Identifier
- St000958: Permutations ⟶ ℤ
Values
=>
[1]=>1
[1,2]=>1
[2,1]=>1
[1,2,3]=>1
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>4
[1,2,3,4]=>1
[1,2,4,3]=>1
[1,3,2,4]=>1
[1,3,4,2]=>2
[1,4,2,3]=>2
[1,4,3,2]=>4
[2,1,3,4]=>1
[2,1,4,3]=>2
[2,3,1,4]=>2
[2,3,4,1]=>6
[2,4,1,3]=>6
[2,4,3,1]=>16
[3,1,2,4]=>2
[3,1,4,2]=>6
[3,2,1,4]=>4
[3,2,4,1]=>16
[3,4,1,2]=>20
[3,4,2,1]=>52
[4,1,2,3]=>6
[4,1,3,2]=>16
[4,2,1,3]=>16
[4,2,3,1]=>64
[4,3,1,2]=>52
[4,3,2,1]=>168
[1,2,3,4,5]=>1
[1,2,3,5,4]=>1
[1,2,4,3,5]=>1
[1,2,4,5,3]=>2
[1,2,5,3,4]=>2
[1,2,5,4,3]=>4
[1,3,2,4,5]=>1
[1,3,2,5,4]=>2
[1,3,4,2,5]=>2
[1,3,4,5,2]=>6
[1,3,5,2,4]=>6
[1,3,5,4,2]=>16
[1,4,2,3,5]=>2
[1,4,2,5,3]=>6
[1,4,3,2,5]=>4
[1,4,3,5,2]=>16
[1,4,5,2,3]=>20
[1,4,5,3,2]=>52
[1,5,2,3,4]=>6
[1,5,2,4,3]=>16
[1,5,3,2,4]=>16
[1,5,3,4,2]=>64
[1,5,4,2,3]=>52
[1,5,4,3,2]=>168
[2,1,3,4,5]=>1
[2,1,3,5,4]=>2
[2,1,4,3,5]=>2
[2,1,4,5,3]=>6
[2,1,5,3,4]=>6
[2,1,5,4,3]=>16
[2,3,1,4,5]=>2
[2,3,1,5,4]=>6
[2,3,4,1,5]=>6
[2,3,4,5,1]=>24
[2,3,5,1,4]=>24
[2,3,5,4,1]=>80
[2,4,1,3,5]=>6
[2,4,1,5,3]=>24
[2,4,3,1,5]=>16
[2,4,3,5,1]=>80
[2,4,5,1,3]=>100
[2,4,5,3,1]=>312
[2,5,1,3,4]=>24
[2,5,1,4,3]=>80
[2,5,3,1,4]=>80
[2,5,3,4,1]=>384
[2,5,4,1,3]=>312
[2,5,4,3,1]=>1176
[3,1,2,4,5]=>2
[3,1,2,5,4]=>6
[3,1,4,2,5]=>6
[3,1,4,5,2]=>24
[3,1,5,2,4]=>24
[3,1,5,4,2]=>80
[3,2,1,4,5]=>4
[3,2,1,5,4]=>16
[3,2,4,1,5]=>16
[3,2,4,5,1]=>80
[3,2,5,1,4]=>80
[3,2,5,4,1]=>320
[3,4,1,2,5]=>20
[3,4,1,5,2]=>100
[3,4,2,1,5]=>52
[3,4,2,5,1]=>312
[3,4,5,1,2]=>464
[3,4,5,2,1]=>1408
[3,5,1,2,4]=>100
[3,5,1,4,2]=>424
[3,5,2,1,4]=>312
[3,5,2,4,1]=>1752
[3,5,4,1,2]=>1680
[3,5,4,2,1]=>6016
[4,1,2,3,5]=>6
[4,1,2,5,3]=>24
[4,1,3,2,5]=>16
[4,1,3,5,2]=>80
[4,1,5,2,3]=>100
[4,1,5,3,2]=>312
[4,2,1,3,5]=>16
[4,2,1,5,3]=>80
[4,2,3,1,5]=>64
[4,2,3,5,1]=>384
[4,2,5,1,3]=>424
[4,2,5,3,1]=>1752
[4,3,1,2,5]=>52
[4,3,1,5,2]=>312
