Identifier
- St000255: Permutations ⟶ ℤ
Values
=>
[1]=>1
[1,2]=>1
[2,1]=>1
[1,2,3]=>1
[1,3,2]=>2
[2,1,3]=>1
[2,3,1]=>1
[3,1,2]=>1
[3,2,1]=>1
[1,2,3,4]=>1
[1,2,4,3]=>3
[1,3,2,4]=>2
[1,3,4,2]=>3
[1,4,2,3]=>3
[1,4,3,2]=>5
[2,1,3,4]=>1
[2,1,4,3]=>3
[2,3,1,4]=>1
[2,3,4,1]=>1
[2,4,1,3]=>2
[2,4,3,1]=>2
[3,1,2,4]=>1
[3,1,4,2]=>2
[3,2,1,4]=>1
[3,2,4,1]=>1
[3,4,1,2]=>1
[3,4,2,1]=>1
[4,1,2,3]=>1
[4,1,3,2]=>2
[4,2,1,3]=>1
[4,2,3,1]=>1
[4,3,1,2]=>1
[4,3,2,1]=>1
[1,2,3,4,5]=>1
[1,2,3,5,4]=>4
[1,2,4,3,5]=>3
[1,2,4,5,3]=>6
[1,2,5,3,4]=>6
[1,2,5,4,3]=>14
[1,3,2,4,5]=>2
[1,3,2,5,4]=>8
[1,3,4,2,5]=>3
[1,3,4,5,2]=>4
[1,3,5,2,4]=>8
[1,3,5,4,2]=>11
[1,4,2,3,5]=>3
[1,4,2,5,3]=>8
[1,4,3,2,5]=>5
[1,4,3,5,2]=>7
[1,4,5,2,3]=>6
[1,4,5,3,2]=>9
[1,5,2,3,4]=>4
[1,5,2,4,3]=>11
[1,5,3,2,4]=>7
[1,5,3,4,2]=>10
[1,5,4,2,3]=>9
[1,5,4,3,2]=>14
[2,1,3,4,5]=>1
[2,1,3,5,4]=>4
[2,1,4,3,5]=>3
[2,1,4,5,3]=>6
[2,1,5,3,4]=>6
[2,1,5,4,3]=>14
[2,3,1,4,5]=>1
[2,3,1,5,4]=>4
[2,3,4,1,5]=>1
[2,3,4,5,1]=>1
[2,3,5,1,4]=>3
[2,3,5,4,1]=>3
[2,4,1,3,5]=>2
[2,4,1,5,3]=>5
[2,4,3,1,5]=>2
[2,4,3,5,1]=>2
[2,4,5,1,3]=>3
[2,4,5,3,1]=>3
[2,5,1,3,4]=>3
[2,5,1,4,3]=>8
[2,5,3,1,4]=>3
[2,5,3,4,1]=>3
[2,5,4,1,3]=>5
[2,5,4,3,1]=>5
[3,1,2,4,5]=>1
[3,1,2,5,4]=>4
[3,1,4,2,5]=>2
[3,1,4,5,2]=>3
[3,1,5,2,4]=>5
[3,1,5,4,2]=>8
[3,2,1,4,5]=>1
[3,2,1,5,4]=>4
[3,2,4,1,5]=>1
[3,2,4,5,1]=>1
[3,2,5,1,4]=>3
[3,2,5,4,1]=>3
[3,4,1,2,5]=>1
[3,4,1,5,2]=>2
[3,4,2,1,5]=>1
[3,4,2,5,1]=>1
[3,4,5,1,2]=>1
[3,4,5,2,1]=>1
[3,5,1,2,4]=>2
[3,5,1,4,2]=>4
[3,5,2,1,4]=>2
[3,5,2,4,1]=>2
[3,5,4,1,2]=>2
[3,5,4,2,1]=>2
[4,1,2,3,5]=>1
[4,1,2,5,3]=>3
[4,1,3,2,5]=>2
[4,1,3,5,2]=>3
[4,1,5,2,3]=>3
[4,1,5,3,2]=>5
[4,2,1,3,5]=>1
[4,2,1,5,3]=>3
[4,2,3,1,5]=>1
[4,2,3,5,1]=>1
[4,2,5,1,3]=>2
[4,2,5,3,1]=>2
[4,3,1,2,5]=>1
[4,3,1,5,2]=>2
[4,3,2,1,5]=>1
[4,3,2,5,1]=>1
[4,3,5,1,2]=>1
[4,3,5,2,1]=>1
[4,5,1,2,3]=>1
[4,5,1,3,2]=>2
[4,5,2,1,3]=>1
[4,5,2,3,1]=>1
[4,5,3,1,2]=>1
[4,5,3,2,1]=>1
[5,1,2,3,4]=>1
[5,1,2,4,3]=>3
[5,1,3,2,4]=>2
[5,1,3,4,2]=>3
[5,1,4,2,3]=>3
[5,1,4,3,2]=>5
[5,2,1,3,4]=>1
[5,2,1,4,3]=>3
[5,2,3,1,4]=>1
[5,2,3,4,1]=>1
[5,2,4,1,3]=>2
[5,2,4,3,1]=>2
[5,3,1,2,4]=>1
[5,3,1,4,2]=>2
[5,3,2,1,4]=>1
[5,3,2,4,1]=>1
[5,3,4,1,2]=>1
[5,3,4,2,1]=>1
[5,4,1,2,3]=>1
[5,4,1,3,2]=>2
[5,4,2,1,3]=>1
[5,4,2,3,1]=>1
[5,4,3,1,2]=>1
[5,4,3,2,1]=>1
[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>5
