Identifier
- St001346: Permutations ⟶ ℤ
Values
=>
[1,2]=>2
[2,1]=>1
[1,2,3]=>6
[1,3,2]=>2
[2,1,3]=>3
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>1
[1,2,3,4]=>24
[1,2,4,3]=>6
[1,3,2,4]=>8
[1,3,4,2]=>4
[1,4,2,3]=>6
[1,4,3,2]=>2
[2,1,3,4]=>12
[2,1,4,3]=>3
[2,3,1,4]=>8
[2,3,4,1]=>6
[2,4,1,3]=>3
[2,4,3,1]=>2
[3,1,2,4]=>8
[3,1,4,2]=>4
[3,2,1,4]=>4
[3,2,4,1]=>3
[3,4,1,2]=>4
[3,4,2,1]=>2
[4,1,2,3]=>6
[4,1,3,2]=>2
[4,2,1,3]=>3
[4,2,3,1]=>2
[4,3,1,2]=>2
[4,3,2,1]=>1
[1,2,3,4,5]=>120
[1,2,3,5,4]=>24
[1,2,4,3,5]=>30
[1,2,4,5,3]=>12
[1,2,5,3,4]=>24
[1,2,5,4,3]=>6
[1,3,2,4,5]=>40
[1,3,2,5,4]=>8
[1,3,4,2,5]=>20
[1,3,4,5,2]=>12
[1,3,5,2,4]=>8
[1,3,5,4,2]=>4
[1,4,2,3,5]=>30
[1,4,2,5,3]=>12
[1,4,3,2,5]=>10
[1,4,3,5,2]=>6
[1,4,5,2,3]=>12
[1,4,5,3,2]=>4
[1,5,2,3,4]=>24
[1,5,2,4,3]=>6
[1,5,3,2,4]=>8
[1,5,3,4,2]=>4
[1,5,4,2,3]=>6
[1,5,4,3,2]=>2
[2,1,3,4,5]=>60
[2,1,3,5,4]=>12
[2,1,4,3,5]=>15
[2,1,4,5,3]=>6
[2,1,5,3,4]=>12
[2,1,5,4,3]=>3
[2,3,1,4,5]=>40
[2,3,1,5,4]=>8
[2,3,4,1,5]=>30
[2,3,4,5,1]=>24
[2,3,5,1,4]=>8
[2,3,5,4,1]=>6
[2,4,1,3,5]=>15
[2,4,1,5,3]=>6
[2,4,3,1,5]=>10
[2,4,3,5,1]=>8
[2,4,5,1,3]=>6
[2,4,5,3,1]=>4
[2,5,1,3,4]=>12
[2,5,1,4,3]=>3
[2,5,3,1,4]=>8
[2,5,3,4,1]=>6
[2,5,4,1,3]=>3
[2,5,4,3,1]=>2
[3,1,2,4,5]=>40
[3,1,2,5,4]=>8
[3,1,4,2,5]=>20
[3,1,4,5,2]=>12
[3,1,5,2,4]=>8
[3,1,5,4,2]=>4
[3,2,1,4,5]=>20
[3,2,1,5,4]=>4
[3,2,4,1,5]=>15
[3,2,4,5,1]=>12
[3,2,5,1,4]=>4
[3,2,5,4,1]=>3
[3,4,1,2,5]=>20
[3,4,1,5,2]=>12
[3,4,2,1,5]=>10
[3,4,2,5,1]=>8
[3,4,5,1,2]=>12
[3,4,5,2,1]=>6
[3,5,1,2,4]=>8
[3,5,1,4,2]=>4
[3,5,2,1,4]=>4
[3,5,2,4,1]=>3
[3,5,4,1,2]=>4
[3,5,4,2,1]=>2
[4,1,2,3,5]=>30
[4,1,2,5,3]=>12
[4,1,3,2,5]=>10
[4,1,3,5,2]=>6
[4,1,5,2,3]=>12
[4,1,5,3,2]=>4
[4,2,1,3,5]=>15
[4,2,1,5,3]=>6
[4,2,3,1,5]=>10
[4,2,3,5,1]=>8
[4,2,5,1,3]=>6
[4,2,5,3,1]=>4
[4,3,1,2,5]=>10
[4,3,1,5,2]=>6
[4,3,2,1,5]=>5
[4,3,2,5,1]=>4
[4,3,5,1,2]=>6
[4,3,5,2,1]=>3
[4,5,1,2,3]=>12
[4,5,1,3,2]=>4
[4,5,2,1,3]=>6
[4,5,2,3,1]=>4
[4,5,3,1,2]=>4
[4,5,3,2,1]=>2
[5,1,2,3,4]=>24
[5,1,2,4,3]=>6
[5,1,3,2,4]=>8
[5,1,3,4,2]=>4