[4,3,2,1,5]=>168
[4,3,2,5,1]=>1176
[4,3,5,1,2]=>1680
[4,3,5,2,1]=>6016
[4,5,1,2,3]=>464
[4,5,1,3,2]=>1680
[4,5,2,1,3]=>1680
[4,5,2,3,1]=>9216
[4,5,3,1,2]=>6720
[4,5,3,2,1]=>27968
[5,1,2,3,4]=>24
[5,1,2,4,3]=>80
[5,1,3,2,4]=>80
[5,1,3,4,2]=>384
[5,1,4,2,3]=>312
[5,1,4,3,2]=>1176
[5,2,1,3,4]=>80
[5,2,1,4,3]=>320
[5,2,3,1,4]=>384
[5,2,3,4,1]=>2176
[5,2,4,1,3]=>1752
[5,2,4,3,1]=>8032
[5,3,1,2,4]=>312
[5,3,1,4,2]=>1752
[5,3,2,1,4]=>1176
[5,3,2,4,1]=>8032
[5,3,4,1,2]=>9216
[5,3,4,2,1]=>37312
[5,4,1,2,3]=>1408
[5,4,1,3,2]=>6016
[5,4,2,1,3]=>6016
[5,4,2,3,1]=>37312
[5,4,3,1,2]=>27968
[5,4,3,2,1]=>130560
[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]=>2
[1,2,3,6,4,5]=>2
[1,2,3,6,5,4]=>4
[1,2,4,3,5,6]=>1
[1,2,4,3,6,5]=>2
[1,2,4,5,3,6]=>2
[1,2,4,5,6,3]=>6
[1,2,4,6,3,5]=>6
[1,2,4,6,5,3]=>16
[1,2,5,3,4,6]=>2
[1,2,5,3,6,4]=>6
[1,2,5,4,3,6]=>4
[1,2,5,4,6,3]=>16
[1,2,5,6,3,4]=>20
[1,2,5,6,4,3]=>52
[1,2,6,3,4,5]=>6
[1,2,6,3,5,4]=>16
[1,2,6,4,3,5]=>16
[1,2,6,4,5,3]=>64
[1,2,6,5,3,4]=>52
[1,2,6,5,4,3]=>168
[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]=>6
[1,3,2,6,4,5]=>6
[1,3,2,6,5,4]=>16
[1,3,4,2,5,6]=>2
[1,3,4,2,6,5]=>6
[1,3,4,5,2,6]=>6
[1,3,4,5,6,2]=>24
[1,3,4,6,2,5]=>24
[1,3,4,6,5,2]=>80
[1,3,5,2,4,6]=>6
[1,3,5,2,6,4]=>24
[1,3,5,4,2,6]=>16
[1,3,5,4,6,2]=>80
[1,3,5,6,2,4]=>100
[1,3,5,6,4,2]=>312
[1,3,6,2,4,5]=>24
[1,3,6,2,5,4]=>80
[1,3,6,4,2,5]=>80
[1,3,6,4,5,2]=>384
[1,3,6,5,2,4]=>312
[1,3,6,5,4,2]=>1176
[1,4,2,3,5,6]=>2
[1,4,2,3,6,5]=>6
[1,4,2,5,3,6]=>6
[1,4,2,5,6,3]=>24
[1,4,2,6,3,5]=>24
[1,4,2,6,5,3]=>80
[1,4,3,2,5,6]=>4
[1,4,3,2,6,5]=>16
[1,4,3,5,2,6]=>16
[1,4,3,5,6,2]=>80
[1,4,3,6,2,5]=>80
[1,4,3,6,5,2]=>320
[1,4,5,2,3,6]=>20
[1,4,5,2,6,3]=>100
[1,4,5,3,2,6]=>52
[1,4,5,3,6,2]=>312
[1,4,5,6,2,3]=>464
[1,4,5,6,3,2]=>1408
[1,4,6,2,3,5]=>100
[1,4,6,2,5,3]=>424
[1,4,6,3,2,5]=>312
[1,4,6,3,5,2]=>1752