[1,2,3,5,4,6]=>4
[1,2,3,5,6,4]=>10
[1,2,3,6,4,5]=>10
[1,2,3,6,5,4]=>30
[1,2,4,3,5,6]=>3
[1,2,4,3,6,5]=>15
[1,2,4,5,3,6]=>6
[1,2,4,5,6,3]=>10
[1,2,4,6,3,5]=>20
[1,2,4,6,5,3]=>35
[1,2,5,3,4,6]=>6
[1,2,5,3,6,4]=>20
[1,2,5,4,3,6]=>14
[1,2,5,4,6,3]=>25
[1,2,5,6,3,4]=>20
[1,2,5,6,4,3]=>40
[1,2,6,3,4,5]=>10
[1,2,6,3,5,4]=>35
[1,2,6,4,3,5]=>25
[1,2,6,4,5,3]=>46
[1,2,6,5,3,4]=>40
[1,2,6,5,4,3]=>84
[1,3,2,4,5,6]=>2
[1,3,2,4,6,5]=>10
[1,3,2,5,4,6]=>8
[1,3,2,5,6,4]=>20
[1,3,2,6,4,5]=>20
[1,3,2,6,5,4]=>60
[1,3,4,2,5,6]=>3
[1,3,4,2,6,5]=>15
[1,3,4,5,2,6]=>4
[1,3,4,5,6,2]=>5
[1,3,4,6,2,5]=>15
[1,3,4,6,5,2]=>19
[1,3,5,2,4,6]=>8
[1,3,5,2,6,4]=>25
[1,3,5,4,2,6]=>11
[1,3,5,4,6,2]=>14
[1,3,5,6,2,4]=>20
[1,3,5,6,4,2]=>26
[1,3,6,2,4,5]=>15
[1,3,6,2,5,4]=>51
[1,3,6,4,2,5]=>21
[1,3,6,4,5,2]=>27
[1,3,6,5,2,4]=>44
[1,3,6,5,4,2]=>58
[1,4,2,3,5,6]=>3
[1,4,2,3,6,5]=>15
[1,4,2,5,3,6]=>8
[1,4,2,5,6,3]=>15
[1,4,2,6,3,5]=>25
[1,4,2,6,5,3]=>51
[1,4,3,2,5,6]=>5
[1,4,3,2,6,5]=>25
[1,4,3,5,2,6]=>7
[1,4,3,5,6,2]=>9
[1,4,3,6,2,5]=>26
[1,4,3,6,5,2]=>34
[1,4,5,2,3,6]=>6
[1,4,5,2,6,3]=>15
[1,4,5,3,2,6]=>9
[1,4,5,3,6,2]=>12
[1,4,5,6,2,3]=>10
[1,4,5,6,3,2]=>14
[1,4,6,2,3,5]=>15
[1,4,6,2,5,3]=>38
[1,4,6,3,2,5]=>23
[1,4,6,3,5,2]=>31
[1,4,6,5,2,3]=>26
[1,4,6,5,3,2]=>37
[1,5,2,3,4,6]=>4
[1,5,2,3,6,4]=>15
[1,5,2,4,3,6]=>11
[1,5,2,4,6,3]=>21
[1,5,2,6,3,4]=>20
[1,5,2,6,4,3]=>44
[1,5,3,2,4,6]=>7
[1,5,3,2,6,4]=>26
[1,5,3,4,2,6]=>10
[1,5,3,4,6,2]=>13
[1,5,3,6,2,4]=>24
[1,5,3,6,4,2]=>32
[1,5,4,2,3,6]=>9
[1,5,4,2,6,3]=>23
[1,5,4,3,2,6]=>14
[1,5,4,3,6,2]=>19
[1,5,4,6,2,3]=>16
[1,5,4,6,3,2]=>23
[1,5,6,2,3,4]=>10
[1,5,6,2,4,3]=>26
[1,5,6,3,2,4]=>16
[1,5,6,3,4,2]=>22
[1,5,6,4,2,3]=>19
[1,5,6,4,3,2]=>28
[1,6,2,3,4,5]=>5
[1,6,2,3,5,4]=>19
[1,6,2,4,3,5]=>14
[1,6,2,4,5,3]=>27
[1,6,2,5,3,4]=>26
[1,6,2,5,4,3]=>58
[1,6,3,2,4,5]=>9
[1,6,3,2,5,4]=>34
[1,6,3,4,2,5]=>13
[1,6,3,4,5,2]=>17
[1,6,3,5,2,4]=>32
[1,6,3,5,4,2]=>43
[1,6,4,2,3,5]=>12
[1,6,4,2,5,3]=>31
[1,6,4,3,2,5]=>19
[1,6,4,3,5,2]=>26
[1,6,4,5,2,3]=>22
[1,6,4,5,3,2]=>32
[1,6,5,2,3,4]=>14
[1,6,5,2,4,3]=>37
[1,6,5,3,2,4]=>23
[1,6,5,3,4,2]=>32
[1,6,5,4,2,3]=>28
[1,6,5,4,3,2]=>42
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>5
[2,1,3,5,4,6]=>4
[2,1,3,5,6,4]=>10
[2,1,3,6,4,5]=>10
[2,1,3,6,5,4]=>30
[2,1,4,3,5,6]=>3
[2,1,4,3,6,5]=>15
