Identifier
Values
=>
[1]=>0
[1,1]=>1
[2]=>0
[1,1,1]=>3
[1,2]=>1
[2,1]=>2
[3]=>0
[1,1,1,1]=>6
[1,1,2]=>3
[1,2,1]=>4
[1,3]=>1
[2,1,1]=>5
[2,2]=>2
[3,1]=>3
[4]=>0
[1,1,1,1,1]=>10
[1,1,1,2]=>6
[1,1,2,1]=>7
[1,1,3]=>3
[1,2,1,1]=>8
[1,2,2]=>4
[1,3,1]=>5
[1,4]=>1
[2,1,1,1]=>9
[2,1,2]=>5
[2,2,1]=>6
[2,3]=>2
[3,1,1]=>7
[3,2]=>3
[4,1]=>4
[5]=>0
[1,1,1,1,1,1]=>15
[1,1,1,1,2]=>10
[1,1,1,2,1]=>11
[1,1,1,3]=>6
[1,1,2,1,1]=>12
[1,1,2,2]=>7
[1,1,3,1]=>8
[1,1,4]=>3
[1,2,1,1,1]=>13
[1,2,1,2]=>8
[1,2,2,1]=>9
[1,2,3]=>4
[1,3,1,1]=>10
[1,3,2]=>5
[1,4,1]=>6
[1,5]=>1
[2,1,1,1,1]=>14
[2,1,1,2]=>9
[2,1,2,1]=>10
[2,1,3]=>5
[2,2,1,1]=>11
[2,2,2]=>6
[2,3,1]=>7
[2,4]=>2
[3,1,1,1]=>12
[3,1,2]=>7
[3,2,1]=>8
[3,3]=>3
[4,1,1]=>9
[4,2]=>4
[5,1]=>5
[6]=>0
[1,1,1,1,1,1,1]=>21
[1,1,1,1,1,2]=>15
[1,1,1,1,2,1]=>16
[1,1,1,1,3]=>10
[1,1,1,2,1,1]=>17
[1,1,1,2,2]=>11
[1,1,1,3,1]=>12
[1,1,1,4]=>6
[1,1,2,1,1,1]=>18
[1,1,2,1,2]=>12
[1,1,2,2,1]=>13
[1,1,2,3]=>7
[1,1,3,1,1]=>14
[1,1,3,2]=>8
[1,1,4,1]=>9
[1,1,5]=>3
[1,2,1,1,1,1]=>19
[1,2,1,1,2]=>13
[1,2,1,2,1]=>14
[1,2,1,3]=>8
[1,2,2,1,1]=>15
[1,2,2,2]=>9
[1,2,3,1]=>10
[1,2,4]=>4
[1,3,1,1,1]=>16
[1,3,1,2]=>10
[1,3,2,1]=>11
[1,3,3]=>5
[1,4,1,1]=>12
[1,4,2]=>6
[1,5,1]=>7
[1,6]=>1
[2,1,1,1,1,1]=>20
[2,1,1,1,2]=>14
[2,1,1,2,1]=>15
[2,1,1,3]=>9
[2,1,2,1,1]=>16
[2,1,2,2]=>10
[2,1,3,1]=>11
[2,1,4]=>5
[2,2,1,1,1]=>17
[2,2,1,2]=>11
[2,2,2,1]=>12
[2,2,3]=>6
[2,3,1,1]=>13
[2,3,2]=>7
[2,4,1]=>8
[2,5]=>2
[3,1,1,1,1]=>18
[3,1,1,2]=>12
[3,1,2,1]=>13
[3,1,3]=>7
[3,2,1,1]=>14
[3,2,2]=>8
[3,3,1]=>9
[3,4]=>3
[4,1,1,1]=>15
[4,1,2]=>9
[4,2,1]=>10
[4,3]=>4
[5,1,1]=>11
[5,2]=>5
[6,1]=>6
[7]=>0
[1,1,1,1,1,1,1,1]=>28
[1,1,1,1,1,1,2]=>21
[1,1,1,1,1,2,1]=>22
[1,1,1,1,1,3]=>15
[1,1,1,1,2,1,1]=>23
[1,1,1,1,2,2]=>16
[1,1,1,1,3,1]=>17
[1,1,1,1,4]=>10
[1,1,1,2,1,1,1]=>24
[1,1,1,2,1,2]=>17
[1,1,1,2,2,1]=>18
[1,1,1,2,3]=>11
[1,1,1,3,1,1]=>19
[1,1,1,3,2]=>12
[1,1,1,4,1]=>13
[1,1,1,5]=>6
[1,1,2,1,1,1,1]=>25
[1,1,2,1,1,2]=>18
[1,1,2,1,2,1]=>19