[1,4,6,5,2,3]=>1680
[1,4,6,5,3,2]=>6016
[1,5,2,3,4,6]=>6
[1,5,2,3,6,4]=>24
[1,5,2,4,3,6]=>16
[1,5,2,4,6,3]=>80
[1,5,2,6,3,4]=>100
[1,5,2,6,4,3]=>312
[1,5,3,2,4,6]=>16
[1,5,3,2,6,4]=>80
[1,5,3,4,2,6]=>64
[1,5,3,4,6,2]=>384
[1,5,3,6,2,4]=>424
[1,5,3,6,4,2]=>1752
[1,5,4,2,3,6]=>52
[1,5,4,2,6,3]=>312
[1,5,4,3,2,6]=>168
[1,5,4,3,6,2]=>1176
[1,5,4,6,2,3]=>1680
[1,5,4,6,3,2]=>6016
[1,5,6,2,3,4]=>464
[1,5,6,2,4,3]=>1680
[1,5,6,3,2,4]=>1680
[1,5,6,3,4,2]=>9216
[1,5,6,4,2,3]=>6720
[1,5,6,4,3,2]=>27968
[1,6,2,3,4,5]=>24
[1,6,2,3,5,4]=>80
[1,6,2,4,3,5]=>80
[1,6,2,4,5,3]=>384
[1,6,2,5,3,4]=>312
[1,6,2,5,4,3]=>1176
[1,6,3,2,4,5]=>80
[1,6,3,2,5,4]=>320
[1,6,3,4,2,5]=>384
[1,6,3,4,5,2]=>2176
[1,6,3,5,2,4]=>1752
[1,6,3,5,4,2]=>8032
[1,6,4,2,3,5]=>312
[1,6,4,2,5,3]=>1752
[1,6,4,3,2,5]=>1176
[1,6,4,3,5,2]=>8032
[1,6,4,5,2,3]=>9216
[1,6,4,5,3,2]=>37312
[1,6,5,2,3,4]=>1408
[1,6,5,2,4,3]=>6016
[1,6,5,3,2,4]=>6016
[1,6,5,3,4,2]=>37312
[1,6,5,4,2,3]=>27968
[1,6,5,4,3,2]=>130560
[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]=>6
[2,1,3,6,4,5]=>6
[2,1,3,6,5,4]=>16
[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>6
[2,1,4,5,3,6]=>6
[2,1,4,5,6,3]=>24
[2,1,4,6,3,5]=>24
[2,1,4,6,5,3]=>80
[2,1,5,3,4,6]=>6
[2,1,5,3,6,4]=>24
[2,1,5,4,3,6]=>16
[2,1,5,4,6,3]=>80
[2,1,5,6,3,4]=>100
[2,1,5,6,4,3]=>312
[2,1,6,3,4,5]=>24
[2,1,6,3,5,4]=>80
[2,1,6,4,3,5]=>80
[2,1,6,4,5,3]=>384
[2,1,6,5,3,4]=>312
[2,1,6,5,4,3]=>1176
[2,3,1,4,5,6]=>2
[2,3,1,4,6,5]=>6
[2,3,1,5,4,6]=>6
[2,3,1,5,6,4]=>24
[2,3,1,6,4,5]=>24
[2,3,1,6,5,4]=>80
[2,3,4,1,5,6]=>6
[2,3,4,1,6,5]=>24
[2,3,4,5,1,6]=>24
[2,3,4,5,6,1]=>120
[2,3,4,6,1,5]=>120
[2,3,4,6,5,1]=>480
[2,3,5,1,4,6]=>24
[2,3,5,1,6,4]=>120
[2,3,5,4,1,6]=>80
[2,3,5,4,6,1]=>480
[2,3,5,6,1,4]=>600
[2,3,5,6,4,1]=>2184
[2,3,6,1,4,5]=>120
[2,3,6,1,5,4]=>480
[2,3,6,4,1,5]=>480
[2,3,6,4,5,1]=>2688
[2,3,6,5,1,4]=>2184