[5,1,4,2,3]=>6
[5,1,4,3,2]=>2
[5,2,1,3,4]=>12
[5,2,1,4,3]=>3
[5,2,3,1,4]=>8
[5,2,3,4,1]=>6
[5,2,4,1,3]=>3
[5,2,4,3,1]=>2
[5,3,1,2,4]=>8
[5,3,1,4,2]=>4
[5,3,2,1,4]=>4
[5,3,2,4,1]=>3
[5,3,4,1,2]=>4
[5,3,4,2,1]=>2
[5,4,1,2,3]=>6
[5,4,1,3,2]=>2
[5,4,2,1,3]=>3
[5,4,2,3,1]=>2
[5,4,3,1,2]=>2
[5,4,3,2,1]=>1
[1,2,3,4,5,6]=>720
[1,2,3,4,6,5]=>120
[1,2,3,5,4,6]=>144
[1,2,3,5,6,4]=>48
[1,2,3,6,4,5]=>120
[1,2,3,6,5,4]=>24
[1,2,4,3,5,6]=>180
[1,2,4,3,6,5]=>30
[1,2,4,5,3,6]=>72
[1,2,4,5,6,3]=>36
[1,2,4,6,3,5]=>30
[1,2,4,6,5,3]=>12
[1,2,5,3,4,6]=>144
[1,2,5,3,6,4]=>48
[1,2,5,4,3,6]=>36
[1,2,5,4,6,3]=>18
[1,2,5,6,3,4]=>48
[1,2,5,6,4,3]=>12
[1,2,6,3,4,5]=>120
[1,2,6,3,5,4]=>24
[1,2,6,4,3,5]=>30
[1,2,6,4,5,3]=>12
[1,2,6,5,3,4]=>24
[1,2,6,5,4,3]=>6
[1,3,2,4,5,6]=>240
[1,3,2,4,6,5]=>40
[1,3,2,5,4,6]=>48
[1,3,2,5,6,4]=>16
[1,3,2,6,4,5]=>40
[1,3,2,6,5,4]=>8
[1,3,4,2,5,6]=>120
[1,3,4,2,6,5]=>20
[1,3,4,5,2,6]=>72
[1,3,4,5,6,2]=>48
[1,3,4,6,2,5]=>20
[1,3,4,6,5,2]=>12
[1,3,5,2,4,6]=>48
[1,3,5,2,6,4]=>16
[1,3,5,4,2,6]=>24
[1,3,5,4,6,2]=>16
[1,3,5,6,2,4]=>16
[1,3,5,6,4,2]=>8
[1,3,6,2,4,5]=>40
[1,3,6,2,5,4]=>8
[1,3,6,4,2,5]=>20
[1,3,6,4,5,2]=>12
[1,3,6,5,2,4]=>8
[1,3,6,5,4,2]=>4
[1,4,2,3,5,6]=>180
[1,4,2,3,6,5]=>30
[1,4,2,5,3,6]=>72
[1,4,2,5,6,3]=>36
[1,4,2,6,3,5]=>30
[1,4,2,6,5,3]=>12
[1,4,3,2,5,6]=>60
[1,4,3,2,6,5]=>10
[1,4,3,5,2,6]=>36
[1,4,3,5,6,2]=>24
[1,4,3,6,2,5]=>10
[1,4,3,6,5,2]=>6
[1,4,5,2,3,6]=>72
[1,4,5,2,6,3]=>36
[1,4,5,3,2,6]=>24
[1,4,5,3,6,2]=>16
[1,4,5,6,2,3]=>36
[1,4,5,6,3,2]=>12
[1,4,6,2,3,5]=>30
[1,4,6,2,5,3]=>12
[1,4,6,3,2,5]=>10
[1,4,6,3,5,2]=>6
[1,4,6,5,2,3]=>12
[1,4,6,5,3,2]=>4
[1,5,2,3,4,6]=>144
[1,5,2,3,6,4]=>48
[1,5,2,4,3,6]=>36
[1,5,2,4,6,3]=>18
[1,5,2,6,3,4]=>48
[1,5,2,6,4,3]=>12
[1,5,3,2,4,6]=>48
[1,5,3,2,6,4]=>16
[1,5,3,4,2,6]=>24
[1,5,3,4,6,2]=>16
[1,5,3,6,2,4]=>16
[1,5,3,6,4,2]=>8
[1,5,4,2,3,6]=>36
[1,5,4,2,6,3]=>18
[1,5,4,3,2,6]=>12
[1,5,4,3,6,2]=>8
[1,5,4,6,2,3]=>18
[1,5,4,6,3,2]=>6
[1,5,6,2,3,4]=>48
[1,5,6,2,4,3]=>12
[1,5,6,3,2,4]=>16
[1,5,6,3,4,2]=>8
[1,5,6,4,2,3]=>12
[1,5,6,4,3,2]=>4
