Identifier
- St000001: Permutations ⟶ ℤ
Values
=>
[]=>1
[1]=>1
[1,2]=>1
[2,1]=>1
[1,2,3]=>1
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>1
[3,1,2]=>1
[3,2,1]=>2
[1,2,3,4]=>1
[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]=>2
[2,4,3,1]=>3
[3,1,2,4]=>1
[3,1,4,2]=>2
[3,2,1,4]=>2
[3,2,4,1]=>3
[3,4,1,2]=>2
[3,4,2,1]=>5
[4,1,2,3]=>1
[4,1,3,2]=>3
[4,2,1,3]=>3
[4,2,3,1]=>6
[4,3,1,2]=>5
[4,3,2,1]=>16
[1,2,3,4,5]=>1
[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]=>2
[1,3,5,4,2]=>3
[1,4,2,3,5]=>1
[1,4,2,5,3]=>2
[1,4,3,2,5]=>2
[1,4,3,5,2]=>3
[1,4,5,2,3]=>2
[1,4,5,3,2]=>5
[1,5,2,3,4]=>1
[1,5,2,4,3]=>3
[1,5,3,2,4]=>3
[1,5,3,4,2]=>6
[1,5,4,2,3]=>5
[1,5,4,3,2]=>16
[2,1,3,4,5]=>1
[2,1,3,5,4]=>2
[2,1,4,3,5]=>2
[2,1,4,5,3]=>3
[2,1,5,3,4]=>3
[2,1,5,4,3]=>8
[2,3,1,4,5]=>1
[2,3,1,5,4]=>3
[2,3,4,1,5]=>1
[2,3,4,5,1]=>1
[2,3,5,1,4]=>3
[2,3,5,4,1]=>4
[2,4,1,3,5]=>2
[2,4,1,5,3]=>5
[2,4,3,1,5]=>3
[2,4,3,5,1]=>4
[2,4,5,1,3]=>5
[2,4,5,3,1]=>9
[2,5,1,3,4]=>3
[2,5,1,4,3]=>11
[2,5,3,1,4]=>6
[2,5,3,4,1]=>10
[2,5,4,1,3]=>16
[2,5,4,3,1]=>35
[3,1,2,4,5]=>1
[3,1,2,5,4]=>3
[3,1,4,2,5]=>2
[3,1,4,5,2]=>3
[3,1,5,2,4]=>5
[3,1,5,4,2]=>11
[3,2,1,4,5]=>2
[3,2,1,5,4]=>8
[3,2,4,1,5]=>3
[3,2,4,5,1]=>4
[3,2,5,1,4]=>11
[3,2,5,4,1]=>19
[3,4,1,2,5]=>2
[3,4,1,5,2]=>5
[3,4,2,1,5]=>5
[3,4,2,5,1]=>9
[3,4,5,1,2]=>5
[3,4,5,2,1]=>14
[3,5,1,2,4]=>5
[3,5,1,4,2]=>16
[3,5,2,1,4]=>16
[3,5,2,4,1]=>35
[3,5,4,1,2]=>21
[3,5,4,2,1]=>70
[4,1,2,3,5]=>1
[4,1,2,5,3]=>3
[4,1,3,2,5]=>3
[4,1,3,5,2]=>6
[4,1,5,2,3]=>5
[4,1,5,3,2]=>16
[4,2,1,3,5]=>3
[4,2,1,5,3]=>11
[4,2,3,1,5]=>6
[4,2,3,5,1]=>10
[4,2,5,1,3]=>16
[4,2,5,3,1]=>35
[4,3,1,2,5]=>5
[4,3,1,5,2]=>16
[4,3,2,1,5]=>16
[4,3,2,5,1]=>35
[4,3,5,1,2]=>21
[4,3,5,2,1]=>70
[4,5,1,2,3]=>5
[4,5,1,3,2]=>21
[4,5,2,1,3]=>21
[4,5,2,3,1]=>56
[4,5,3,1,2]=>42
[4,5,3,2,1]=>168
[5,1,2,3,4]=>1
[5,1,2,4,3]=>4
[5,1,3,2,4]=>4
[5,1,3,4,2]=>10
[5,1,4,2,3]=>9
[5,1,4,3,2]=>35
[5,2,1,3,4]=>4
[5,2,1,4,3]=>19
[5,2,3,1,4]=>10
[5,2,3,4,1]=>20
[5,2,4,1,3]=>35
[5,2,4,3,1]=>90
[5,3,1,2,4]=>9
[5,3,1,4,2]=>35
[5,3,2,1,4]=>35
[5,3,2,4,1]=>90
[5,3,4,1,2]=>56
[5,3,4,2,1]=>216
[5,4,1,2,3]=>14
[5,4,1,3,2]=>70
[5,4,2,1,3]=>70
[5,4,2,3,1]=>216
[5,4,3,1,2]=>168
[5,4,3,2,1]=>768
[1,2,3,4,5,6]=>1
[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]=>2
[1,2,4,6,5,3]=>3
[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]=>3
[1,2,5,6,3,4]=>2
[1,2,5,6,4,3]=>5
[1,2,6,3,4,5]=>1
[1,2,6,3,5,4]=>3
[1,2,6,4,3,5]=>3
[1,2,6,4,5,3]=>6
[1,2,6,5,3,4]=>5
[1,2,6,5,4,3]=>16
[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]=>3
[1,3,2,6,4,5]=>3
[1,3,2,6,5,4]=>8
[1,3,4,2,5,6]=>1
[1,3,4,2,6,5]=>3
[1,3,4,5,2,6]=>1
[1,3,4,5,6,2]=>1
[1,3,4,6,2,5]=>3
[1,3,4,6,5,2]=>4
[1,3,5,2,4,6]=>2
[1,3,5,2,6,4]=>5
[1,3,5,4,2,6]=>3
[1,3,5,4,6,2]=>4
[1,3,5,6,2,4]=>5
[1,3,5,6,4,2]=>9
[1,3,6,2,4,5]=>3
[1,3,6,2,5,4]=>11
[1,3,6,4,2,5]=>6
[1,3,6,4,5,2]=>10
[1,3,6,5,2,4]=>16
[1,3,6,5,4,2]=>35
[1,4,2,3,5,6]=>1
[1,4,2,3,6,5]=>3
[1,4,2,5,3,6]=>2