[2,1,4,5,3,6]=>6
[2,1,4,5,6,3]=>10
[2,1,4,6,3,5]=>20
[2,1,4,6,5,3]=>35
[2,1,5,3,4,6]=>6
[2,1,5,3,6,4]=>20
[2,1,5,4,3,6]=>14
[2,1,5,4,6,3]=>25
[2,1,5,6,3,4]=>20
[2,1,5,6,4,3]=>40
[2,1,6,3,4,5]=>10
[2,1,6,3,5,4]=>35
[2,1,6,4,3,5]=>25
[2,1,6,4,5,3]=>46
[2,1,6,5,3,4]=>40
[2,1,6,5,4,3]=>84
[2,3,1,4,5,6]=>1
[2,3,1,4,6,5]=>5
[2,3,1,5,4,6]=>4
[2,3,1,5,6,4]=>10
[2,3,1,6,4,5]=>10
[2,3,1,6,5,4]=>30
[2,3,4,1,5,6]=>1
[2,3,4,1,6,5]=>5
[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]=>4
[2,3,5,1,4,6]=>3
[2,3,5,1,6,4]=>9
[2,3,5,4,1,6]=>3
[2,3,5,4,6,1]=>3
[2,3,5,6,1,4]=>6
[2,3,5,6,4,1]=>6
[2,3,6,1,4,5]=>6
[2,3,6,1,5,4]=>20
[2,3,6,4,1,5]=>6
[2,3,6,4,5,1]=>6
[2,3,6,5,1,4]=>14
[2,3,6,5,4,1]=>14
[2,4,1,3,5,6]=>2
[2,4,1,3,6,5]=>10
[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]=>31
[2,4,3,1,5,6]=>2
[2,4,3,1,6,5]=>10
[2,4,3,5,1,6]=>2
[2,4,3,5,6,1]=>2
[2,4,3,6,1,5]=>8
[2,4,3,6,5,1]=>8
[2,4,5,1,3,6]=>3
[2,4,5,1,6,3]=>7
[2,4,5,3,1,6]=>3
[2,4,5,3,6,1]=>3
[2,4,5,6,1,3]=>4
[2,4,5,6,3,1]=>4
[2,4,6,1,3,5]=>8
[2,4,6,1,5,3]=>19
[2,4,6,3,1,5]=>8
[2,4,6,3,5,1]=>8
[2,4,6,5,1,3]=>11
[2,4,6,5,3,1]=>11
[2,5,1,3,4,6]=>3
[2,5,1,3,6,4]=>11
[2,5,1,4,3,6]=>8
[2,5,1,4,6,3]=>15
[2,5,1,6,3,4]=>14
[2,5,1,6,4,3]=>30
[2,5,3,1,4,6]=>3
[2,5,3,1,6,4]=>11
[2,5,3,4,1,6]=>3
[2,5,3,4,6,1]=>3
[2,5,3,6,1,4]=>8
[2,5,3,6,4,1]=>8
[2,5,4,1,3,6]=>5
[2,5,4,1,6,3]=>12
[2,5,4,3,1,6]=>5
[2,5,4,3,6,1]=>5
[2,5,4,6,1,3]=>7
[2,5,4,6,3,1]=>7
[2,5,6,1,3,4]=>6
[2,5,6,1,4,3]=>15
[2,5,6,3,1,4]=>6
[2,5,6,3,4,1]=>6
[2,5,6,4,1,3]=>9
[2,5,6,4,3,1]=>9
[2,6,1,3,4,5]=>4
[2,6,1,3,5,4]=>15
[2,6,1,4,3,5]=>11
[2,6,1,4,5,3]=>21
[2,6,1,5,3,4]=>20
[2,6,1,5,4,3]=>44
[2,6,3,1,4,5]=>4
[2,6,3,1,5,4]=>15
[2,6,3,4,1,5]=>4
[2,6,3,4,5,1]=>4
[2,6,3,5,1,4]=>11
[2,6,3,5,4,1]=>11
[2,6,4,1,3,5]=>7
[2,6,4,1,5,3]=>17
[2,6,4,3,1,5]=>7
[2,6,4,3,5,1]=>7
[2,6,4,5,1,3]=>10
[2,6,4,5,3,1]=>10
[2,6,5,1,3,4]=>9
[2,6,5,1,4,3]=>23
[2,6,5,3,1,4]=>9
[2,6,5,3,4,1]=>9
[2,6,5,4,1,3]=>14
[2,6,5,4,3,1]=>14
[3,1,2,4,5,6]=>1
[3,1,2,4,6,5]=>5
[3,1,2,5,4,6]=>4
[3,1,2,5,6,4]=>10
[3,1,2,6,4,5]=>10
[3,1,2,6,5,4]=>30
[3,1,4,2,5,6]=>2
[3,1,4,2,6,5]=>10
[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]=>15
[3,1,5,2,4,6]=>5
[3,1,5,2,6,4]=>16
[3,1,5,4,2,6]=>8
[3,1,5,4,6,2]=>11
[3,1,5,6,2,4]=>14
[3,1,5,6,4,2]=>20
[3,1,6,2,4,5]=>9
[3,1,6,2,5,4]=>31
[3,1,6,4,2,5]=>15