[1,6,2,3,4,5]=>120
[1,6,2,3,5,4]=>24
[1,6,2,4,3,5]=>30
[1,6,2,4,5,3]=>12
[1,6,2,5,3,4]=>24
[1,6,2,5,4,3]=>6
[1,6,3,2,4,5]=>40
[1,6,3,2,5,4]=>8
[1,6,3,4,2,5]=>20
[1,6,3,4,5,2]=>12
[1,6,3,5,2,4]=>8
[1,6,3,5,4,2]=>4
[1,6,4,2,3,5]=>30
[1,6,4,2,5,3]=>12
[1,6,4,3,2,5]=>10
[1,6,4,3,5,2]=>6
[1,6,4,5,2,3]=>12
[1,6,4,5,3,2]=>4
[1,6,5,2,3,4]=>24
[1,6,5,2,4,3]=>6
[1,6,5,3,2,4]=>8
[1,6,5,3,4,2]=>4
[1,6,5,4,2,3]=>6
[1,6,5,4,3,2]=>2
[2,1,3,4,5,6]=>360
[2,1,3,4,6,5]=>60
[2,1,3,5,4,6]=>72
[2,1,3,5,6,4]=>24
[2,1,3,6,4,5]=>60
[2,1,3,6,5,4]=>12
[2,1,4,3,5,6]=>90
[2,1,4,3,6,5]=>15
[2,1,4,5,3,6]=>36
[2,1,4,5,6,3]=>18
[2,1,4,6,3,5]=>15
[2,1,4,6,5,3]=>6
[2,1,5,3,4,6]=>72
[2,1,5,3,6,4]=>24
[2,1,5,4,3,6]=>18
[2,1,5,4,6,3]=>9
[2,1,5,6,3,4]=>24
[2,1,5,6,4,3]=>6
[2,1,6,3,4,5]=>60
[2,1,6,3,5,4]=>12
[2,1,6,4,3,5]=>15
[2,1,6,4,5,3]=>6
[2,1,6,5,3,4]=>12
[2,1,6,5,4,3]=>3
[2,3,1,4,5,6]=>240
[2,3,1,4,6,5]=>40
[2,3,1,5,4,6]=>48
[2,3,1,5,6,4]=>16
[2,3,1,6,4,5]=>40
[2,3,1,6,5,4]=>8
[2,3,4,1,5,6]=>180
[2,3,4,1,6,5]=>30
[2,3,4,5,1,6]=>144
[2,3,4,5,6,1]=>120
[2,3,4,6,1,5]=>30
[2,3,4,6,5,1]=>24
[2,3,5,1,4,6]=>48
[2,3,5,1,6,4]=>16
[2,3,5,4,1,6]=>36
[2,3,5,4,6,1]=>30
[2,3,5,6,1,4]=>16
[2,3,5,6,4,1]=>12
[2,3,6,1,4,5]=>40
[2,3,6,1,5,4]=>8
[2,3,6,4,1,5]=>30
[2,3,6,4,5,1]=>24
[2,3,6,5,1,4]=>8
[2,3,6,5,4,1]=>6
[2,4,1,3,5,6]=>90
[2,4,1,3,6,5]=>15
[2,4,1,5,3,6]=>36
[2,4,1,5,6,3]=>18
[2,4,1,6,3,5]=>15
[2,4,1,6,5,3]=>6
[2,4,3,1,5,6]=>60
[2,4,3,1,6,5]=>10
[2,4,3,5,1,6]=>48
[2,4,3,5,6,1]=>40
[2,4,3,6,1,5]=>10
[2,4,3,6,5,1]=>8
[2,4,5,1,3,6]=>36
[2,4,5,1,6,3]=>18
[2,4,5,3,1,6]=>24
[2,4,5,3,6,1]=>20
[2,4,5,6,1,3]=>18
[2,4,5,6,3,1]=>12
[2,4,6,1,3,5]=>15
[2,4,6,1,5,3]=>6
[2,4,6,3,1,5]=>10
[2,4,6,3,5,1]=>8
[2,4,6,5,1,3]=>6
[2,4,6,5,3,1]=>4
[2,5,1,3,4,6]=>72
[2,5,1,3,6,4]=>24
[2,5,1,4,3,6]=>18
[2,5,1,4,6,3]=>9
[2,5,1,6,3,4]=>24
[2,5,1,6,4,3]=>6
[2,5,3,1,4,6]=>48
[2,5,3,1,6,4]=>16
[2,5,3,4,1,6]=>36
[2,5,3,4,6,1]=>30
[2,5,3,6,1,4]=>16
[2,5,3,6,4,1]=>12
[2,5,4,1,3,6]=>18
[2,5,4,1,6,3]=>9
[2,5,4,3,1,6]=>12
[2,5,4,3,6,1]=>10
[2,5,4,6,1,3]=>9