[1,1,2,1,3]=>12
[1,1,2,2,1,1]=>20
[1,1,2,2,2]=>13
[1,1,2,3,1]=>14
[1,1,2,4]=>7
[1,1,3,1,1,1]=>21
[1,1,3,1,2]=>14
[1,1,3,2,1]=>15
[1,1,3,3]=>8
[1,1,4,1,1]=>16
[1,1,4,2]=>9
[1,1,5,1]=>10
[1,1,6]=>3
[1,2,1,1,1,1,1]=>26
[1,2,1,1,1,2]=>19
[1,2,1,1,2,1]=>20
[1,2,1,1,3]=>13
[1,2,1,2,1,1]=>21
[1,2,1,2,2]=>14
[1,2,1,3,1]=>15
[1,2,1,4]=>8
[1,2,2,1,1,1]=>22
[1,2,2,1,2]=>15
[1,2,2,2,1]=>16
[1,2,2,3]=>9
[1,2,3,1,1]=>17
[1,2,3,2]=>10
[1,2,4,1]=>11
[1,2,5]=>4
[1,3,1,1,1,1]=>23
[1,3,1,1,2]=>16
[1,3,1,2,1]=>17
[1,3,1,3]=>10
[1,3,2,1,1]=>18
[1,3,2,2]=>11
[1,3,3,1]=>12
[1,3,4]=>5
[1,4,1,1,1]=>19
[1,4,1,2]=>12
[1,4,2,1]=>13
[1,4,3]=>6
[1,5,1,1]=>14
[1,5,2]=>7
[1,6,1]=>8
[1,7]=>1
[2,1,1,1,1,1,1]=>27
[2,1,1,1,1,2]=>20
[2,1,1,1,2,1]=>21
[2,1,1,1,3]=>14
[2,1,1,2,1,1]=>22
[2,1,1,2,2]=>15
[2,1,1,3,1]=>16
[2,1,1,4]=>9
[2,1,2,1,1,1]=>23
[2,1,2,1,2]=>16
[2,1,2,2,1]=>17
[2,1,2,3]=>10
[2,1,3,1,1]=>18
[2,1,3,2]=>11
[2,1,4,1]=>12
[2,1,5]=>5
[2,2,1,1,1,1]=>24
[2,2,1,1,2]=>17
[2,2,1,2,1]=>18
[2,2,1,3]=>11
[2,2,2,1,1]=>19
[2,2,2,2]=>12
[2,2,3,1]=>13
[2,2,4]=>6
[2,3,1,1,1]=>20
[2,3,1,2]=>13
[2,3,2,1]=>14
[2,3,3]=>7
[2,4,1,1]=>15
[2,4,2]=>8
[2,5,1]=>9
[2,6]=>2
[3,1,1,1,1,1]=>25
[3,1,1,1,2]=>18
[3,1,1,2,1]=>19
[3,1,1,3]=>12
[3,1,2,1,1]=>20
[3,1,2,2]=>13
[3,1,3,1]=>14
[3,1,4]=>7
[3,2,1,1,1]=>21
[3,2,1,2]=>14
[3,2,2,1]=>15
[3,2,3]=>8
[3,3,1,1]=>16
[3,3,2]=>9
[3,4,1]=>10
[3,5]=>3
[4,1,1,1,1]=>22
[4,1,1,2]=>15
[4,1,2,1]=>16
[4,1,3]=>9
[4,2,1,1]=>17
[4,2,2]=>10
[4,3,1]=>11
[4,4]=>4
[5,1,1,1]=>18
[5,1,2]=>11
[5,2,1]=>12
[5,3]=>5
[6,1,1]=>13
[6,2]=>6
[7,1]=>7
[8]=>0
[1,1,1,1,4,1]=>18
[1,1,1,2,3,1]=>19
[1,1,2,1,3,1]=>20
[1,1,6,1]=>11
[1,2,1,1,3,1]=>21
[1,2,1,2,2,1]=>22
[1,2,2,1,2,1]=>23
[1,2,5,1]=>12
[1,3,1,1,2,1]=>24
[1,3,1,2,1,1]=>25
[1,3,2,1,1,1]=>26
[1,3,4,1]=>13
[1,4,1,1,1,1]=>27
[1,4,1,3]=>12
[1,4,2,2]=>13
[1,4,3,1]=>14
[1,5,1,2]=>14
[1,5,2,1]=>15
[1,6,1,1]=>16
[1,6,2]=>8
[1,7,1]=>9
[1,8]=>1
[2,1,5,1]=>13
[2,2,4,1]=>14
[3,1,4,1]=>15
[6,2,1]=>14
[7,1,1]=>15
[8,1]=>8