[1,4,2,5,6,3]=>3
[1,4,2,6,3,5]=>5
[1,4,2,6,5,3]=>11
[1,4,3,2,5,6]=>2
[1,4,3,2,6,5]=>8
[1,4,3,5,2,6]=>3
[1,4,3,5,6,2]=>4
[1,4,3,6,2,5]=>11
[1,4,3,6,5,2]=>19
[1,4,5,2,3,6]=>2
[1,4,5,2,6,3]=>5
[1,4,5,3,2,6]=>5
[1,4,5,3,6,2]=>9
[1,4,5,6,2,3]=>5
[1,4,5,6,3,2]=>14
[1,4,6,2,3,5]=>5
[1,4,6,2,5,3]=>16
[1,4,6,3,2,5]=>16
[1,4,6,3,5,2]=>35
[1,4,6,5,2,3]=>21
[1,4,6,5,3,2]=>70
[1,5,2,3,4,6]=>1
[1,5,2,3,6,4]=>3
[1,5,2,4,3,6]=>3
[1,5,2,4,6,3]=>6
[1,5,2,6,3,4]=>5
[1,5,2,6,4,3]=>16
[1,5,3,2,4,6]=>3
[1,5,3,2,6,4]=>11
[1,5,3,4,2,6]=>6
[1,5,3,4,6,2]=>10
[1,5,3,6,2,4]=>16
[1,5,3,6,4,2]=>35
[1,5,4,2,3,6]=>5
[1,5,4,2,6,3]=>16
[1,5,4,3,2,6]=>16
[1,5,4,3,6,2]=>35
[1,5,4,6,2,3]=>21
[1,5,4,6,3,2]=>70
[1,5,6,2,3,4]=>5
[1,5,6,2,4,3]=>21
[1,5,6,3,2,4]=>21
[1,5,6,3,4,2]=>56
[1,5,6,4,2,3]=>42
[1,5,6,4,3,2]=>168
[1,6,2,3,4,5]=>1
[1,6,2,3,5,4]=>4
[1,6,2,4,3,5]=>4
[1,6,2,4,5,3]=>10
[1,6,2,5,3,4]=>9
[1,6,2,5,4,3]=>35
[1,6,3,2,4,5]=>4
[1,6,3,2,5,4]=>19
[1,6,3,4,2,5]=>10
[1,6,3,4,5,2]=>20
[1,6,3,5,2,4]=>35
[1,6,3,5,4,2]=>90
[1,6,4,2,3,5]=>9
[1,6,4,2,5,3]=>35
[1,6,4,3,2,5]=>35
[1,6,4,3,5,2]=>90
[1,6,4,5,2,3]=>56
[1,6,4,5,3,2]=>216
[1,6,5,2,3,4]=>14
[1,6,5,2,4,3]=>70
[1,6,5,3,2,4]=>70
[1,6,5,3,4,2]=>216
[1,6,5,4,2,3]=>168
[1,6,5,4,3,2]=>768
[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]=>3
[2,1,3,6,4,5]=>3
[2,1,3,6,5,4]=>8
[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>6
[2,1,4,5,3,6]=>3
[2,1,4,5,6,3]=>4
[2,1,4,6,3,5]=>8
[2,1,4,6,5,3]=>15
[2,1,5,3,4,6]=>3
[2,1,5,3,6,4]=>8
[2,1,5,4,3,6]=>8
[2,1,5,4,6,3]=>15
[2,1,5,6,3,4]=>10
[2,1,5,6,4,3]=>30
[2,1,6,3,4,5]=>4
[2,1,6,3,5,4]=>15
[2,1,6,4,3,5]=>15
[2,1,6,4,5,3]=>36
[2,1,6,5,3,4]=>30
[2,1,6,5,4,3]=>112
[2,3,1,4,5,6]=>1
[2,3,1,4,6,5]=>3
[2,3,1,5,4,6]=>3
[2,3,1,5,6,4]=>6
[2,3,1,6,4,5]=>6
[2,3,1,6,5,4]=>20
[2,3,4,1,5,6]=>1
[2,3,4,1,6,5]=>4
[2,3,4,5,1,6]=>1
[2,3,4,5,6,1]=>1
[2,3,4,6,1,5]=>4
[2,3,4,6,5,1]=>5
[2,3,5,1,4,6]=>3
[2,3,5,1,6,4]=>9
[2,3,5,4,1,6]=>4
[2,3,5,4,6,1]=>5
[2,3,5,6,1,4]=>9
[2,3,5,6,4,1]=>14
[2,3,6,1,4,5]=>6
[2,3,6,1,5,4]=>26
[2,3,6,4,1,5]=>10
[2,3,6,4,5,1]=>15
[2,3,6,5,1,4]=>35
[2,3,6,5,4,1]=>64
[2,4,1,3,5,6]=>2
[2,4,1,3,6,5]=>8
[2,4,1,5,3,6]=>5
[2,4,1,5,6,3]=>9
[2,4,1,6,3,5]=>16
[2,4,1,6,5,3]=>40
[2,4,3,1,5,6]=>3
[2,4,3,1,6,5]=>15
[2,4,3,5,1,6]=>4
[2,4,3,5,6,1]=>5
[2,4,3,6,1,5]=>19
[2,4,3,6,5,1]=>29
[2,4,5,1,3,6]=>5
[2,4,5,1,6,3]=>14
[2,4,5,3,1,6]=>9
[2,4,5,3,6,1]=>14
[2,4,5,6,1,3]=>14
[2,4,5,6,3,1]=>28
[2,4,6,1,3,5]=>16
[2,4,6,1,5,3]=>56
[2,4,6,3,1,5]=>35
[2,4,6,3,5,1]=>64
[2,4,6,5,1,3]=>70
[2,4,6,5,3,1]=>162
[2,5,1,3,4,6]=>3
[2,5,1,3,6,4]=>11
[2,5,1,4,3,6]=>11
[2,5,1,4,6,3]=>26
[2,5,1,6,3,4]=>21
[2,5,1,6,4,3]=>77
[2,5,3,1,4,6]=>6
[2,5,3,1,6,4]=>26
[2,5,3,4,1,6]=>10
[2,5,3,4,6,1]=>15
[2,5,3,6,1,4]=>35
[2,5,3,6,4,1]=>64
[2,5,4,1,3,6]=>16
[2,5,4,1,6,3]=>56
[2,5,4,3,1,6]=>35
[2,5,4,3,6,1]=>64
[2,5,4,6,1,3]=>70
[2,5,4,6,3,1]=>162
[2,5,6,1,3,4]=>21
[2,5,6,1,4,3]=>98
[2,5,6,3,1,4]=>56
[2,5,6,3,4,1]=>120
[2,5,6,4,1,3]=>168
[2,5,6,4,3,1]=>450