[2,5,4,6,3,1]=>6
[2,5,6,1,3,4]=>24
[2,5,6,1,4,3]=>6
[2,5,6,3,1,4]=>16
[2,5,6,3,4,1]=>12
[2,5,6,4,1,3]=>6
[2,5,6,4,3,1]=>4
[2,6,1,3,4,5]=>60
[2,6,1,3,5,4]=>12
[2,6,1,4,3,5]=>15
[2,6,1,4,5,3]=>6
[2,6,1,5,3,4]=>12
[2,6,1,5,4,3]=>3
[2,6,3,1,4,5]=>40
[2,6,3,1,5,4]=>8
[2,6,3,4,1,5]=>30
[2,6,3,4,5,1]=>24
[2,6,3,5,1,4]=>8
[2,6,3,5,4,1]=>6
[2,6,4,1,3,5]=>15
[2,6,4,1,5,3]=>6
[2,6,4,3,1,5]=>10
[2,6,4,3,5,1]=>8
[2,6,4,5,1,3]=>6
[2,6,4,5,3,1]=>4
[2,6,5,1,3,4]=>12
[2,6,5,1,4,3]=>3
[2,6,5,3,1,4]=>8
[2,6,5,3,4,1]=>6
[2,6,5,4,1,3]=>3
[2,6,5,4,3,1]=>2
[3,1,2,4,5,6]=>240
[3,1,2,4,6,5]=>40
[3,1,2,5,4,6]=>48
[3,1,2,5,6,4]=>16
[3,1,2,6,4,5]=>40
[3,1,2,6,5,4]=>8
[3,1,4,2,5,6]=>120
[3,1,4,2,6,5]=>20
[3,1,4,5,2,6]=>72
[3,1,4,5,6,2]=>48
[3,1,4,6,2,5]=>20
[3,1,4,6,5,2]=>12
[3,1,5,2,4,6]=>48
[3,1,5,2,6,4]=>16
[3,1,5,4,2,6]=>24
[3,1,5,4,6,2]=>16
[3,1,5,6,2,4]=>16
[3,1,5,6,4,2]=>8
[3,1,6,2,4,5]=>40
[3,1,6,2,5,4]=>8
[3,1,6,4,2,5]=>20
[3,1,6,4,5,2]=>12
[3,1,6,5,2,4]=>8
[3,1,6,5,4,2]=>4
[3,2,1,4,5,6]=>120
[3,2,1,4,6,5]=>20
[3,2,1,5,4,6]=>24
[3,2,1,5,6,4]=>8
[3,2,1,6,4,5]=>20
[3,2,1,6,5,4]=>4
[3,2,4,1,5,6]=>90
[3,2,4,1,6,5]=>15
[3,2,4,5,1,6]=>72
[3,2,4,5,6,1]=>60
[3,2,4,6,1,5]=>15
[3,2,4,6,5,1]=>12
[3,2,5,1,4,6]=>24
[3,2,5,1,6,4]=>8
[3,2,5,4,1,6]=>18
[3,2,5,4,6,1]=>15
[3,2,5,6,1,4]=>8
[3,2,5,6,4,1]=>6
[3,2,6,1,4,5]=>20
[3,2,6,1,5,4]=>4
[3,2,6,4,1,5]=>15
[3,2,6,4,5,1]=>12
[3,2,6,5,1,4]=>4
[3,2,6,5,4,1]=>3
[3,4,1,2,5,6]=>120
[3,4,1,2,6,5]=>20
[3,4,1,5,2,6]=>72
[3,4,1,5,6,2]=>48
[3,4,1,6,2,5]=>20
[3,4,1,6,5,2]=>12
[3,4,2,1,5,6]=>60
[3,4,2,1,6,5]=>10
[3,4,2,5,1,6]=>48
[3,4,2,5,6,1]=>40
[3,4,2,6,1,5]=>10
[3,4,2,6,5,1]=>8
[3,4,5,1,2,6]=>72
[3,4,5,1,6,2]=>48
[3,4,5,2,1,6]=>36
[3,4,5,2,6,1]=>30
[3,4,5,6,1,2]=>48
[3,4,5,6,2,1]=>24
[3,4,6,1,2,5]=>20
[3,4,6,1,5,2]=>12
[3,4,6,2,1,5]=>10
[3,4,6,2,5,1]=>8
[3,4,6,5,1,2]=>12
[3,4,6,5,2,1]=>6
[3,5,1,2,4,6]=>48
[3,5,1,2,6,4]=>16
[3,5,1,4,2,6]=>24
[3,5,1,4,6,2]=>16
[3,5,1,6,2,4]=>16
[3,5,1,6,4,2]=>8
[3,5,2,1,4,6]=>24
[3,5,2,1,6,4]=>8
[3,5,2,4,1,6]=>18
[3,5,2,4,6,1]=>15
[3,5,2,6,1,4]=>8