[2,3,6,5,4,1]=>9408
[2,4,1,3,5,6]=>6
[2,4,1,3,6,5]=>24
[2,4,1,5,3,6]=>24
[2,4,1,5,6,3]=>120
[2,4,1,6,3,5]=>120
[2,4,1,6,5,3]=>480
[2,4,3,1,5,6]=>16
[2,4,3,1,6,5]=>80
[2,4,3,5,1,6]=>80
[2,4,3,5,6,1]=>480
[2,4,3,6,1,5]=>480
[2,4,3,6,5,1]=>2240
[2,4,5,1,3,6]=>100
[2,4,5,1,6,3]=>600
[2,4,5,3,1,6]=>312
[2,4,5,3,6,1]=>2184
[2,4,5,6,1,3]=>3248
[2,4,5,6,3,1]=>11264
[2,4,6,1,3,5]=>600
[2,4,6,1,5,3]=>2968
[2,4,6,3,1,5]=>2184
[2,4,6,3,5,1]=>14016
[2,4,6,5,1,3]=>13440
[2,4,6,5,3,1]=>54144
[2,5,1,3,4,6]=>24
[2,5,1,3,6,4]=>120
[2,5,1,4,3,6]=>80
[2,5,1,4,6,3]=>480
[2,5,1,6,3,4]=>600
[2,5,1,6,4,3]=>2184
[2,5,3,1,4,6]=>80
[2,5,3,1,6,4]=>480
[2,5,3,4,1,6]=>384
[2,5,3,4,6,1]=>2688
[2,5,3,6,1,4]=>2968
[2,5,3,6,4,1]=>14016
[2,5,4,1,3,6]=>312
[2,5,4,1,6,3]=>2184
[2,5,4,3,1,6]=>1176
[2,5,4,3,6,1]=>9408
[2,5,4,6,1,3]=>13440
[2,5,4,6,3,1]=>54144
[2,5,6,1,3,4]=>3248
[2,5,6,1,4,3]=>13440
[2,5,6,3,1,4]=>13440
[2,5,6,3,4,1]=>82944
[2,5,6,4,1,3]=>60480
[2,5,6,4,3,1]=>279680
[2,6,1,3,4,5]=>120
[2,6,1,3,5,4]=>480
[2,6,1,4,3,5]=>480
[2,6,1,4,5,3]=>2688
[2,6,1,5,3,4]=>2184
[2,6,1,5,4,3]=>9408
[2,6,3,1,4,5]=>480
[2,6,3,1,5,4]=>2240
[2,6,3,4,1,5]=>2688
[2,6,3,4,5,1]=>17408
[2,6,3,5,1,4]=>14016
[2,6,3,5,4,1]=>72288
[2,6,4,1,3,5]=>2184
[2,6,4,1,5,3]=>14016
[2,6,4,3,1,5]=>9408
[2,6,4,3,5,1]=>72288
[2,6,4,5,1,3]=>82944
[2,6,4,5,3,1]=>373120
[2,6,5,1,3,4]=>11264
[2,6,5,1,4,3]=>54144
[2,6,5,3,1,4]=>54144
[2,6,5,3,4,1]=>373120
[2,6,5,4,1,3]=>279680
[2,6,5,4,3,1]=>1436160
[3,1,2,4,5,6]=>2
[3,1,2,4,6,5]=>6
[3,1,2,5,4,6]=>6
[3,1,2,5,6,4]=>24
[3,1,2,6,4,5]=>24
[3,1,2,6,5,4]=>80
[3,1,4,2,5,6]=>6
[3,1,4,2,6,5]=>24
[3,1,4,5,2,6]=>24
[3,1,4,5,6,2]=>120
[3,1,4,6,2,5]=>120
[3,1,4,6,5,2]=>480
[3,1,5,2,4,6]=>24
[3,1,5,2,6,4]=>120
[3,1,5,4,2,6]=>80
[3,1,5,4,6,2]=>480
[3,1,5,6,2,4]=>600
[3,1,5,6,4,2]=>2184
[3,1,6,2,4,5]=>120
[3,1,6,2,5,4]=>480
[3,1,6,4,2,5]=>480