[2,6,1,3,4,5]=>4
[2,6,1,3,5,4]=>19
[2,6,1,4,3,5]=>19
[2,6,1,4,5,3]=>55
[2,6,1,5,3,4]=>49
[2,6,1,5,4,3]=>216
[2,6,3,1,4,5]=>10
[2,6,3,1,5,4]=>55
[2,6,3,4,1,5]=>20
[2,6,3,4,5,1]=>35
[2,6,3,5,1,4]=>90
[2,6,3,5,4,1]=>189
[2,6,4,1,3,5]=>35
[2,6,4,1,5,3]=>146
[2,6,4,3,1,5]=>90
[2,6,4,3,5,1]=>189
[2,6,4,5,1,3]=>216
[2,6,4,5,3,1]=>567
[2,6,5,1,3,4]=>70
[2,6,5,1,4,3]=>384
[2,6,5,3,1,4]=>216
[2,6,5,3,4,1]=>525
[2,6,5,4,1,3]=>768
[2,6,5,4,3,1]=>2310
[3,1,2,4,5,6]=>1
[3,1,2,4,6,5]=>3
[3,1,2,5,4,6]=>3
[3,1,2,5,6,4]=>6
[3,1,2,6,4,5]=>6
[3,1,2,6,5,4]=>20
[3,1,4,2,5,6]=>2
[3,1,4,2,6,5]=>8
[3,1,4,5,2,6]=>3
[3,1,4,5,6,2]=>4
[3,1,4,6,2,5]=>11
[3,1,4,6,5,2]=>19
[3,1,5,2,4,6]=>5
[3,1,5,2,6,4]=>16
[3,1,5,4,2,6]=>11
[3,1,5,4,6,2]=>19
[3,1,5,6,2,4]=>21
[3,1,5,6,4,2]=>49
[3,1,6,2,4,5]=>9
[3,1,6,2,5,4]=>40
[3,1,6,4,2,5]=>26
[3,1,6,4,5,2]=>55
[3,1,6,5,2,4]=>77
[3,1,6,5,4,2]=>216
[3,2,1,4,5,6]=>2
[3,2,1,4,6,5]=>8
[3,2,1,5,4,6]=>8
[3,2,1,5,6,4]=>20
[3,2,1,6,4,5]=>20
[3,2,1,6,5,4]=>80
[3,2,4,1,5,6]=>3
[3,2,4,1,6,5]=>15
[3,2,4,5,1,6]=>4
[3,2,4,5,6,1]=>5
[3,2,4,6,1,5]=>19
[3,2,4,6,5,1]=>29
[3,2,5,1,4,6]=>11
[3,2,5,1,6,4]=>40
[3,2,5,4,1,6]=>19
[3,2,5,4,6,1]=>29
[3,2,5,6,1,4]=>49
[3,2,5,6,4,1]=>92
[3,2,6,1,4,5]=>26
[3,2,6,1,5,4]=>132
[3,2,6,4,1,5]=>55
[3,2,6,4,5,1]=>99
[3,2,6,5,1,4]=>216
[3,2,6,5,4,1]=>471
[3,4,1,2,5,6]=>2
[3,4,1,2,6,5]=>10
[3,4,1,5,2,6]=>5
[3,4,1,5,6,2]=>9
[3,4,1,6,2,5]=>21
[3,4,1,6,5,2]=>49
[3,4,2,1,5,6]=>5
[3,4,2,1,6,5]=>30
[3,4,2,5,1,6]=>9
[3,4,2,5,6,1]=>14
[3,4,2,6,1,5]=>49
[3,4,2,6,5,1]=>92
[3,4,5,1,2,6]=>5
[3,4,5,1,6,2]=>14
[3,4,5,2,1,6]=>14
[3,4,5,2,6,1]=>28
[3,4,5,6,1,2]=>14
[3,4,5,6,2,1]=>42
[3,4,6,1,2,5]=>21
[3,4,6,1,5,2]=>70
[3,4,6,2,1,5]=>70
[3,4,6,2,5,1]=>162
[3,4,6,5,1,2]=>84
[3,4,6,5,2,1]=>288
[3,5,1,2,4,6]=>5
[3,5,1,2,6,4]=>21
[3,5,1,4,2,6]=>16
[3,5,1,4,6,2]=>35
[3,5,1,6,2,4]=>42
[3,5,1,6,4,2]=>126
[3,5,2,1,4,6]=>16
[3,5,2,1,6,4]=>77
[3,5,2,4,1,6]=>35
[3,5,2,4,6,1]=>64
[3,5,2,6,1,4]=>126
[3,5,2,6,4,1]=>282
[3,5,4,1,2,6]=>21
[3,5,4,1,6,2]=>70
[3,5,4,2,1,6]=>70
[3,5,4,2,6,1]=>162
[3,5,4,6,1,2]=>84
[3,5,4,6,2,1]=>288
[3,5,6,1,2,4]=>42
[3,5,6,1,4,2]=>168
[3,5,6,2,1,4]=>168
[3,5,6,2,4,1]=>450
[3,5,6,4,1,2]=>252
[3,5,6,4,2,1]=>990
[3,6,1,2,4,5]=>9
[3,6,1,2,5,4]=>49
[3,6,1,4,2,5]=>35
[3,6,1,4,5,2]=>90
[3,6,1,5,2,4]=>126
[3,6,1,5,4,2]=>432
[3,6,2,1,4,5]=>35
[3,6,2,1,5,4]=>216
[3,6,2,4,1,5]=>90
[3,6,2,4,5,1]=>189
[3,6,2,5,1,4]=>432
[3,6,2,5,4,1]=>1092
[3,6,4,1,2,5]=>56
[3,6,4,1,5,2]=>216
[3,6,4,2,1,5]=>216
[3,6,4,2,5,1]=>567
[3,6,4,5,1,2]=>300
[3,6,4,5,2,1]=>1155
[3,6,5,1,2,4]=>168
[3,6,5,1,4,2]=>768
[3,6,5,2,1,4]=>768
[3,6,5,2,4,1]=>2310
[3,6,5,4,1,2]=>1320
[3,6,5,4,2,1]=>5775
[4,1,2,3,5,6]=>1
[4,1,2,3,6,5]=>4
[4,1,2,5,3,6]=>3
[4,1,2,5,6,3]=>6
[4,1,2,6,3,5]=>9
[4,1,2,6,5,3]=>26
[4,1,3,2,5,6]=>3
[4,1,3,2,6,5]=>15
[4,1,3,5,2,6]=>6
[4,1,3,5,6,2]=>10
[4,1,3,6,2,5]=>26
[4,1,3,6,5,2]=>55
[4,1,5,2,3,6]=>5
[4,1,5,2,6,3]=>16
[4,1,5,3,2,6]=>16
[4,1,5,3,6,2]=>35
[4,1,5,6,2,3]=>21