[3,5,2,6,4,1]=>6
[3,5,4,1,2,6]=>24
[3,5,4,1,6,2]=>16
[3,5,4,2,1,6]=>12
[3,5,4,2,6,1]=>10
[3,5,4,6,1,2]=>16
[3,5,4,6,2,1]=>8
[3,5,6,1,2,4]=>16
[3,5,6,1,4,2]=>8
[3,5,6,2,1,4]=>8
[3,5,6,2,4,1]=>6
[3,5,6,4,1,2]=>8
[3,5,6,4,2,1]=>4
[3,6,1,2,4,5]=>40
[3,6,1,2,5,4]=>8
[3,6,1,4,2,5]=>20
[3,6,1,4,5,2]=>12
[3,6,1,5,2,4]=>8
[3,6,1,5,4,2]=>4
[3,6,2,1,4,5]=>20
[3,6,2,1,5,4]=>4
[3,6,2,4,1,5]=>15
[3,6,2,4,5,1]=>12
[3,6,2,5,1,4]=>4
[3,6,2,5,4,1]=>3
[3,6,4,1,2,5]=>20
[3,6,4,1,5,2]=>12
[3,6,4,2,1,5]=>10
[3,6,4,2,5,1]=>8
[3,6,4,5,1,2]=>12
[3,6,4,5,2,1]=>6
[3,6,5,1,2,4]=>8
[3,6,5,1,4,2]=>4
[3,6,5,2,1,4]=>4
[3,6,5,2,4,1]=>3
[3,6,5,4,1,2]=>4
[3,6,5,4,2,1]=>2
[4,1,2,3,5,6]=>180
[4,1,2,3,6,5]=>30
[4,1,2,5,3,6]=>72
[4,1,2,5,6,3]=>36
[4,1,2,6,3,5]=>30
[4,1,2,6,5,3]=>12
[4,1,3,2,5,6]=>60
[4,1,3,2,6,5]=>10
[4,1,3,5,2,6]=>36
[4,1,3,5,6,2]=>24
[4,1,3,6,2,5]=>10
[4,1,3,6,5,2]=>6
[4,1,5,2,3,6]=>72
[4,1,5,2,6,3]=>36
[4,1,5,3,2,6]=>24
[4,1,5,3,6,2]=>16
[4,1,5,6,2,3]=>36
[4,1,5,6,3,2]=>12
[4,1,6,2,3,5]=>30
[4,1,6,2,5,3]=>12
[4,1,6,3,2,5]=>10
[4,1,6,3,5,2]=>6
[4,1,6,5,2,3]=>12
[4,1,6,5,3,2]=>4
[4,2,1,3,5,6]=>90
[4,2,1,3,6,5]=>15
[4,2,1,5,3,6]=>36
[4,2,1,5,6,3]=>18
[4,2,1,6,3,5]=>15
[4,2,1,6,5,3]=>6
[4,2,3,1,5,6]=>60
[4,2,3,1,6,5]=>10
[4,2,3,5,1,6]=>48
[4,2,3,5,6,1]=>40
[4,2,3,6,1,5]=>10
[4,2,3,6,5,1]=>8
[4,2,5,1,3,6]=>36
[4,2,5,1,6,3]=>18
[4,2,5,3,1,6]=>24
[4,2,5,3,6,1]=>20
[4,2,5,6,1,3]=>18
[4,2,5,6,3,1]=>12
[4,2,6,1,3,5]=>15
[4,2,6,1,5,3]=>6
[4,2,6,3,1,5]=>10
[4,2,6,3,5,1]=>8
[4,2,6,5,1,3]=>6
[4,2,6,5,3,1]=>4
[4,3,1,2,5,6]=>60
[4,3,1,2,6,5]=>10
[4,3,1,5,2,6]=>36
[4,3,1,5,6,2]=>24
[4,3,1,6,2,5]=>10
[4,3,1,6,5,2]=>6
[4,3,2,1,5,6]=>30
[4,3,2,1,6,5]=>5
[4,3,2,5,1,6]=>24
[4,3,2,5,6,1]=>20
[4,3,2,6,1,5]=>5
[4,3,2,6,5,1]=>4
[4,3,5,1,2,6]=>36
[4,3,5,1,6,2]=>24
[4,3,5,2,1,6]=>18
[4,3,5,2,6,1]=>15
[4,3,5,6,1,2]=>24
[4,3,5,6,2,1]=>12
[4,3,6,1,2,5]=>10
[4,3,6,1,5,2]=>6
[4,3,6,2,1,5]=>5
[4,3,6,2,5,1]=>4
[4,3,6,5,1,2]=>6
[4,3,6,5,2,1]=>3
[4,5,1,2,3,6]=>72
[4,5,1,2,6,3]=>36
[4,5,1,3,2,6]=>24
[4,5,1,3,6,2]=>16
[4,5,1,6,2,3]=>36