[3,1,6,4,5,2]=>2688
[3,1,6,5,2,4]=>2184
[3,1,6,5,4,2]=>9408
[3,2,1,4,5,6]=>4
[3,2,1,4,6,5]=>16
[3,2,1,5,4,6]=>16
[3,2,1,5,6,4]=>80
[3,2,1,6,4,5]=>80
[3,2,1,6,5,4]=>320
[3,2,4,1,5,6]=>16
[3,2,4,1,6,5]=>80
[3,2,4,5,1,6]=>80
[3,2,4,5,6,1]=>480
[3,2,4,6,1,5]=>480
[3,2,4,6,5,1]=>2240
[3,2,5,1,4,6]=>80
[3,2,5,1,6,4]=>480
[3,2,5,4,1,6]=>320
[3,2,5,4,6,1]=>2240
[3,2,5,6,1,4]=>2800
[3,2,5,6,4,1]=>11648
[3,2,6,1,4,5]=>480
[3,2,6,1,5,4]=>2240
[3,2,6,4,1,5]=>2240
[3,2,6,4,5,1]=>14336
[3,2,6,5,1,4]=>11648
[3,2,6,5,4,1]=>56448
[3,4,1,2,5,6]=>20
[3,4,1,2,6,5]=>100
[3,4,1,5,2,6]=>100
[3,4,1,5,6,2]=>600
[3,4,1,6,2,5]=>600
[3,4,1,6,5,2]=>2800
[3,4,2,1,5,6]=>52
[3,4,2,1,6,5]=>312
[3,4,2,5,1,6]=>312
[3,4,2,5,6,1]=>2184
[3,4,2,6,1,5]=>2184
[3,4,2,6,5,1]=>11648
[3,4,5,1,2,6]=>464
[3,4,5,1,6,2]=>3248
[3,4,5,2,1,6]=>1408
[3,4,5,2,6,1]=>11264
[3,4,5,6,1,2]=>19280
[3,4,5,6,2,1]=>65104
[3,4,6,1,2,5]=>3248
[3,4,6,1,5,2]=>18944
[3,4,6,2,1,5]=>11264
[3,4,6,2,5,1]=>81472
[3,4,6,5,1,2]=>90000
[3,4,6,5,2,1]=>347168
[3,5,1,2,4,6]=>100
[3,5,1,2,6,4]=>600
[3,5,1,4,2,6]=>424
[3,5,1,4,6,2]=>2968
[3,5,1,6,2,4]=>3568
[3,5,1,6,4,2]=>15456
[3,5,2,1,4,6]=>312
[3,5,2,1,6,4]=>2184
[3,5,2,4,1,6]=>1752
[3,5,2,4,6,1]=>14016
[3,5,2,6,1,4]=>15456
[3,5,2,6,4,1]=>82240
[3,5,4,1,2,6]=>1680
[3,5,4,1,6,2]=>13440
[3,5,4,2,1,6]=>6016
[3,5,4,2,6,1]=>54144
[3,5,4,6,1,2]=>89104
[3,5,4,6,2,1]=>344736
[3,5,6,1,2,4]=>20032
[3,5,6,1,4,2]=>99936
[3,5,6,2,1,4]=>77856
[3,5,6,2,4,1]=>535040
[3,5,6,4,1,2]=>445344
[3,5,6,4,2,1]=>1951968
[3,6,1,2,4,5]=>600
[3,6,1,2,5,4]=>2800
[3,6,1,4,2,5]=>2968
[3,6,1,4,5,2]=>19088
[3,6,1,5,2,4]=>15456
[3,6,1,5,4,2]=>76848
[3,6,2,1,4,5]=>2184
[3,6,2,1,5,4]=>11648
[3,6,2,4,1,5]=>14016
[3,6,2,4,5,1]=>102160
[3,6,2,5,1,4]=>82240
[3,6,2,5,4,1]=>472224
[3,6,4,1,2,5]=>13440
[3,6,4,1,5,2]=>98608
[3,6,4,2,1,5]=>54144
[3,6,4,2,5,1]=>462816