[4,1,5,6,3,2]=>70
[4,1,6,2,3,5]=>14
[4,1,6,2,5,3]=>56
[4,1,6,3,2,5]=>56
[4,1,6,3,5,2]=>146
[4,1,6,5,2,3]=>98
[4,1,6,5,3,2]=>384
[4,2,1,3,5,6]=>3
[4,2,1,3,6,5]=>15
[4,2,1,5,3,6]=>11
[4,2,1,5,6,3]=>26
[4,2,1,6,3,5]=>40
[4,2,1,6,5,3]=>132
[4,2,3,1,5,6]=>6
[4,2,3,1,6,5]=>36
[4,2,3,5,1,6]=>10
[4,2,3,5,6,1]=>15
[4,2,3,6,1,5]=>55
[4,2,3,6,5,1]=>99
[4,2,5,1,3,6]=>16
[4,2,5,1,6,3]=>56
[4,2,5,3,1,6]=>35
[4,2,5,3,6,1]=>64
[4,2,5,6,1,3]=>70
[4,2,5,6,3,1]=>162
[4,2,6,1,3,5]=>56
[4,2,6,1,5,3]=>244
[4,2,6,3,1,5]=>146
[4,2,6,3,5,1]=>309
[4,2,6,5,1,3]=>384
[4,2,6,5,3,1]=>1017
[4,3,1,2,5,6]=>5
[4,3,1,2,6,5]=>30
[4,3,1,5,2,6]=>16
[4,3,1,5,6,2]=>35
[4,3,1,6,2,5]=>77
[4,3,1,6,5,2]=>216
[4,3,2,1,5,6]=>16
[4,3,2,1,6,5]=>112
[4,3,2,5,1,6]=>35
[4,3,2,5,6,1]=>64
[4,3,2,6,1,5]=>216
[4,3,2,6,5,1]=>471
[4,3,5,1,2,6]=>21
[4,3,5,1,6,2]=>70
[4,3,5,2,1,6]=>70
[4,3,5,2,6,1]=>162
[4,3,5,6,1,2]=>84
[4,3,5,6,2,1]=>288
[4,3,6,1,2,5]=>98
[4,3,6,1,5,2]=>384
[4,3,6,2,1,5]=>384
[4,3,6,2,5,1]=>1017
[4,3,6,5,1,2]=>552
[4,3,6,5,2,1]=>2145
[4,5,1,2,3,6]=>5
[4,5,1,2,6,3]=>21
[4,5,1,3,2,6]=>21
[4,5,1,3,6,2]=>56
[4,5,1,6,2,3]=>42
[4,5,1,6,3,2]=>168
[4,5,2,1,3,6]=>21
[4,5,2,1,6,3]=>98
[4,5,2,3,1,6]=>56
[4,5,2,3,6,1]=>120
[4,5,2,6,1,3]=>168
[4,5,2,6,3,1]=>450
[4,5,3,1,2,6]=>42
[4,5,3,1,6,2]=>168
[4,5,3,2,1,6]=>168
[4,5,3,2,6,1]=>450
[4,5,3,6,1,2]=>252
[4,5,3,6,2,1]=>990
[4,5,6,1,2,3]=>42
[4,5,6,1,3,2]=>210
[4,5,6,2,1,3]=>210
[4,5,6,2,3,1]=>660
[4,5,6,3,1,2]=>462
[4,5,6,3,2,1]=>2112
[4,6,1,2,3,5]=>14
[4,6,1,2,5,3]=>70
[4,6,1,3,2,5]=>70
[4,6,1,3,5,2]=>216
[4,6,1,5,2,3]=>168
[4,6,1,5,3,2]=>768
[4,6,2,1,3,5]=>70
[4,6,2,1,5,3]=>384
[4,6,2,3,1,5]=>216
[4,6,2,3,5,1]=>525
[4,6,2,5,1,3]=>768
[4,6,2,5,3,1]=>2310
[4,6,3,1,2,5]=>168
[4,6,3,1,5,2]=>768
[4,6,3,2,1,5]=>768
[4,6,3,2,5,1]=>2310
[4,6,3,5,1,2]=>1320
[4,6,3,5,2,1]=>5775
[4,6,5,1,2,3]=>210
[4,6,5,1,3,2]=>1188
[4,6,5,2,1,3]=>1188
[4,6,5,2,3,1]=>4158
[4,6,5,3,1,2]=>2970
[4,6,5,3,2,1]=>15015
[5,1,2,3,4,6]=>1
[5,1,2,3,6,4]=>4
[5,1,2,4,3,6]=>4
[5,1,2,4,6,3]=>10
[5,1,2,6,3,4]=>9
[5,1,2,6,4,3]=>35
[5,1,3,2,4,6]=>4
[5,1,3,2,6,4]=>19
[5,1,3,4,2,6]=>10
[5,1,3,4,6,2]=>20
[5,1,3,6,2,4]=>35
[5,1,3,6,4,2]=>90
[5,1,4,2,3,6]=>9
[5,1,4,2,6,3]=>35
[5,1,4,3,2,6]=>35
[5,1,4,3,6,2]=>90
[5,1,4,6,2,3]=>56
[5,1,4,6,3,2]=>216
[5,1,6,2,3,4]=>14
[5,1,6,2,4,3]=>70
[5,1,6,3,2,4]=>70
[5,1,6,3,4,2]=>216
[5,1,6,4,2,3]=>168
[5,1,6,4,3,2]=>768
[5,2,1,3,4,6]=>4
[5,2,1,3,6,4]=>19
[5,2,1,4,3,6]=>19
[5,2,1,4,6,3]=>55
[5,2,1,6,3,4]=>49
[5,2,1,6,4,3]=>216
[5,2,3,1,4,6]=>10
[5,2,3,1,6,4]=>55
[5,2,3,4,1,6]=>20
[5,2,3,4,6,1]=>35
[5,2,3,6,1,4]=>90
[5,2,3,6,4,1]=>189
[5,2,4,1,3,6]=>35
[5,2,4,1,6,3]=>146
[5,2,4,3,1,6]=>90
[5,2,4,3,6,1]=>189
[5,2,4,6,1,3]=>216
[5,2,4,6,3,1]=>567
[5,2,6,1,3,4]=>70
[5,2,6,1,4,3]=>384
[5,2,6,3,1,4]=>216
[5,2,6,3,4,1]=>525
[5,2,6,4,1,3]=>768
[5,2,6,4,3,1]=>2310
[5,3,1,2,4,6]=>9
[5,3,1,2,6,4]=>49
[5,3,1,4,2,6]=>35
[5,3,1,4,6,2]=>90
[5,3,1,6,2,4]=>126
[5,3,1,6,4,2]=>432
[5,3,2,1,4,6]=>35
[5,3,2,1,6,4]=>216