[4,5,1,6,3,2]=>12
[4,5,2,1,3,6]=>36
[4,5,2,1,6,3]=>18
[4,5,2,3,1,6]=>24
[4,5,2,3,6,1]=>20
[4,5,2,6,1,3]=>18
[4,5,2,6,3,1]=>12
[4,5,3,1,2,6]=>24
[4,5,3,1,6,2]=>16
[4,5,3,2,1,6]=>12
[4,5,3,2,6,1]=>10
[4,5,3,6,1,2]=>16
[4,5,3,6,2,1]=>8
[4,5,6,1,2,3]=>36
[4,5,6,1,3,2]=>12
[4,5,6,2,1,3]=>18
[4,5,6,2,3,1]=>12
[4,5,6,3,1,2]=>12
[4,5,6,3,2,1]=>6
[4,6,1,2,3,5]=>30
[4,6,1,2,5,3]=>12
[4,6,1,3,2,5]=>10
[4,6,1,3,5,2]=>6
[4,6,1,5,2,3]=>12
[4,6,1,5,3,2]=>4
[4,6,2,1,3,5]=>15
[4,6,2,1,5,3]=>6
[4,6,2,3,1,5]=>10
[4,6,2,3,5,1]=>8
[4,6,2,5,1,3]=>6
[4,6,2,5,3,1]=>4
[4,6,3,1,2,5]=>10
[4,6,3,1,5,2]=>6
[4,6,3,2,1,5]=>5
[4,6,3,2,5,1]=>4
[4,6,3,5,1,2]=>6
[4,6,3,5,2,1]=>3
[4,6,5,1,2,3]=>12
[4,6,5,1,3,2]=>4
[4,6,5,2,1,3]=>6
[4,6,5,2,3,1]=>4
[4,6,5,3,1,2]=>4
[4,6,5,3,2,1]=>2
[5,1,2,3,4,6]=>144
[5,1,2,3,6,4]=>48
[5,1,2,4,3,6]=>36
[5,1,2,4,6,3]=>18
[5,1,2,6,3,4]=>48
[5,1,2,6,4,3]=>12
[5,1,3,2,4,6]=>48
[5,1,3,2,6,4]=>16
[5,1,3,4,2,6]=>24
[5,1,3,4,6,2]=>16
[5,1,3,6,2,4]=>16
[5,1,3,6,4,2]=>8
[5,1,4,2,3,6]=>36
[5,1,4,2,6,3]=>18
[5,1,4,3,2,6]=>12
[5,1,4,3,6,2]=>8
[5,1,4,6,2,3]=>18
[5,1,4,6,3,2]=>6
[5,1,6,2,3,4]=>48
[5,1,6,2,4,3]=>12
[5,1,6,3,2,4]=>16
[5,1,6,3,4,2]=>8
[5,1,6,4,2,3]=>12
[5,1,6,4,3,2]=>4
[5,2,1,3,4,6]=>72
[5,2,1,3,6,4]=>24
[5,2,1,4,3,6]=>18
[5,2,1,4,6,3]=>9
[5,2,1,6,3,4]=>24
[5,2,1,6,4,3]=>6
[5,2,3,1,4,6]=>48
[5,2,3,1,6,4]=>16
[5,2,3,4,1,6]=>36
[5,2,3,4,6,1]=>30
[5,2,3,6,1,4]=>16
[5,2,3,6,4,1]=>12
[5,2,4,1,3,6]=>18
[5,2,4,1,6,3]=>9
[5,2,4,3,1,6]=>12
[5,2,4,3,6,1]=>10
[5,2,4,6,1,3]=>9
[5,2,4,6,3,1]=>6
[5,2,6,1,3,4]=>24
[5,2,6,1,4,3]=>6
[5,2,6,3,1,4]=>16
[5,2,6,3,4,1]=>12
[5,2,6,4,1,3]=>6
[5,2,6,4,3,1]=>4
[5,3,1,2,4,6]=>48
[5,3,1,2,6,4]=>16
[5,3,1,4,2,6]=>24
[5,3,1,4,6,2]=>16
[5,3,1,6,2,4]=>16
[5,3,1,6,4,2]=>8
[5,3,2,1,4,6]=>24
[5,3,2,1,6,4]=>8
[5,3,2,4,1,6]=>18
[5,3,2,4,6,1]=>15
[5,3,2,6,1,4]=>8
[5,3,2,6,4,1]=>6
[5,3,4,1,2,6]=>24
[5,3,4,1,6,2]=>16
[5,3,4,2,1,6]=>12
[5,3,4,2,6,1]=>10
[5,3,4,6,1,2]=>16
[5,3,4,6,2,1]=>8
[5,3,6,1,2,4]=>16
[5,3,6,1,4,2]=>8
[5,3,6,2,1,4]=>8
[5,3,6,2,4,1]=>6
[5,3,6,4,1,2]=>8
[5,3,6,4,2,1]=>4
