]=>504
[1,2,4,7,3,5,6]=>504
[1,2,4,7,3,6,5]=>210
[1,2,4,7,5,3,6]=>210
[1,2,4,7,5,6,3]=>70
[1,2,4,7,6,3,5]=>504
[1,2,4,7,6,5,3]=>420
[1,2,5,3,4,6,7]=>70
[1,2,5,3,4,7,6]=>420
[1,2,5,3,6,4,7]=>210
[1,2,5,3,6,7,4]=>504
[1,2,5,3,7,4,6]=>504
[1,2,5,3,7,6,4]=>210
[1,2,5,4,3,6,7]=>21
[1,2,5,4,3,7,6]=>105
[1,2,5,4,6,3,7]=>70
[1,2,5,4,6,7,3]=>210
[1,2,5,4,7,3,6]=>210
[1,2,5,4,7,6,3]=>70
[1,2,5,6,3,4,7]=>105
[1,2,5,6,3,7,4]=>420
[1,2,5,6,4,3,7]=>210
[1,2,5,6,4,7,3]=>504
[1,2,5,6,7,3,4]=>504
[1,2,5,6,7,4,3]=>420
[1,2,5,7,3,4,6]=>420
[1,2,5,7,3,6,4]=>105
[1,2,5,7,4,3,6]=>504
[1,2,5,7,4,6,3]=>210
[1,2,5,7,6,3,4]=>420
[1,2,5,7,6,4,3]=>504
[1,2,6,3,4,5,7]=>210
[1,2,6,3,4,7,5]=>504
[1,2,6,3,5,4,7]=>70
[1,2,6,3,5,7,4]=>210
[1,2,6,3,7,4,5]=>420
[1,2,6,3,7,5,4]=>504
[1,2,6,4,3,5,7]=>70
[1,2,6,4,3,7,5]=>210
[1,2,6,4,5,3,7]=>21
[1,2,6,4,5,7,3]=>70
[1,2,6,4,7,3,5]=>105
[1,2,6,4,7,5,3]=>210
[1,2,6,5,3,4,7]=>210
[1,2,6,5,3,7,4]=>504
[1,2,6,5,4,3,7]=>105
[1,2,6,5,4,7,3]=>420
[1,2,6,5,7,3,4]=>420
[1,2,6,5,7,4,3]=>504
[1,2,6,7,3,4,5]=>504
[1,2,6,7,3,5,4]=>420
[1,2,6,7,4,3,5]=>420
[1,2,6,7,4,5,3]=>504
[1,2,6,7,5,3,4]=>105
[1,2,6,7,5,4,3]=>210
[1,2,7,3,4,5,6]=>504
[1,2,7,3,4,6,5]=>210
[1,2,7,3,5,4,6]=>210
[1,2,7,3,5,6,4]=>70
[1,2,7,3,6,4,5]=>504
[1,2,7,3,6,5,4]=>420
[1,2,7,4,3,5,6]=>210
[1,2,7,4,3,6,5]=>70
[1,2,7,4,5,3,6]=>70
[1,2,7,4,5,6,3]=>21
[1,2,7,4,6,3,5]=>210
[1,2,7,4,6,5,3]=>105
[1,2,7,5,3,4,6]=>504
[1,2,7,5,3,6,4]=>210
[1,2,7,5,4,3,6]=>420
[1,2,7,5,4,6,3]=>105
[1,2,7,5,6,3,4]=>504
[1,2,7,5,6,4,3]=>420
[1,2,7,6,3,4,5]=>420
[1,2,7,6,3,5,4]=>504
[1,2,7,6,4,3,5]=>504
[1,2,7,6,4,5,3]=>420
[1,2,7,6,5,3,4]=>210
[1,2,7,6,5,4,3]=>105
[1,3,2,4,5,6,7]=>21
[1,3,2,4,5,7,6]=>105
[1,3,2,4,6,5,7]=>105
[1,3,2,4,6,7,5]=>420
[1,3,2,4,7,5,6]=>420
[1,3,2,4,7,6,5]=>105
[1,3,2,5,4,6,7]=>105
[1,3,2,5,4,7,6]=>105
[1,3,2,5,6,4,7]=>420
[1,3,2,5,6,7,4]=>630
[1,3,2,5,7,4,6]=>630
[1,3,2,5,7,6,4]=>420
[1,3,2,6,4,5,7]=>420
[1,3,2,6,4,7,5]=>630
[1,3,2,6,5,4,7]=>105
[1,3,2,6,5,7,4]=>420
[1,3,2,6,7,4,5]=>105
[1,3,2,6,7,5,4]=>630
[1,3,2,7,4,5,6]=>630
[1,3,2,7,4,6,5]=>420
[1,3,2,7,5,4,6]=>420
[1,3,2,7,5,6,4]=>105
[1,3,2,7,6,4,5]=>630
[1,3,2,7,6,5,4]=>105
[1,3,4,2,5,6,7]=>70
[1,3,4,2,5,7,6]=>420
[1,3,4,2,6,5,7]=>420
[1,3,4,2,6,7,5]=>280