[5,3,2,4,1,6]=>90
[5,3,2,4,6,1]=>189
[5,3,2,6,1,4]=>432
[5,3,2,6,4,1]=>1092
[5,3,4,1,2,6]=>56
[5,3,4,1,6,2]=>216
[5,3,4,2,1,6]=>216
[5,3,4,2,6,1]=>567
[5,3,4,6,1,2]=>300
[5,3,4,6,2,1]=>1155
[5,3,6,1,2,4]=>168
[5,3,6,1,4,2]=>768
[5,3,6,2,1,4]=>768
[5,3,6,2,4,1]=>2310
[5,3,6,4,1,2]=>1320
[5,3,6,4,2,1]=>5775
[5,4,1,2,3,6]=>14
[5,4,1,2,6,3]=>70
[5,4,1,3,2,6]=>70
[5,4,1,3,6,2]=>216
[5,4,1,6,2,3]=>168
[5,4,1,6,3,2]=>768
[5,4,2,1,3,6]=>70
[5,4,2,1,6,3]=>384
[5,4,2,3,1,6]=>216
[5,4,2,3,6,1]=>525
[5,4,2,6,1,3]=>768
[5,4,2,6,3,1]=>2310
[5,4,3,1,2,6]=>168
[5,4,3,1,6,2]=>768
[5,4,3,2,1,6]=>768
[5,4,3,2,6,1]=>2310
[5,4,3,6,1,2]=>1320
[5,4,3,6,2,1]=>5775
[5,4,6,1,2,3]=>210
[5,4,6,1,3,2]=>1188
[5,4,6,2,1,3]=>1188
[5,4,6,2,3,1]=>4158
[5,4,6,3,1,2]=>2970
[5,4,6,3,2,1]=>15015
[5,6,1,2,3,4]=>14
[5,6,1,2,4,3]=>84
[5,6,1,3,2,4]=>84
[5,6,1,3,4,2]=>300
[5,6,1,4,2,3]=>252
[5,6,1,4,3,2]=>1320
[5,6,2,1,3,4]=>84
[5,6,2,1,4,3]=>552
[5,6,2,3,1,4]=>300
[5,6,2,3,4,1]=>825
[5,6,2,4,1,3]=>1320
[5,6,2,4,3,1]=>4455
[5,6,3,1,2,4]=>252
[5,6,3,1,4,2]=>1320
[5,6,3,2,1,4]=>1320
[5,6,3,2,4,1]=>4455
[5,6,3,4,1,2]=>2640
[5,6,3,4,2,1]=>12870
[5,6,4,1,2,3]=>462
[5,6,4,1,3,2]=>2970
[5,6,4,2,1,3]=>2970
[5,6,4,2,3,1]=>11583
[5,6,4,3,1,2]=>8580
[5,6,4,3,2,1]=>48048
[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>5
[6,1,2,4,3,5]=>5
[6,1,2,4,5,3]=>15
[6,1,2,5,3,4]=>14
[6,1,2,5,4,3]=>64
[6,1,3,2,4,5]=>5
[6,1,3,2,5,4]=>29
[6,1,3,4,2,5]=>15
[6,1,3,4,5,2]=>35
[6,1,3,5,2,4]=>64
[6,1,3,5,4,2]=>189
[6,1,4,2,3,5]=>14
[6,1,4,2,5,3]=>64
[6,1,4,3,2,5]=>64
[6,1,4,3,5,2]=>189
[6,1,4,5,2,3]=>120
[6,1,4,5,3,2]=>525
[6,1,5,2,3,4]=>28
[6,1,5,2,4,3]=>162
[6,1,5,3,2,4]=>162
[6,1,5,3,4,2]=>567
[6,1,5,4,2,3]=>450
[6,1,5,4,3,2]=>2310
[6,2,1,3,4,5]=>5
[6,2,1,3,5,4]=>29
[6,2,1,4,3,5]=>29
[6,2,1,4,5,3]=>99
[6,2,1,5,3,4]=>92
[6,2,1,5,4,3]=>471
[6,2,3,1,4,5]=>15
[6,2,3,1,5,4]=>99
[6,2,3,4,1,5]=>35
[6,2,3,4,5,1]=>70
[6,2,3,5,1,4]=>189
[6,2,3,5,4,1]=>448
[6,2,4,1,3,5]=>64
[6,2,4,1,5,3]=>309
[6,2,4,3,1,5]=>189
[6,2,4,3,5,1]=>448
[6,2,4,5,1,3]=>525
[6,2,4,5,3,1]=>1540
[6,2,5,1,3,4]=>162
[6,2,5,1,4,3]=>1017
[6,2,5,3,1,4]=>567
[6,2,5,3,4,1]=>1540
[6,2,5,4,1,3]=>2310
[6,2,5,4,3,1]=>7700
[6,3,1,2,4,5]=>14
[6,3,1,2,5,4]=>92
[6,3,1,4,2,5]=>64
[6,3,1,4,5,2]=>189
[6,3,1,5,2,4]=>282
[6,3,1,5,4,2]=>1092
[6,3,2,1,4,5]=>64
[6,3,2,1,5,4]=>471
[6,3,2,4,1,5]=>189
[6,3,2,4,5,1]=>448
[6,3,2,5,1,4]=>1092
[6,3,2,5,4,1]=>3080
[6,3,4,1,2,5]=>120
[6,3,4,1,5,2]=>525
[6,3,4,2,1,5]=>525
[6,3,4,2,5,1]=>1540
[6,3,4,5,1,2]=>825
[6,3,4,5,2,1]=>3520
[6,3,5,1,2,4]=>450
[6,3,5,1,4,2]=>2310
[6,3,5,2,1,4]=>2310
[6,3,5,2,4,1]=>7700
[6,3,5,4,1,2]=>4455
[6,3,5,4,2,1]=>21450
[6,4,1,2,3,5]=>28
[6,4,1,2,5,3]=>162
[6,4,1,3,2,5]=>162
[6,4,1,3,5,2]=>567
[6,4,1,5,2,3]=>450
[6,4,1,5,3,2]=>2310
[6,4,2,1,3,5]=>162
[6,4,2,1,5,3]=>1017
[6,4,2,3,1,5]=>567
[6,4,2,3,5,1]=>1540
[6,4,2,5,1,3]=>2310
[6,4,2,5,3,1]=>7700
[6,4,3,1,2,5]=>450
[6,4,3,1,5,2]=>2310
[6,4,3,2,1,5]=>2310
[6,4,3,2,5,1]=>7700