[5,4,1,2,3,6]=>36
[5,4,1,2,6,3]=>18
[5,4,1,3,2,6]=>12
[5,4,1,3,6,2]=>8
[5,4,1,6,2,3]=>18
[5,4,1,6,3,2]=>6
[5,4,2,1,3,6]=>18
[5,4,2,1,6,3]=>9
[5,4,2,3,1,6]=>12
[5,4,2,3,6,1]=>10
[5,4,2,6,1,3]=>9
[5,4,2,6,3,1]=>6
[5,4,3,1,2,6]=>12
[5,4,3,1,6,2]=>8
[5,4,3,2,1,6]=>6
[5,4,3,2,6,1]=>5
[5,4,3,6,1,2]=>8
[5,4,3,6,2,1]=>4
[5,4,6,1,2,3]=>18
[5,4,6,1,3,2]=>6
[5,4,6,2,1,3]=>9
[5,4,6,2,3,1]=>6
[5,4,6,3,1,2]=>6
[5,4,6,3,2,1]=>3
[5,6,1,2,3,4]=>48
[5,6,1,2,4,3]=>12
[5,6,1,3,2,4]=>16
[5,6,1,3,4,2]=>8
[5,6,1,4,2,3]=>12
[5,6,1,4,3,2]=>4
[5,6,2,1,3,4]=>24
[5,6,2,1,4,3]=>6
[5,6,2,3,1,4]=>16
[5,6,2,3,4,1]=>12
[5,6,2,4,1,3]=>6
[5,6,2,4,3,1]=>4
[5,6,3,1,2,4]=>16
[5,6,3,1,4,2]=>8
[5,6,3,2,1,4]=>8
[5,6,3,2,4,1]=>6
[5,6,3,4,1,2]=>8
[5,6,3,4,2,1]=>4
[5,6,4,1,2,3]=>12
[5,6,4,1,3,2]=>4
[5,6,4,2,1,3]=>6
[5,6,4,2,3,1]=>4
[5,6,4,3,1,2]=>4
[5,6,4,3,2,1]=>2
[6,1,2,3,4,5]=>120
[6,1,2,3,5,4]=>24
[6,1,2,4,3,5]=>30
[6,1,2,4,5,3]=>12
[6,1,2,5,3,4]=>24
[6,1,2,5,4,3]=>6
[6,1,3,2,4,5]=>40
[6,1,3,2,5,4]=>8
[6,1,3,4,2,5]=>20
[6,1,3,4,5,2]=>12
[6,1,3,5,2,4]=>8
[6,1,3,5,4,2]=>4
[6,1,4,2,3,5]=>30
[6,1,4,2,5,3]=>12
[6,1,4,3,2,5]=>10
[6,1,4,3,5,2]=>6
[6,1,4,5,2,3]=>12
[6,1,4,5,3,2]=>4
[6,1,5,2,3,4]=>24
[6,1,5,2,4,3]=>6
[6,1,5,3,2,4]=>8
[6,1,5,3,4,2]=>4
[6,1,5,4,2,3]=>6
[6,1,5,4,3,2]=>2
[6,2,1,3,4,5]=>60
[6,2,1,3,5,4]=>12
[6,2,1,4,3,5]=>15
[6,2,1,4,5,3]=>6
[6,2,1,5,3,4]=>12
[6,2,1,5,4,3]=>3
[6,2,3,1,4,5]=>40
[6,2,3,1,5,4]=>8
[6,2,3,4,1,5]=>30
[6,2,3,4,5,1]=>24
[6,2,3,5,1,4]=>8
[6,2,3,5,4,1]=>6
[6,2,4,1,3,5]=>15
[6,2,4,1,5,3]=>6
[6,2,4,3,1,5]=>10
[6,2,4,3,5,1]=>8
[6,2,4,5,1,3]=>6
[6,2,4,5,3,1]=>4
[6,2,5,1,3,4]=>12
[6,2,5,1,4,3]=>3
[6,2,5,3,1,4]=>8
[6,2,5,3,4,1]=>6
[6,2,5,4,1,3]=>3
[6,2,5,4,3,1]=>2
[6,3,1,2,4,5]=>40
[6,3,1,2,5,4]=>8
[6,3,1,4,2,5]=>20
[6,3,1,4,5,2]=>12
[6,3,1,5,2,4]=>8
[6,3,1,5,4,2]=>4
[6,3,2,1,4,5]=>20
[6,3,2,1,5,4]=>4
[6,3,2,4,1,5]=>15
[6,3,2,4,5,1]=>12
[6,3,2,5,1,4]=>4
[6,3,2,5,4,1]=>3
[6,3,4,1,2,5]=>20
[6,3,4,1,5,2]=>12
[6,3,4,2,1,5]=>10
[6,3,4,2,5,1]=>8
[6,3,4,5,1,2]=>12
[6,3,4,5,2,1]=>6
[6,3,5,1,2,4]=>8