[3,1,6,4,5,2]=>21
[3,1,6,5,2,4]=>30
[3,1,6,5,4,2]=>44
[3,2,1,4,5,6]=>1
[3,2,1,4,6,5]=>5
[3,2,1,5,4,6]=>4
[3,2,1,5,6,4]=>10
[3,2,1,6,4,5]=>10
[3,2,1,6,5,4]=>30
[3,2,4,1,5,6]=>1
[3,2,4,1,6,5]=>5
[3,2,4,5,1,6]=>1
[3,2,4,5,6,1]=>1
[3,2,4,6,1,5]=>4
[3,2,4,6,5,1]=>4
[3,2,5,1,4,6]=>3
[3,2,5,1,6,4]=>9
[3,2,5,4,1,6]=>3
[3,2,5,4,6,1]=>3
[3,2,5,6,1,4]=>6
[3,2,5,6,4,1]=>6
[3,2,6,1,4,5]=>6
[3,2,6,1,5,4]=>20
[3,2,6,4,1,5]=>6
[3,2,6,4,5,1]=>6
[3,2,6,5,1,4]=>14
[3,2,6,5,4,1]=>14
[3,4,1,2,5,6]=>1
[3,4,1,2,6,5]=>5
[3,4,1,5,2,6]=>2
[3,4,1,5,6,2]=>3
[3,4,1,6,2,5]=>7
[3,4,1,6,5,2]=>11
[3,4,2,1,5,6]=>1
[3,4,2,1,6,5]=>5
[3,4,2,5,1,6]=>1
[3,4,2,5,6,1]=>1
[3,4,2,6,1,5]=>4
[3,4,2,6,5,1]=>4
[3,4,5,1,2,6]=>1
[3,4,5,1,6,2]=>2
[3,4,5,2,1,6]=>1
[3,4,5,2,6,1]=>1
[3,4,5,6,1,2]=>1
[3,4,5,6,2,1]=>1
[3,4,6,1,2,5]=>3
[3,4,6,1,5,2]=>6
[3,4,6,2,1,5]=>3
[3,4,6,2,5,1]=>3
[3,4,6,5,1,2]=>3
[3,4,6,5,2,1]=>3
[3,5,1,2,4,6]=>2
[3,5,1,2,6,4]=>7
[3,5,1,4,2,6]=>4
[3,5,1,4,6,2]=>6
[3,5,1,6,2,4]=>8
[3,5,1,6,4,2]=>13
[3,5,2,1,4,6]=>2
[3,5,2,1,6,4]=>7
[3,5,2,4,1,6]=>2
[3,5,2,4,6,1]=>2
[3,5,2,6,1,4]=>5
[3,5,2,6,4,1]=>5
[3,5,4,1,2,6]=>2
[3,5,4,1,6,2]=>4
[3,5,4,2,1,6]=>2
[3,5,4,2,6,1]=>2
[3,5,4,6,1,2]=>2
[3,5,4,6,2,1]=>2
[3,5,6,1,2,4]=>3
[3,5,6,1,4,2]=>6
[3,5,6,2,1,4]=>3
[3,5,6,2,4,1]=>3
[3,5,6,4,1,2]=>3
[3,5,6,4,2,1]=>3
[3,6,1,2,4,5]=>3
[3,6,1,2,5,4]=>11
[3,6,1,4,2,5]=>6
[3,6,1,4,5,2]=>9
[3,6,1,5,2,4]=>13
[3,6,1,5,4,2]=>21
[3,6,2,1,4,5]=>3
[3,6,2,1,5,4]=>11
[3,6,2,4,1,5]=>3
[3,6,2,4,5,1]=>3
[3,6,2,5,1,4]=>8
[3,6,2,5,4,1]=>8
[3,6,4,1,2,5]=>3
[3,6,4,1,5,2]=>6
[3,6,4,2,1,5]=>3
[3,6,4,2,5,1]=>3
[3,6,4,5,1,2]=>3
[3,6,4,5,2,1]=>3
[3,6,5,1,2,4]=>5
[3,6,5,1,4,2]=>10
[3,6,5,2,1,4]=>5
[3,6,5,2,4,1]=>5
[3,6,5,4,1,2]=>5
[3,6,5,4,2,1]=>5
[4,1,2,3,5,6]=>1
[4,1,2,3,6,5]=>5
[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]=>20
[4,1,3,2,5,6]=>2
[4,1,3,2,6,5]=>10
[4,1,3,5,2,6]=>3
[4,1,3,5,6,2]=>4
[4,1,3,6,2,5]=>11
[4,1,3,6,5,2]=>15
[4,1,5,2,3,6]=>3
[4,1,5,2,6,3]=>8
[4,1,5,3,2,6]=>5
[4,1,5,3,6,2]=>7
[4,1,5,6,2,3]=>6
[4,1,5,6,3,2]=>9
[4,1,6,2,3,5]=>7
[4,1,6,2,5,3]=>19
[4,1,6,3,2,5]=>12
[4,1,6,3,5,2]=>17
[4,1,6,5,2,3]=>15
[4,1,6,5,3,2]=>23
[4,2,1,3,5,6]=>1
[4,2,1,3,6,5]=>5
[4,2,1,5,3,6]=>3
[4,2,1,5,6,3]=>6
[4,2,1,6,3,5]=>9
[4,2,1,6,5,3]=>20
[4,2,3,1,5,6]=>1
[4,2,3,1,6,5]=>5
[4,2,3,5,1,6]=>1
[4,2,3,5,6,1]=>1
[4,2,3,6,1,5]=>4