[6,4,3,5,1,2]=>4455
[6,4,3,5,2,1]=>21450
[6,4,5,1,2,3]=>660
[6,4,5,1,3,2]=>4158
[6,4,5,2,1,3]=>4158
[6,4,5,2,3,1]=>16016
[6,4,5,3,1,2]=>11583
[6,4,5,3,2,1]=>64064
[6,5,1,2,3,4]=>42
[6,5,1,2,4,3]=>288
[6,5,1,3,2,4]=>288
[6,5,1,3,4,2]=>1155
[6,5,1,4,2,3]=>990
[6,5,1,4,3,2]=>5775
[6,5,2,1,3,4]=>288
[6,5,2,1,4,3]=>2145
[6,5,2,3,1,4]=>1155
[6,5,2,3,4,1]=>3520
[6,5,2,4,1,3]=>5775
[6,5,2,4,3,1]=>21450
[6,5,3,1,2,4]=>990
[6,5,3,1,4,2]=>5775
[6,5,3,2,1,4]=>5775
[6,5,3,2,4,1]=>21450
[6,5,3,4,1,2]=>12870
[6,5,3,4,2,1]=>68640
[6,5,4,1,2,3]=>2112
[6,5,4,1,3,2]=>15015
[6,5,4,2,1,3]=>15015
[6,5,4,2,3,1]=>64064
[6,5,4,3,1,2]=>48048
[6,5,4,3,2,1]=>292864
[1,2,3,4,5,6,7]=>1
[1,2,3,4,5,7,6]=>1
[1,2,3,4,6,5,7]=>1
[1,2,3,6,4,7,5]=>2
[1,2,6,3,4,7,5]=>3
[1,3,2,4,5,6,7]=>1
[1,3,7,2,4,5,6]=>4
[1,3,7,6,5,4,2]=>2310
[1,4,6,7,2,3,5]=>42
[1,4,6,7,5,3,2]=>990
[1,4,7,2,3,5,6]=>9
[1,4,7,6,5,3,2]=>5775
[1,5,2,3,4,7,6]=>4
[1,5,2,7,3,4,6]=>14
[1,5,4,7,6,3,2]=>2145
[1,5,6,2,7,3,4]=>42
[1,5,6,4,7,3,2]=>990
[1,5,6,7,2,3,4]=>42
[1,5,6,7,4,3,2]=>2112
[1,5,7,2,3,4,6]=>14
[1,5,7,6,4,3,2]=>15015
[1,6,2,3,4,7,5]=>4
[1,6,2,3,7,4,5]=>9
[1,6,2,7,3,4,5]=>14
[1,6,5,4,3,7,2]=>2310
[1,6,5,4,7,3,2]=>5775
[1,6,5,7,4,3,2]=>15015
[1,6,7,2,3,4,5]=>14
[1,6,7,5,4,3,2]=>48048
[1,7,2,3,4,5,6]=>1
[1,7,3,5,6,4,2]=>1540
[1,7,3,6,5,4,2]=>7700
[1,7,4,3,6,5,2]=>3080
[1,7,4,5,3,6,2]=>1540
[1,7,4,5,6,3,2]=>3520
[1,7,4,6,5,3,2]=>21450
[1,7,5,4,3,6,2]=>7700
[1,7,5,4,6,3,2]=>21450
[1,7,6,4,5,3,2]=>68640
[1,7,6,5,4,3,2]=>292864
[2,1,3,4,5,6,7]=>1
[2,1,3,4,7,5,6]=>3
[2,1,3,7,4,5,6]=>4
[2,1,6,3,4,5,7]=>4
[2,1,7,3,4,5,6]=>5
[2,1,7,6,5,4,3]=>8448
[2,3,1,4,5,6,7]=>1
[2,3,4,1,5,6,7]=>1
[2,3,4,1,5,7,6]=>4
[2,3,4,5,1,6,7]=>1
[2,3,4,5,1,7,6]=>5
[2,3,4,5,6,1,7]=>1
[2,3,4,5,6,7,1]=>1
[2,3,4,5,7,1,6]=>5
[2,3,4,6,1,7,5]=>14
[2,3,4,6,7,1,5]=>14
[2,3,4,7,1,5,6]=>10
[2,3,5,6,7,1,4]=>28
[2,4,1,3,5,6,7]=>2
[2,5,1,3,4,6,7]=>3
[2,5,7,1,3,4,6]=>70
[2,6,1,3,4,5,7]=>4
[2,6,1,7,3,4,5]=>84
[2,6,5,4,3,1,7]=>2310
[2,6,7,1,3,4,5]=>84
[2,7,1,3,4,5,6]=>5
[3,1,2,4,5,6,7]=>1
[3,1,2,4,5,7,6]=>3
[3,2,1,4,5,6,7]=>2
[3,2,4,5,6,7,1]=>6
[3,4,1,2,5,6,7]=>2
[3,4,2,5,6,7,1]=>20
[3,4,5,2,6,7,1]=>48
[3,4,5,6,2,7,1]=>90
[3,4,5,6,7,1,2]=>42
[3,5,6,1,2,4,7]=>42
[3,5,6,4,2,1,7]=>990
[3,6,1,2,4,5,7]=>9
[3,6,5,4,2,1,7]=>5775
[4,1,2,3,5,6,7]=>1
[4,1,2,3,5,7,6]=>4
[4,1,6,2,3,5,7]=>14
[4,2,3,5,6,7,1]=>21
[4,2,5,1,3,6,7]=>16
[4,3,2,1,5,6,7]=>16
[4,3,2,5,6,7,1]=>105
[4,3,5,2,6,7,1]=>315
[4,3,6,5,2,1,7]=>2145
[4,5,1,6,2,3,7]=>42
[4,5,2,3,6,7,1]=>225
[4,5,3,6,2,1,7]=>990
[4,5,6,1,2,3,7]=>42
[4,5,6,3,2,1,7]=>2112
[4,6,1,2,3,5,7]=>14
[4,6,1,2,3,7,5]=>84
[4,6,5,3,2,1,7]=>15015
[5,1,2,3,4,6,7]=>1
[5,1,2,3,4,7,6]=>5
[5,1,2,3,6,4,7]=>4
[5,1,2,3,6,7,4]=>10
[5,1,2,3,7,4,6]=>14
[5,1,2,6,3,4,7]=>9
[5,1,6,2,3,4,7]=>14
[5,1,6,2,3,7,4]=>70
[5,2,3,4,6,7,1]=>56
[5,2,6,7,1,3,4]=>1188
[5,3,2,4,6,7,1]=>350
[5,3,2,6,1,4,7]=>432
[5,3,6,7,1,2,4]=>2970
[5,4,3,2,1,6,7]=>768
[5,4,3,2,1,7,6]=>8448
[5,4,3,2,6,1,7]=>2310