[3,6,4,5,1,2]=>611200
[3,6,4,5,2,1]=>2611264
[3,6,5,1,2,4]=>77856
[3,6,5,1,4,2]=>444704
[3,6,5,2,1,4]=>346240
[3,6,5,2,4,1]=>2634144
[3,6,5,4,1,2]=>2257728
[3,6,5,4,2,1]=>10891264
[4,1,2,3,5,6]=>6
[4,1,2,3,6,5]=>24
[4,1,2,5,3,6]=>24
[4,1,2,5,6,3]=>120
[4,1,2,6,3,5]=>120
[4,1,2,6,5,3]=>480
[4,1,3,2,5,6]=>16
[4,1,3,2,6,5]=>80
[4,1,3,5,2,6]=>80
[4,1,3,5,6,2]=>480
[4,1,3,6,2,5]=>480
[4,1,3,6,5,2]=>2240
[4,1,5,2,3,6]=>100
[4,1,5,2,6,3]=>600
[4,1,5,3,2,6]=>312
[4,1,5,3,6,2]=>2184
[4,1,5,6,2,3]=>3248
[4,1,5,6,3,2]=>11264
[4,1,6,2,3,5]=>600
[4,1,6,2,5,3]=>2968
[4,1,6,3,2,5]=>2184
[4,1,6,3,5,2]=>14016
[4,1,6,5,2,3]=>13440
[4,1,6,5,3,2]=>54144
[4,2,1,3,5,6]=>16
[4,2,1,3,6,5]=>80
[4,2,1,5,3,6]=>80
[4,2,1,5,6,3]=>480
[4,2,1,6,3,5]=>480
[4,2,1,6,5,3]=>2240
[4,2,3,1,5,6]=>64
[4,2,3,1,6,5]=>384
[4,2,3,5,1,6]=>384
[4,2,3,5,6,1]=>2688
[4,2,3,6,1,5]=>2688
[4,2,3,6,5,1]=>14336
[4,2,5,1,3,6]=>424
[4,2,5,1,6,3]=>2968
[4,2,5,3,1,6]=>1752
[4,2,5,3,6,1]=>14016
[4,2,5,6,1,3]=>18944
[4,2,5,6,3,1]=>81472
[4,2,6,1,3,5]=>2968
[4,2,6,1,5,3]=>16352
[4,2,6,3,1,5]=>14016
[4,2,6,3,5,1]=>101088
[4,2,6,5,1,3]=>87840
[4,2,6,5,3,1]=>435136
[4,3,1,2,5,6]=>52
[4,3,1,2,6,5]=>312
[4,3,1,5,2,6]=>312
[4,3,1,5,6,2]=>2184
[4,3,1,6,2,5]=>2184
[4,3,1,6,5,2]=>11648
[4,3,2,1,5,6]=>168
[4,3,2,1,6,5]=>1176
[4,3,2,5,1,6]=>1176
[4,3,2,5,6,1]=>9408
[4,3,2,6,1,5]=>9408
[4,3,2,6,5,1]=>56448
[4,3,5,1,2,6]=>1680
[4,3,5,1,6,2]=>13440
[4,3,5,2,1,6]=>6016
[4,3,5,2,6,1]=>54144
[4,3,5,6,1,2]=>90000
[4,3,5,6,2,1]=>347168
[4,3,6,1,2,5]=>13440
[4,3,6,1,5,2]=>87840
[4,3,6,2,1,5]=>54144
[4,3,6,2,5,1]=>435136
[4,3,6,5,1,2]=>463968
[4,3,6,5,2,1]=>2028576
[4,5,1,2,3,6]=>464
[4,5,1,2,6,3]=>3248
[4,5,1,3,2,6]=>1680
[4,5,1,3,6,2]=>13440
[4,5,1,6,2,3]=>20032
[4,5,1,6,3,2]=>77856
[4,5,2,1,3,6]=>1680
[4,5,2,1,6,3]=>13440
[4,5,2,3,1,6]=>9216
[4,5,2,3,6,1]=>82944
[4,5,2,6,1,3]=>99936