[4,2,3,6,5,1]=>4
[4,2,5,1,3,6]=>2
[4,2,5,1,6,3]=>5
[4,2,5,3,1,6]=>2
[4,2,5,3,6,1]=>2
[4,2,5,6,1,3]=>3
[4,2,5,6,3,1]=>3
[4,2,6,1,3,5]=>5
[4,2,6,1,5,3]=>13
[4,2,6,3,1,5]=>5
[4,2,6,3,5,1]=>5
[4,2,6,5,1,3]=>8
[4,2,6,5,3,1]=>8
[4,3,1,2,5,6]=>1
[4,3,1,2,6,5]=>5
[4,3,1,5,2,6]=>2
[4,3,1,5,6,2]=>3
[4,3,1,6,2,5]=>7
[4,3,1,6,5,2]=>11
[4,3,2,1,5,6]=>1
[4,3,2,1,6,5]=>5
[4,3,2,5,1,6]=>1
[4,3,2,5,6,1]=>1
[4,3,2,6,1,5]=>4
[4,3,2,6,5,1]=>4
[4,3,5,1,2,6]=>1
[4,3,5,1,6,2]=>2
[4,3,5,2,1,6]=>1
[4,3,5,2,6,1]=>1
[4,3,5,6,1,2]=>1
[4,3,5,6,2,1]=>1
[4,3,6,1,2,5]=>3
[4,3,6,1,5,2]=>6
[4,3,6,2,1,5]=>3
[4,3,6,2,5,1]=>3
[4,3,6,5,1,2]=>3
[4,3,6,5,2,1]=>3
[4,5,1,2,3,6]=>1
[4,5,1,2,6,3]=>3
[4,5,1,3,2,6]=>2
[4,5,1,3,6,2]=>3
[4,5,1,6,2,3]=>3
[4,5,1,6,3,2]=>5
[4,5,2,1,3,6]=>1
[4,5,2,1,6,3]=>3
[4,5,2,3,1,6]=>1
[4,5,2,3,6,1]=>1
[4,5,2,6,1,3]=>2
[4,5,2,6,3,1]=>2
[4,5,3,1,2,6]=>1
[4,5,3,1,6,2]=>2
[4,5,3,2,1,6]=>1
[4,5,3,2,6,1]=>1
[4,5,3,6,1,2]=>1
[4,5,3,6,2,1]=>1
[4,5,6,1,2,3]=>1
[4,5,6,1,3,2]=>2
[4,5,6,2,1,3]=>1
[4,5,6,2,3,1]=>1
[4,5,6,3,1,2]=>1
[4,5,6,3,2,1]=>1
[4,6,1,2,3,5]=>2
[4,6,1,2,5,3]=>6
[4,6,1,3,2,5]=>4
[4,6,1,3,5,2]=>6
[4,6,1,5,2,3]=>6
[4,6,1,5,3,2]=>10
[4,6,2,1,3,5]=>2
[4,6,2,1,5,3]=>6
[4,6,2,3,1,5]=>2
[4,6,2,3,5,1]=>2
[4,6,2,5,1,3]=>4
[4,6,2,5,3,1]=>4
[4,6,3,1,2,5]=>2
[4,6,3,1,5,2]=>4
[4,6,3,2,1,5]=>2
[4,6,3,2,5,1]=>2
[4,6,3,5,1,2]=>2
[4,6,3,5,2,1]=>2
[4,6,5,1,2,3]=>2
[4,6,5,1,3,2]=>4
[4,6,5,2,1,3]=>2
[4,6,5,2,3,1]=>2
[4,6,5,3,1,2]=>2
[4,6,5,3,2,1]=>2
[5,1,2,3,4,6]=>1
[5,1,2,3,6,4]=>4
[5,1,2,4,3,6]=>3
[5,1,2,4,6,3]=>6
[5,1,2,6,3,4]=>6
[5,1,2,6,4,3]=>14
[5,1,3,2,4,6]=>2
[5,1,3,2,6,4]=>8
[5,1,3,4,2,6]=>3
[5,1,3,4,6,2]=>4
[5,1,3,6,2,4]=>8
[5,1,3,6,4,2]=>11
[5,1,4,2,3,6]=>3
[5,1,4,2,6,3]=>8
[5,1,4,3,2,6]=>5
[5,1,4,3,6,2]=>7
[5,1,4,6,2,3]=>6
[5,1,4,6,3,2]=>9
[5,1,6,2,3,4]=>4
[5,1,6,2,4,3]=>11
[5,1,6,3,2,4]=>7
[5,1,6,3,4,2]=>10
[5,1,6,4,2,3]=>9
[5,1,6,4,3,2]=>14
[5,2,1,3,4,6]=>1
[5,2,1,3,6,4]=>4
[5,2,1,4,3,6]=>3
[5,2,1,4,6,3]=>6
[5,2,1,6,3,4]=>6
[5,2,1,6,4,3]=>14
[5,2,3,1,4,6]=>1
[5,2,3,1,6,4]=>4
[5,2,3,4,1,6]=>1
[5,2,3,4,6,1]=>1
[5,2,3,6,1,4]=>3
[5,2,3,6,4,1]=>3
[5,2,4,1,3,6]=>2
[5,2,4,1,6,3]=>5
[5,2,4,3,1,6]=>2
[5,2,4,3,6,1]=>2
[5,2,4,6,1,3]=>3
[5,2,4,6,3,1]=>3
[5,2,6,1,3,4]=>3
[5,2,6,1,4,3]=>8
[5,2,6,3,1,4]=>3
[5,2,6,3,4,1]=>3
[5,2,6,4,1,3]=>5
[5,2,6,4,3,1]=>5
[5,3,1,2,4,6]=>1
[5,3,1,2,6,4]=>4