[6,3,5,1,4,2]=>4
[6,3,5,2,1,4]=>4
[6,3,5,2,4,1]=>3
[6,3,5,4,1,2]=>4
[6,3,5,4,2,1]=>2
[6,4,1,2,3,5]=>30
[6,4,1,2,5,3]=>12
[6,4,1,3,2,5]=>10
[6,4,1,3,5,2]=>6
[6,4,1,5,2,3]=>12
[6,4,1,5,3,2]=>4
[6,4,2,1,3,5]=>15
[6,4,2,1,5,3]=>6
[6,4,2,3,1,5]=>10
[6,4,2,3,5,1]=>8
[6,4,2,5,1,3]=>6
[6,4,2,5,3,1]=>4
[6,4,3,1,2,5]=>10
[6,4,3,1,5,2]=>6
[6,4,3,2,1,5]=>5
[6,4,3,2,5,1]=>4
[6,4,3,5,1,2]=>6
[6,4,3,5,2,1]=>3
[6,4,5,1,2,3]=>12
[6,4,5,1,3,2]=>4
[6,4,5,2,1,3]=>6
[6,4,5,2,3,1]=>4
[6,4,5,3,1,2]=>4
[6,4,5,3,2,1]=>2
[6,5,1,2,3,4]=>24
[6,5,1,2,4,3]=>6
[6,5,1,3,2,4]=>8
[6,5,1,3,4,2]=>4
[6,5,1,4,2,3]=>6
[6,5,1,4,3,2]=>2
[6,5,2,1,3,4]=>12
[6,5,2,1,4,3]=>3
[6,5,2,3,1,4]=>8
[6,5,2,3,4,1]=>6
[6,5,2,4,1,3]=>3
[6,5,2,4,3,1]=>2
[6,5,3,1,2,4]=>8
[6,5,3,1,4,2]=>4
[6,5,3,2,1,4]=>4
[6,5,3,2,4,1]=>3
[6,5,3,4,1,2]=>4
[6,5,3,4,2,1]=>2
[6,5,4,1,2,3]=>6
[6,5,4,1,3,2]=>2
[6,5,4,2,1,3]=>3
[6,5,4,2,3,1]=>2
[6,5,4,3,1,2]=>2
[6,5,4,3,2,1]=>1
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Description
The number of parking functions that give the same permutation.
A parking function $(a_1,\dots,a_n)$ is a list of preferred parking spots of $n$ cars entering a one-way street. Once the cars have parked, the order of the cars gives a permutation of $\{1,\dots,n\}$. This statistic records the number of parking functions that yield the same permutation of cars.
A parking function $(a_1,\dots,a_n)$ is a list of preferred parking spots of $n$ cars entering a one-way street. Once the cars have parked, the order of the cars gives a permutation of $\{1,\dots,n\}$. This statistic records the number of parking functions that yield the same permutation of cars.
Code
from collections import defaultdict
@cached_function
def PF_to_Perms(n):
out = defaultdict(list)
for pf in ParkingFunctions(n):
out[pf.parking_permutation()].append(pf)
return out
def statistic(pi):
return len(PF_to_Perms(len(pi))[pi])
Created
Jan 26, 2019 at 13:10 by Raman Sanyal
Updated
Feb 09, 2021 at 15:34 by Martin Rubey
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