[5,4,3,6,2,1,7]=>5775
[5,4,6,3,2,1,7]=>15015
[5,4,6,7,1,2,3]=>3432
[5,6,1,2,3,4,7]=>14
[5,6,1,2,3,7,4]=>84
[5,6,3,4,1,2,7]=>2640
[5,6,4,3,2,1,7]=>48048
[5,6,7,1,2,3,4]=>462
[6,1,2,3,4,5,7]=>1
[6,1,2,3,4,7,5]=>5
[6,1,2,3,7,4,5]=>14
[6,1,2,7,3,4,5]=>28
[6,2,3,4,5,7,1]=>126
[6,2,4,5,3,1,7]=>1540
[6,2,5,4,3,1,7]=>7700
[6,3,2,5,4,1,7]=>3080
[6,3,4,2,5,1,7]=>1540
[6,3,4,5,2,1,7]=>3520
[6,3,4,7,1,2,5]=>4455
[6,3,5,4,2,1,7]=>21450
[6,4,3,2,5,1,7]=>7700
[6,4,3,2,7,1,5]=>58916
[6,4,3,5,2,1,7]=>21450
[6,4,5,7,1,2,3]=>15015
[6,4,7,2,5,1,3]=>292864
[6,4,7,3,5,1,2]=>640640
[6,5,3,4,2,1,7]=>68640
[6,5,4,3,2,1,7]=>292864
[6,5,7,3,4,1,2]=>1361360
[6,7,1,2,3,4,5]=>42
[6,7,3,4,1,2,5]=>21450
[6,7,4,5,1,2,3]=>171600
[7,1,2,3,4,5,6]=>1
[7,2,1,3,4,5,6]=>6
[7,2,3,1,4,5,6]=>21
[7,2,3,4,1,5,6]=>56
[7,2,3,4,5,1,6]=>126
[7,3,1,2,4,5,6]=>20
[7,3,2,1,4,5,6]=>105
[7,3,2,4,1,5,6]=>350
[7,3,4,1,2,5,6]=>225
[7,4,1,2,3,5,6]=>48
[7,4,2,1,3,5,6]=>315
[7,4,5,6,1,2,3]=>50050
[7,5,1,2,3,4,6]=>90
[7,5,6,1,2,3,4]=>9009
[7,5,6,3,4,1,2]=>6534528
[7,6,1,2,3,4,5]=>132
[7,6,4,5,1,2,3]=>972400
[7,6,5,1,2,3,4]=>30030
[1,2,3,4,5,6,7,8]=>1
[1,7,8,6,5,4,3,2]=>141892608
[1,6,8,7,5,4,3,2]=>34918884
[1,7,6,8,5,4,3,2]=>34918884
[1,6,7,8,5,4,3,2]=>3734016
[1,5,8,7,6,4,3,2]=>10720710
[1,7,6,5,8,4,3,2]=>10720710
[1,3,5,7,8,6,4,2]=>2673
[1,4,3,8,7,6,5,2]=>61204
[1,6,5,4,3,8,7,2]=>61204
[1,4,3,6,5,8,7,2]=>314
[1,2,6,7,8,5,4,3]=>2112
[1,2,3,5,6,7,8,4]=>1
[1,2,3,4,5,6,8,7]=>1
[1,4,3,2,7,6,5,8]=>80
[1,3,4,2,6,7,5,8]=>6
[1,3,2,5,4,7,6,8]=>6
[1,2,3,5,4,7,6,8]=>2
[1,3,2,4,5,7,6,8]=>2
[1,2,3,4,5,7,6,8]=>1
[1,2,4,3,6,5,7,8]=>2
[1,3,2,5,4,6,7,8]=>2
[1,2,3,5,4,6,7,8]=>1
[1,3,2,4,5,6,7,8]=>1
[1,3,2,5,4,8,6,7]=>12
[1,3,5,8,2,4,6,7]=>35
[1,3,5,6,2,7,4,8]=>14
[1,3,2,6,4,7,5,8]=>8
[1,3,2,6,4,8,5,7]=>25
[1,3,2,6,4,5,7,8]=>3
[1,3,2,7,4,8,5,6]=>30
[1,3,2,7,4,5,6,8]=>4
[1,3,2,8,4,5,6,7]=>5
[1,3,2,4,5,8,6,7]=>3
[1,4,2,5,3,7,6,8]=>8
[1,4,2,5,3,8,6,7]=>20
[1,4,2,5,3,6,7,8]=>2
[1,4,5,6,7,2,3,8]=>14
[1,4,2,6,3,7,5,8]=>16
[1,4,2,6,7,8,3,5]=>84
[1,4,2,6,3,8,5,7]=>61
[1,4,2,6,3,5,7,8]=>5
[1,4,2,7,3,8,5,6]=>91
[1,4,2,7,3,5,6,8]=>9
[1,4,2,3,7,5,6,8]=>6
[1,4,2,3,5,7,6,8]=>3
[1,4,2,8,3,5,6,7]=>14
[1,4,2,3,5,8,6,7]=>6
[1,4,2,3,5,6,7,8]=>1
[1,5,2,6,3,7,4,8]=>16
[1,5,2,6,3,8,4,7]=>77
[1,5,2,6,3,4,7,8]=>5
[1,2,5,6,3,4,7,8]=>2
[1,5,2,7,3,8,4,6]=>168
[1,5,2,7,3,4,6,8]=>14
[1,5,2,3,4,7,6,8]=>4
[1,5,2,8,3,4,6,7]=>28
[1,5,8,2,3,4,6,7]=>28
[1,5,2,3,4,8,6,7]=>10
[1,2,3,5,4,8,6,7]=>3
[1,5,2,3,4,6,7,8]=>1
[1,6,2,7,3,8,4,5]=>168
[1,6,7,8,2,3,4,5]=>462
[1,6,2,7,3,4,5,8]=>14
[1,6,7,2,3,4,5,8]=>14
[1,6,2,3,4,7,5,8]=>4
[1,2,3,6,4,7,5,8]=>2
[1,6,2,8,3,4,5,7]=>42
[1,6,8,2,3,4,5,7]=>42
[1,6,2,3,4,8,5,7]=>14
[1,2,3,6,4,8,5,7]=>5
[1,6,2,3,4,5,7,8]=>1
[1,2,3,6,4,5,7,8]=>1
[1,7,2,8,3,4,5,6]=>42
[1,7,8,2,3,4,5,6]=>42
[1,7,2,3,8,4,5,6]=>28
[1,7,2,3,4,8,5,6]=>14
[1,2,3,7,4,8,5,6]=>5
[1,7,2,3,4,5,8,6]=>5
[1,2,7,3,4,5,8,6]=>4
[1,7,2,3,4,5,6,8]=>1
[1,2,3,7,4,5,6,8]=>1
[1,2,3,8,4,5,6,7]=>1