[5,3,1,4,2,6]=>2
[5,3,1,4,6,2]=>3
[5,3,1,6,2,4]=>5
[5,3,1,6,4,2]=>8
[5,3,2,1,4,6]=>1
[5,3,2,1,6,4]=>4
[5,3,2,4,1,6]=>1
[5,3,2,4,6,1]=>1
[5,3,2,6,1,4]=>3
[5,3,2,6,4,1]=>3
[5,3,4,1,2,6]=>1
[5,3,4,1,6,2]=>2
[5,3,4,2,1,6]=>1
[5,3,4,2,6,1]=>1
[5,3,4,6,1,2]=>1
[5,3,4,6,2,1]=>1
[5,3,6,1,2,4]=>2
[5,3,6,1,4,2]=>4
[5,3,6,2,1,4]=>2
[5,3,6,2,4,1]=>2
[5,3,6,4,1,2]=>2
[5,3,6,4,2,1]=>2
[5,4,1,2,3,6]=>1
[5,4,1,2,6,3]=>3
[5,4,1,3,2,6]=>2
[5,4,1,3,6,2]=>3
[5,4,1,6,2,3]=>3
[5,4,1,6,3,2]=>5
[5,4,2,1,3,6]=>1
[5,4,2,1,6,3]=>3
[5,4,2,3,1,6]=>1
[5,4,2,3,6,1]=>1
[5,4,2,6,1,3]=>2
[5,4,2,6,3,1]=>2
[5,4,3,1,2,6]=>1
[5,4,3,1,6,2]=>2
[5,4,3,2,1,6]=>1
[5,4,3,2,6,1]=>1
[5,4,3,6,1,2]=>1
[5,4,3,6,2,1]=>1
[5,4,6,1,2,3]=>1
[5,4,6,1,3,2]=>2
[5,4,6,2,1,3]=>1
[5,4,6,2,3,1]=>1
[5,4,6,3,1,2]=>1
[5,4,6,3,2,1]=>1
[5,6,1,2,3,4]=>1
[5,6,1,2,4,3]=>3
[5,6,1,3,2,4]=>2
[5,6,1,3,4,2]=>3
[5,6,1,4,2,3]=>3
[5,6,1,4,3,2]=>5
[5,6,2,1,3,4]=>1
[5,6,2,1,4,3]=>3
[5,6,2,3,1,4]=>1
[5,6,2,3,4,1]=>1
[5,6,2,4,1,3]=>2
[5,6,2,4,3,1]=>2
[5,6,3,1,2,4]=>1
[5,6,3,1,4,2]=>2
[5,6,3,2,1,4]=>1
[5,6,3,2,4,1]=>1
[5,6,3,4,1,2]=>1
[5,6,3,4,2,1]=>1
[5,6,4,1,2,3]=>1
[5,6,4,1,3,2]=>2
[5,6,4,2,1,3]=>1
[5,6,4,2,3,1]=>1
[5,6,4,3,1,2]=>1
[5,6,4,3,2,1]=>1
[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>4
[6,1,2,4,3,5]=>3
[6,1,2,4,5,3]=>6
[6,1,2,5,3,4]=>6
[6,1,2,5,4,3]=>14
[6,1,3,2,4,5]=>2
[6,1,3,2,5,4]=>8
[6,1,3,4,2,5]=>3
[6,1,3,4,5,2]=>4
[6,1,3,5,2,4]=>8
[6,1,3,5,4,2]=>11
[6,1,4,2,3,5]=>3
[6,1,4,2,5,3]=>8
[6,1,4,3,2,5]=>5
[6,1,4,3,5,2]=>7
[6,1,4,5,2,3]=>6
[6,1,4,5,3,2]=>9
[6,1,5,2,3,4]=>4
[6,1,5,2,4,3]=>11
[6,1,5,3,2,4]=>7
[6,1,5,3,4,2]=>10
[6,1,5,4,2,3]=>9
[6,1,5,4,3,2]=>14
[6,2,1,3,4,5]=>1
[6,2,1,3,5,4]=>4
[6,2,1,4,3,5]=>3
[6,2,1,4,5,3]=>6
[6,2,1,5,3,4]=>6
[6,2,1,5,4,3]=>14
[6,2,3,1,4,5]=>1
[6,2,3,1,5,4]=>4
[6,2,3,4,1,5]=>1
[6,2,3,4,5,1]=>1
[6,2,3,5,1,4]=>3
[6,2,3,5,4,1]=>3
[6,2,4,1,3,5]=>2
[6,2,4,1,5,3]=>5
[6,2,4,3,1,5]=>2
[6,2,4,3,5,1]=>2
[6,2,4,5,1,3]=>3
[6,2,4,5,3,1]=>3
[6,2,5,1,3,4]=>3
[6,2,5,1,4,3]=>8
[6,2,5,3,1,4]=>3
[6,2,5,3,4,1]=>3
[6,2,5,4,1,3]=>5
[6,2,5,4,3,1]=>5
[6,3,1,2,4,5]=>1
[6,3,1,2,5,4]=>4
[6,3,1,4,2,5]=>2
[6,3,1,4,5,2]=>3
[6,3,1,5,2,4]=>5
[6,3,1,5,4,2]=>8
[6,3,2,1,4,5]=>1
[6,3,2,1,5,4]=>4
[6,3,2,4,1,5]=>1
[6,3,2,4,5,1]=>1
[6,3,2,5,1,4]=>3
[6,3,2,5,4,1]=>3
[6,3,4,1,2,5]=>1
[6,3,4,1,5,2]=>2
[6,3,4,2,1,5]=>1