[1,3,4,2,7,5,6]=>280
[1,3,4,2,7,6,5]=>420
[1,3,4,5,2,6,7]=>210
[1,3,4,5,2,7,6]=>630
[1,3,4,5,6,2,7]=>504
[1,3,4,5,6,7,2]=>840
[1,3,4,5,7,2,6]=>840
[1,3,4,5,7,6,2]=>504
[1,3,4,6,2,5,7]=>504
[1,3,4,6,2,7,5]=>840
[1,3,4,6,5,2,7]=>210
[1,3,4,6,5,7,2]=>504
[1,3,4,6,7,2,5]=>630
[1,3,4,6,7,5,2]=>840
[1,3,4,7,2,5,6]=>840
[1,3,4,7,2,6,5]=>504
[1,3,4,7,5,2,6]=>504
[1,3,4,7,5,6,2]=>210
[1,3,4,7,6,2,5]=>840
[1,3,4,7,6,5,2]=>630
[1,3,5,2,4,6,7]=>210
[1,3,5,2,4,7,6]=>630
[1,3,5,2,6,4,7]=>504
[1,3,5,2,6,7,4]=>840
[1,3,5,2,7,4,6]=>840
[1,3,5,2,7,6,4]=>504
[1,3,5,4,2,6,7]=>70
[1,3,5,4,2,7,6]=>420
[1,3,5,4,6,2,7]=>210
[1,3,5,4,6,7,2]=>504
[1,3,5,4,7,2,6]=>504
[1,3,5,4,7,6,2]=>210
[1,3,5,6,2,4,7]=>420
[1,3,5,6,2,7,4]=>280
[1,3,5,6,4,2,7]=>504
[1,3,5,6,4,7,2]=>840
[1,3,5,6,7,2,4]=>840
[1,3,5,6,7,4,2]=>630
[1,3,5,7,2,4,6]=>280
[1,3,5,7,2,6,4]=>420
[1,3,5,7,4,2,6]=>840
[1,3,5,7,4,6,2]=>504
[1,3,5,7,6,2,4]=>630
[1,3,5,7,6,4,2]=>840
[1,3,6,2,4,5,7]=>504
[1,3,6,2,4,7,5]=>840
[1,3,6,2,5,4,7]=>210
[1,3,6,2,5,7,4]=>504
[1,3,6,2,7,4,5]=>630
[1,3,6,2,7,5,4]=>840
[1,3,6,4,2,5,7]=>210
[1,3,6,4,2,7,5]=>504
[1,3,6,4,5,2,7]=>70
[1,3,6,4,5,7,2]=>210
[1,3,6,4,7,2,5]=>420
[1,3,6,4,7,5,2]=>504
[1,3,6,5,2,4,7]=>504
[1,3,6,5,2,7,4]=>840
[1,3,6,5,4,2,7]=>420
[1,3,6,5,4,7,2]=>630
[1,3,6,5,7,2,4]=>280
[1,3,6,5,7,4,2]=>840
[1,3,6,7,2,4,5]=>840
[1,3,6,7,2,5,4]=>630
[1,3,6,7,4,2,5]=>280
[1,3,6,7,4,5,2]=>840
[1,3,6,7,5,2,4]=>420
[1,3,6,7,5,4,2]=>504
[1,3,7,2,4,5,6]=>840
[1,3,7,2,4,6,5]=>504
[1,3,7,2,5,4,6]=>504
[1,3,7,2,5,6,4]=>210
[1,3,7,2,6,4,5]=>840
[1,3,7,2,6,5,4]=>630
[1,3,7,4,2,5,6]=>504
[1,3,7,4,2,6,5]=>210
[1,3,7,4,5,2,6]=>210
[1,3,7,4,5,6,2]=>70
[1,3,7,4,6,2,5]=>504
[1,3,7,4,6,5,2]=>420
[1,3,7,5,2,4,6]=>840
[1,3,7,5,2,6,4]=>504
[1,3,7,5,4,2,6]=>630
[1,3,7,5,4,6,2]=>420
[1,3,7,5,6,2,4]=>840
[1,3,7,5,6,4,2]=>280
[1,3,7,6,2,4,5]=>630
[1,3,7,6,2,5,4]=>840
[1,3,7,6,4,2,5]=>840
[1,3,7,6,4,5,2]=>280
[1,3,7,6,5,2,4]=>504
[1,3,7,6,5,4,2]=>420
[1,4,2,3,5,6,7]=>70
[1,4,2,3,5,7,6]=>420
[1,4,2,3,6,5,7]=>420
[1,4,2,3,6,7,5]=>280
[1,4,2,3,7,5,6]=>280
[1,4,2,3,7,6,5]=>420
[1,4,2,5,3,6,7]=>210
[1,4,2,5,3,7,6]=>630
[1,4,2,5,6,3,7]=>504
[1,4,2,5,6,7,3]=>840
[1,4,2,5,7,3,6]=>840
[1,4,2,5,7,6,3]=>504
[1,4,2,6,3,5,7]=>504
[1,4,2,6,3,7,5]=>840