[4,5,2,6,3,1]=>535040
[4,5,3,1,2,6]=>6720
[4,5,3,1,6,2]=>60480
[4,5,3,2,1,6]=>27968
[4,5,3,2,6,1]=>279680
[4,5,3,6,1,2]=>445344
[4,5,3,6,2,1]=>1951968
[4,5,6,1,2,3]=>123616
[4,5,6,1,3,2]=>531840
[4,5,6,2,1,3]=>531840
[4,5,6,2,3,1]=>3563392
[4,5,6,3,1,2]=>2418336
[4,5,6,3,2,1]=>11914240
[4,6,1,2,3,5]=>3248
[4,6,1,2,5,3]=>18944
[4,6,1,3,2,5]=>13440
[4,6,1,3,5,2]=>98608
[4,6,1,5,2,3]=>99936
[4,6,1,5,3,2]=>444704
[4,6,2,1,3,5]=>13440
[4,6,2,1,5,3]=>87840
[4,6,2,3,1,5]=>82944
[4,6,2,3,5,1]=>684320
[4,6,2,5,1,3]=>623680
[4,6,2,5,3,1]=>3568224
[4,6,3,1,2,5]=>60480
[4,6,3,1,5,2]=>493856
[4,6,3,2,1,5]=>279680
[4,6,3,2,5,1]=>2635488
[4,6,3,5,1,2]=>3362432
[4,6,3,5,2,1]=>16157952
[4,6,5,1,2,3]=>531840
[4,6,5,1,3,2]=>2577504
[4,6,5,2,1,3]=>2592960
[4,6,5,2,3,1]=>19007872
[4,6,5,3,1,2]=>13208960
[4,6,5,3,2,1]=>71180288
[5,1,2,3,4,6]=>24
[5,1,2,3,6,4]=>120
[5,1,2,4,3,6]=>80
[5,1,2,4,6,3]=>480
[5,1,2,6,3,4]=>600
[5,1,2,6,4,3]=>2184
[5,1,3,2,4,6]=>80
[5,1,3,2,6,4]=>480
[5,1,3,4,2,6]=>384
[5,1,3,4,6,2]=>2688
[5,1,3,6,2,4]=>2968
[5,1,3,6,4,2]=>14016
[5,1,4,2,3,6]=>312
[5,1,4,2,6,3]=>2184
[5,1,4,3,2,6]=>1176
[5,1,4,3,6,2]=>9408
[5,1,4,6,2,3]=>13440
[5,1,4,6,3,2]=>54144
[5,1,6,2,3,4]=>3248
[5,1,6,2,4,3]=>13440
[5,1,6,3,2,4]=>13440
[5,1,6,3,4,2]=>82944
[5,1,6,4,2,3]=>60480
[5,1,6,4,3,2]=>279680
[5,2,1,3,4,6]=>80
[5,2,1,3,6,4]=>480
[5,2,1,4,3,6]=>320
[5,2,1,4,6,3]=>2240
[5,2,1,6,3,4]=>2800
[5,2,1,6,4,3]=>11648
[5,2,3,1,4,6]=>384
[5,2,3,1,6,4]=>2688
[5,2,3,4,1,6]=>2176
[5,2,3,4,6,1]=>17408
[5,2,3,6,1,4]=>19088
[5,2,3,6,4,1]=>102160
[5,2,4,1,3,6]=>1752
[5,2,4,1,6,3]=>14016
[5,2,4,3,1,6]=>8032
[5,2,4,3,6,1]=>72288
[5,2,4,6,1,3]=>98608
[5,2,4,6,3,1]=>462816
[5,2,6,1,3,4]=>18944
[5,2,6,1,4,3]=>87840
[5,2,6,3,1,4]=>98608
[5,2,6,3,4,1]=>684320
[5,2,6,4,1,3]=>493856
[5,2,6,4,3,1]=>2635488
[5,3,1,2,4,6]=>312
[5,3,1,2,6,4]=>2184
[5,3,1,4,2,6]=>1752