[6,3,4,2,5,1]=>1
[6,3,4,5,1,2]=>1
[6,3,4,5,2,1]=>1
[6,3,5,1,2,4]=>2
[6,3,5,1,4,2]=>4
[6,3,5,2,1,4]=>2
[6,3,5,2,4,1]=>2
[6,3,5,4,1,2]=>2
[6,3,5,4,2,1]=>2
[6,4,1,2,3,5]=>1
[6,4,1,2,5,3]=>3
[6,4,1,3,2,5]=>2
[6,4,1,3,5,2]=>3
[6,4,1,5,2,3]=>3
[6,4,1,5,3,2]=>5
[6,4,2,1,3,5]=>1
[6,4,2,1,5,3]=>3
[6,4,2,3,1,5]=>1
[6,4,2,3,5,1]=>1
[6,4,2,5,1,3]=>2
[6,4,2,5,3,1]=>2
[6,4,3,1,2,5]=>1
[6,4,3,1,5,2]=>2
[6,4,3,2,1,5]=>1
[6,4,3,2,5,1]=>1
[6,4,3,5,1,2]=>1
[6,4,3,5,2,1]=>1
[6,4,5,1,2,3]=>1
[6,4,5,1,3,2]=>2
[6,4,5,2,1,3]=>1
[6,4,5,2,3,1]=>1
[6,4,5,3,1,2]=>1
[6,4,5,3,2,1]=>1
[6,5,1,2,3,4]=>1
[6,5,1,2,4,3]=>3
[6,5,1,3,2,4]=>2
[6,5,1,3,4,2]=>3
[6,5,1,4,2,3]=>3
[6,5,1,4,3,2]=>5
[6,5,2,1,3,4]=>1
[6,5,2,1,4,3]=>3
[6,5,2,3,1,4]=>1
[6,5,2,3,4,1]=>1
[6,5,2,4,1,3]=>2
[6,5,2,4,3,1]=>2
[6,5,3,1,2,4]=>1
[6,5,3,1,4,2]=>2
[6,5,3,2,1,4]=>1
[6,5,3,2,4,1]=>1
[6,5,3,4,1,2]=>1
[6,5,3,4,2,1]=>1
[6,5,4,1,2,3]=>1
[6,5,4,1,3,2]=>2
[6,5,4,2,1,3]=>1
[6,5,4,2,3,1]=>1
[6,5,4,3,1,2]=>1
[6,5,4,3,2,1]=>1
[1,2,3,4,5,6,7]=>1
[1,2,3,4,5,7,6]=>6
[1,2,3,4,6,5,7]=>5
[1,2,3,6,4,7,5]=>40
[1,2,6,3,4,7,5]=>45
[1,3,2,4,5,6,7]=>2
[1,3,7,2,4,5,6]=>24
[1,3,7,6,5,4,2]=>378
[1,4,6,7,2,3,5]=>45
[1,4,6,7,5,3,2]=>97
[1,4,7,2,3,5,6]=>27
[1,4,7,6,5,3,2]=>211
[1,5,2,3,4,7,6]=>24
[1,5,2,7,3,4,6]=>56
[1,5,4,7,6,3,2]=>125
[1,5,6,2,7,3,4]=>45
[1,5,6,4,7,3,2]=>43
[1,5,6,7,2,3,4]=>20
[1,5,6,7,4,3,2]=>48
[1,5,7,2,3,4,6]=>24
[1,5,7,6,4,3,2]=>124
[1,6,2,3,4,7,5]=>24
[1,6,2,3,7,4,5]=>45
[1,6,2,7,3,4,5]=>40
[1,6,5,4,3,7,2]=>56
[1,6,5,4,7,3,2]=>66
[1,6,5,7,4,3,2]=>76
[1,6,7,2,3,4,5]=>15
[1,6,7,5,4,3,2]=>90
[1,7,2,3,4,5,6]=>6
[1,7,3,5,6,4,2]=>122
[1,7,3,6,5,4,2]=>251
[1,7,4,3,6,5,2]=>150
[1,7,4,5,3,6,2]=>54
[1,7,4,5,6,3,2]=>62
[1,7,4,6,5,3,2]=>151
[1,7,5,4,3,6,2]=>75
[1,7,5,4,6,3,2]=>89
[1,7,6,4,5,3,2]=>107
[1,7,6,5,4,3,2]=>132
[2,1,3,4,5,6,7]=>1
[2,1,3,4,7,5,6]=>15
[2,1,3,7,4,5,6]=>20
[2,1,6,3,4,5,7]=>10
[2,1,7,3,4,5,6]=>15
[2,1,7,6,5,4,3]=>594
[2,3,1,4,5,6,7]=>1
[2,3,4,1,5,6,7]=>1
[2,3,4,1,5,7,6]=>6
[2,3,4,5,1,6,7]=>1
[2,3,4,5,1,7,6]=>6
[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]=>10
[2,3,4,7,1,5,6]=>10
[2,3,5,6,7,1,4]=>10
[2,4,1,3,5,6,7]=>2
[2,5,1,3,4,6,7]=>3
[2,5,7,1,3,4,6]=>15
[2,6,1,3,4,5,7]=>4
[2,6,1,7,3,4,5]=>30
[2,6,5,4,3,1,7]=>14
[2,6,7,1,3,4,5]=>10
[2,7,1,3,4,5,6]=>5
[3,1,2,4,5,6,7]=>1
[3,1,2,4,5,7,6]=>6
[3,2,1,4,5,6,7]=>1