[1,2,3,4,5,8,6,7]=>1
[1,6,7,4,5,2,3,8]=>2640
[1,5,4,7,6,2,3,8]=>552
[1,5,3,7,2,6,4,8]=>244
[1,6,7,3,2,5,4,8]=>552
[1,7,3,4,2,5,8,6]=>99
[1,5,6,3,4,8,7,2]=>2090
[1,7,5,4,8,3,6,2]=>474903
[1,7,6,8,4,3,5,2]=>2362932
[1,6,7,8,3,4,5,2]=>50050
[1,5,7,3,8,4,6,2]=>23452
[1,4,3,7,8,5,6,2]=>2090
[1,5,8,3,7,6,4,2]=>474903
[1,6,8,7,3,5,4,2]=>2362932
[1,7,8,6,5,3,4,2]=>26604864
[1,4,3,8,7,5,6,2]=>11121
[1,4,6,7,3,2,8,5]=>912
[1,7,4,5,3,2,8,6]=>4675
[1,7,4,8,6,3,5,2]=>1153152
[1,7,3,5,6,8,2,4]=>3520
[1,3,6,7,5,8,2,4]=>990
[1,7,2,5,8,6,4,3]=>21450
[1,7,4,8,2,6,5,3]=>132704
[1,7,2,4,3,5,6,8]=>5
[1,6,2,4,3,5,7,8]=>4
[1,5,2,4,3,6,7,8]=>3
[1,6,2,5,3,4,7,8]=>9
[1,7,2,5,3,4,6,8]=>14
[1,7,2,6,3,4,5,8]=>28
[1,7,2,8,3,5,4,6]=>288
[1,6,2,8,3,5,4,7]=>246
[1,5,2,8,3,6,4,7]=>134
[1,4,2,8,3,6,5,7]=>78
[1,3,2,8,4,6,5,7]=>24
[1,2,3,8,4,6,5,7]=>4
[1,2,3,7,4,6,5,8]=>3
[1,3,2,7,4,6,5,8]=>15
[1,4,2,7,3,6,5,8]=>40
[1,5,2,7,3,6,4,8]=>56
[1,6,2,7,3,5,4,8]=>70
[1,7,2,6,3,5,4,8]=>162
[1,7,2,5,3,6,4,8]=>64
[1,6,2,5,3,7,4,8]=>35
[1,5,2,4,3,7,6,8]=>15
[1,6,2,4,3,7,5,8]=>19
[1,7,2,4,3,6,5,8]=>29
[1,7,2,3,4,6,5,8]=>5
[1,7,2,4,3,8,5,6]=>92
[1,6,2,4,3,8,5,7]=>78
[1,5,2,4,3,8,6,7]=>45
[1,6,2,5,3,8,4,7]=>190
[1,7,2,5,3,8,4,6]=>282
[1,7,2,6,3,8,4,5]=>450
[1,2,3,8,4,7,5,6]=>9
[1,3,2,8,4,7,5,6]=>63
[1,4,2,8,3,7,5,6]=>232
[1,5,2,8,3,7,4,6]=>534
[1,6,2,8,3,7,4,5]=>702
[1,7,2,8,3,6,4,5]=>990
[1,7,2,8,5,3,4,6]=>990
[1,2,8,7,6,3,4,5]=>2112
[1,6,7,2,8,4,3,5]=>2970
[1,7,2,8,4,5,3,6]=>1155
[1,2,7,5,8,3,4,6]=>168
[1,6,4,7,5,8,2,3]=>8580
[1,3,7,4,6,8,2,5]=>567
[1,7,6,5,4,8,2,3]=>640640
[1,2,7,6,8,3,4,5]=>210
[1,6,2,5,8,3,4,7]=>288
[1,5,4,2,8,3,6,7]=>232
[1,7,6,8,5,4,2,3]=>5105100
[1,4,8,6,7,5,2,3]=>126126
[1,3,8,7,5,6,2,4]=>68640
[1,5,8,4,3,2,6,7]=>2310
[1,7,4,3,8,5,2,6]=>11220
[1,5,7,3,8,4,2,6]=>8613
[1,6,8,5,3,7,4,2]=>1153152
[1,7,5,6,3,2,8,4]=>27599
[1,2,8,7,4,5,6,3]=>3520
[1,7,8,5,2,6,4,3]=>640640
[1,2,3,4,5,6,7,9,8]=>1
[1,2,3,4,5,6,7,8,9]=>1
[1,7,9,2,3,4,5,6,8]=>132
[1,2,3,4,5,6,7,8,10,9]=>1
[1,2,3,4,5,6,7,8,9,10]=>1
[1,2,3,4,5,6,7,8,9,11,10]=>1
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Description
The number of reduced words for a permutation.
This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$.
This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$.
References
[1] Edelman, P., Greene, C. Balanced tableaux MathSciNet:0871081
[2] Number of simple allowable sequences on 1..n containing the permutation 12...n. OEIS:A005118
[3] Total number of reduced decompositions for all permutations in S_n. OEIS:A246865
[2] Number of simple allowable sequences on 1..n containing the permutation 12...n. OEIS:A005118
[3] Total number of reduced decompositions for all permutations in S_n. OEIS:A246865
Code
def statistic(x):
return sum(1 for _ in x.reduced_words_iterator())
Created
Sep 13, 2011 at 22:02 by Chris Berg
Updated
May 23, 2019 at 16:07 by Martin Rubey
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