[1,4,2,6,5,3,7]=>210
[1,4,2,6,5,7,3]=>504
[1,4,2,6,7,3,5]=>630
[1,4,2,6,7,5,3]=>840
[1,4,2,7,3,5,6]=>840
[1,4,2,7,3,6,5]=>504
[1,4,2,7,5,3,6]=>504
[1,4,2,7,5,6,3]=>210
[1,4,2,7,6,3,5]=>840
[1,4,2,7,6,5,3]=>630
[1,4,3,2,5,6,7]=>21
[1,4,3,2,5,7,6]=>105
[1,4,3,2,6,5,7]=>105
[1,4,3,2,6,7,5]=>420
[1,4,3,2,7,5,6]=>420
[1,4,3,2,7,6,5]=>105
[1,4,3,5,2,6,7]=>70
[1,4,3,5,2,7,6]=>420
[1,4,3,5,6,2,7]=>210
[1,4,3,5,6,7,2]=>504
[1,4,3,5,7,2,6]=>504
[1,4,3,5,7,6,2]=>210
[1,4,3,6,2,5,7]=>210
[1,4,3,6,2,7,5]=>504
[1,4,3,6,5,2,7]=>70
[1,4,3,6,5,7,2]=>210
[1,4,3,6,7,2,5]=>420
[1,4,3,6,7,5,2]=>504
[1,4,3,7,2,5,6]=>504
[1,4,3,7,2,6,5]=>210
[1,4,3,7,5,2,6]=>210
[1,4,3,7,5,6,2]=>70
[1,4,3,7,6,2,5]=>504
[1,4,3,7,6,5,2]=>420
[1,4,5,2,3,6,7]=>105
[1,4,5,2,3,7,6]=>105
[1,4,5,2,6,3,7]=>420
[1,4,5,2,6,7,3]=>630
[1,4,5,2,7,3,6]=>630
[1,4,5,2,7,6,3]=>420
[1,4,5,3,2,6,7]=>210
[1,4,5,3,2,7,6]=>630
[1,4,5,3,6,2,7]=>504
[1,4,5,3,6,7,2]=>840
[1,4,5,3,7,2,6]=>840
[1,4,5,3,7,6,2]=>504
[1,4,5,6,2,3,7]=>504
[1,4,5,6,2,7,3]=>840
[1,4,5,6,3,2,7]=>420
[1,4,5,6,3,7,2]=>630
[1,4,5,6,7,2,3]=>280
[1,4,5,6,7,3,2]=>840
[1,4,5,7,2,3,6]=>840
[1,4,5,7,2,6,3]=>504
[1,4,5,7,3,2,6]=>630
[1,4,5,7,3,6,2]=>420
[1,4,5,7,6,2,3]=>840
[1,4,5,7,6,3,2]=>280
[1,4,6,2,3,5,7]=>420
[1,4,6,2,3,7,5]=>630
[1,4,6,2,5,3,7]=>105
[1,4,6,2,5,7,3]=>420
[1,4,6,2,7,3,5]=>105
[1,4,6,2,7,5,3]=>630
[1,4,6,3,2,5,7]=>504
[1,4,6,3,2,7,5]=>840
[1,4,6,3,5,2,7]=>210
[1,4,6,3,5,7,2]=>504
[1,4,6,3,7,2,5]=>630
[1,4,6,3,7,5,2]=>840
[1,4,6,5,2,3,7]=>420
[1,4,6,5,2,7,3]=>280
[1,4,6,5,3,2,7]=>504
[1,4,6,5,3,7,2]=>840
                    

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Description

The size of the conjugacy class of a permutation.
Two permutations are conjugate if and only if they have the same cycle type, this statistic is then computed as described in St000182The number of permutations whose cycle type is the given integer partition..

Code

def statistic(pi):
     la = list(pi.cycle_type())
     return factorial(sum(la))/prod(la)/prod(factorial(la.count(j)) for j in [1..la[0]+1])

def statistic_alternative(pi):
    return len(pi.conjugacy_class())

Created

Jan 22, 2017 at 19:17 by Christian Stump

Updated

Jan 22, 2017 at 20:34 by Christian Stump