[3,2,4,5,6,7,1]=>1
[3,4,1,2,5,6,7]=>1
[3,4,2,5,6,7,1]=>1
[3,4,5,2,6,7,1]=>1
[3,4,5,6,2,7,1]=>1
[3,4,5,6,7,1,2]=>1
[3,5,6,1,2,4,7]=>3
[3,5,6,4,2,1,7]=>3
[3,6,1,2,4,5,7]=>3
[3,6,5,4,2,1,7]=>5
[4,1,2,3,5,6,7]=>1
[4,1,2,3,5,7,6]=>6
[4,1,6,2,3,5,7]=>7
[4,2,3,5,6,7,1]=>1
[4,2,5,1,3,6,7]=>2
[4,3,2,1,5,6,7]=>1
[4,3,2,5,6,7,1]=>1
[4,3,5,2,6,7,1]=>1
[4,3,6,5,2,1,7]=>3
[4,5,1,6,2,3,7]=>3
[4,5,2,3,6,7,1]=>1
[4,5,3,6,2,1,7]=>1
[4,5,6,1,2,3,7]=>1
[4,5,6,3,2,1,7]=>1
[4,6,1,2,3,5,7]=>2
[4,6,1,2,3,7,5]=>9
[4,6,5,3,2,1,7]=>2
[5,1,2,3,4,6,7]=>1
[5,1,2,3,4,7,6]=>6
[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]=>6
[5,1,6,2,3,4,7]=>4
[5,1,6,2,3,7,4]=>15
[5,2,3,4,6,7,1]=>1
[5,2,6,7,1,3,4]=>6
[5,3,2,4,6,7,1]=>1
[5,3,2,6,1,4,7]=>3
[5,4,3,2,1,6,7]=>1
[5,4,3,2,1,7,6]=>6
[5,4,3,2,6,1,7]=>1
[5,4,3,6,2,1,7]=>1
[5,4,6,3,2,1,7]=>1
[5,6,1,2,3,4,7]=>1
[5,6,1,2,3,7,4]=>4
[5,6,3,4,1,2,7]=>1
[5,6,4,3,2,1,7]=>1
[5,6,7,1,2,3,4]=>1
[6,1,2,3,4,5,7]=>1
[6,1,2,3,4,7,5]=>5
[6,1,2,3,7,4,5]=>10
[6,1,2,7,3,4,5]=>10
[6,2,3,4,5,7,1]=>1
[6,2,4,5,3,1,7]=>3
[6,2,5,4,3,1,7]=>5
[6,3,2,5,4,1,7]=>3
[6,3,4,2,5,1,7]=>1
[6,3,4,5,2,1,7]=>1
[6,3,5,4,2,1,7]=>2
[6,4,3,2,5,1,7]=>1
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Description
The number of reduced Kogan faces with the permutation as type.
This is equivalent to finding the number of ways to represent the permutation $\pi \in S_{n+1}$ as a reduced subword of $s_n (s_{n-1} s_n) (s_{n-2} s_{n-1} s_n) \dotsm (s_1 \dotsm s_n)$, or the number of reduced pipe dreams for $\pi$.
This is equivalent to finding the number of ways to represent the permutation $\pi \in S_{n+1}$ as a reduced subword of $s_n (s_{n-1} s_n) (s_{n-2} s_{n-1} s_n) \dotsm (s_1 \dotsm s_n)$, or the number of reduced pipe dreams for $\pi$.
References
[1] Kirichenko, V. A., Smirnov, E. Y., Timorin, V. A. Schubert calculus and Gelfand-Zetlin polytopes DOI:10.1070/rm2012v067n04abeh004804 arXiv:1101.0278
Code
def statistic(pi):
n = len(pi)
if pi == Permutations(n).one():
return 1
else:
S = Word([j for i in range(n, 0, -1) for j in range(i, n+1)])
return sum(S.number_of_subword_occurrences(Word(w)) for w in pi.reduced_words())
Created
Jun 15, 2015 at 18:00 by Per Alexandersson
Updated
May 19, 2023 at 14:57 by Martin Rubey
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