[5,3,1,4,6,2]=>14016
[5,3,1,6,2,4]=>15456
[5,3,1,6,4,2]=>82240
[5,3,2,1,4,6]=>1176
[5,3,2,1,6,4]=>9408
[5,3,2,4,1,6]=>8032
[5,3,2,4,6,1]=>72288
[5,3,2,6,1,4]=>76848
[5,3,2,6,4,1]=>472224
[5,3,4,1,2,6]=>9216
[5,3,4,1,6,2]=>82944
[5,3,4,2,1,6]=>37312
[5,3,4,2,6,1]=>373120
[5,3,4,6,1,2]=>611200
[5,3,4,6,2,1]=>2611264
[5,3,6,1,2,4]=>99936
[5,3,6,1,4,2]=>623680
[5,3,6,2,1,4]=>444704
[5,3,6,2,4,1]=>3568224
[5,3,6,4,1,2]=>3362432
[5,3,6,4,2,1]=>16157952
[5,4,1,2,3,6]=>1408
[5,4,1,2,6,3]=>11264
[5,4,1,3,2,6]=>6016
[5,4,1,3,6,2]=>54144
[5,4,1,6,2,3]=>77856
[5,4,1,6,3,2]=>346240
[5,4,2,1,3,6]=>6016
[5,4,2,1,6,3]=>54144
[5,4,2,3,1,6]=>37312
[5,4,2,3,6,1]=>373120
[5,4,2,6,1,3]=>444704
[5,4,2,6,3,1]=>2634144
[5,4,3,1,2,6]=>27968
[5,4,3,1,6,2]=>279680
[5,4,3,2,1,6]=>130560
[5,4,3,2,6,1]=>1436160
[5,4,3,6,1,2]=>2257728
[5,4,3,6,2,1]=>10891264
[5,4,6,1,2,3]=>531840
[5,4,6,1,3,2]=>2592960
[5,4,6,2,1,3]=>2577504
[5,4,6,2,3,1]=>19007872
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Description
The number of Bruhat factorizations of a permutation.
This is the number of factorizations $\pi = t_1 \cdots t_\ell$ for transpositions $\{ t_i \mid 1 \leq i \leq \ell\}$ such that the number of inversions of $t_1 \cdots t_i$ equals $i$ for all $1 \leq i \leq \ell$.
This is the number of factorizations $\pi = t_1 \cdots t_\ell$ for transpositions $\{ t_i \mid 1 \leq i \leq \ell\}$ such that the number of inversions of $t_1 \cdots t_i$ equals $i$ for all $1 \leq i \leq \ell$.
Code
@cached_function
def bruhat_poset(n):
return Permutations(n).bruhat_poset(facade=True)
def statistic(pi):
P = bruhat_poset(len(pi))
I = P.subposet(P.principal_order_ideal(pi))
return len(I.maximal_chains())
Created
Aug 28, 2017 at 11:08 by Christian Stump
Updated
Mar 12, 2026 at 17:42 by Nupur Jain
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