[1,1,1,1,1,1,1,1,1,1]=>45
[1,1,1,1,1,1,2,2]=>29
[1,1,1,1,2,1,1,2]=>31
[1,1,1,1,2,2,1,1]=>33
[1,1,1,1,3,3]=>17
[1,1,1,1,5,1]=>19
[1,1,2,1,1,1,1,2]=>33
[1,1,2,1,1,2,1,1]=>35
[1,1,2,1,2,3]=>19
[1,1,2,2,1,1,1,1]=>37
[1,1,2,2,2,2]=>21
[1,1,3,1,1,3]=>21
[1,1,3,2,1,2]=>23
[1,1,3,3,1,1]=>25
[1,1,4,4]=>9
[1,1,7,1]=>12
[1,2,1,1,4,1]=>22
[1,2,6,1]=>13
[1,3,1,1,3,1]=>25
[1,3,5,1]=>14
[1,4,1,1,2,1]=>28
[1,4,4,1]=>15
[1,5,1,1,1,1]=>31
[1,5,3,1]=>16
[1,6,1,2]=>16
[1,6,2,1]=>17
[1,7,1,1]=>18
[1,8,1]=>10
[1,9]=>1
[2,1,1,1,1,1,1,2]=>35
[2,1,1,1,1,2,1,1]=>37
[2,1,1,1,2,3]=>21
[2,1,1,2,1,1,1,1]=>39
[2,1,1,2,2,2]=>23
[2,1,2,1,1,3]=>23
[2,1,2,2,1,2]=>25
[2,1,2,3,1,1]=>27
[2,1,3,4]=>11
[2,1,6,1]=>14
[2,2,1,1,1,1,1,1]=>41
[2,2,1,1,2,2]=>25
[2,2,2,1,1,2]=>27
[2,2,2,2,1,1]=>29
[2,2,3,3]=>13
[3,1,1,1,1,3]=>25
[3,1,1,2,1,2]=>27
[3,1,1,3,1,1]=>29
[3,1,2,4]=>13
[3,2,1,1,1,2]=>29
[3,2,1,2,1,1]=>31
[3,2,2,3]=>15
[3,3,1,1,1,1]=>33
[3,3,2,2]=>17
[4,1,1,4]=>15
[4,2,1,3]=>17
[4,3,1,2]=>19
[4,4,1,1]=>21
[5,5]=>5
[8,1,1]=>17
[9,1]=>9
[1,10]=>1
[1,8,1,1]=>20
[1,7,2,1]=>19
[1,6,3,1]=>18
[1,5,4,1]=>17
[1,4,5,1]=>16
[1,3,6,1]=>15
[1,2,7,1]=>14
[1,1,8,1]=>13
[10,1]=>10
[1,1,1,1,1,1,1,1,1,1,1,1]=>66
[1,1,1,1,1,1,1,1,2,2]=>46
[1,1,1,1,1,1,2,2,1,1]=>50
[1,1,1,1,1,1,2,1,1,2]=>48
[1,1,1,1,1,1,3,3]=>30
[1,1,1,1,2,2,1,1,1,1]=>54
[1,1,1,1,2,2,2,2]=>34
[1,1,1,1,2,1,1,2,1,1]=>52
[1,1,1,1,2,1,1,1,1,2]=>50
[1,1,1,1,2,1,2,3]=>32
[1,1,1,1,3,3,1,1]=>38
[1,1,1,1,3,2,1,2]=>36
[1,1,1,1,3,1,1,3]=>34
[1,1,1,1,4,4]=>18
[1,1,2,2,1,1,1,1,1,1]=>58
[1,1,2,2,1,1,2,2]=>38
[1,1,2,2,2,2,1,1]=>42
[1,1,2,2,2,1,1,2]=>40
[1,1,2,2,3,3]=>22
[1,1,2,1,1,2,1,1,1,1]=>56
[1,1,2,1,1,2,2,2]=>36
[1,1,2,1,1,1,1,2,1,1]=>54
[1,1,2,1,1,1,1,1,1,2]=>52
[1,1,2,1,1,1,2,3]=>34
[1,1,2,1,2,3,1,1]=>40
[1,1,2,1,2,2,1,2]=>38
[1,1,2,1,2,1,1,3]=>36
[1,1,2,1,3,4]=>20
[1,1,3,3,1,1,1,1]=>46
[1,1,3,3,2,2]=>26
[1,1,3,2,1,2,1,1]=>44
[1,1,3,2,1,1,1,2]=>42
[1,1,3,2,2,3]=>24
[1,1,3,1,1,3,1,1]=>42
[1,1,3,1,1,2,1,2]=>40
[1,1,3,1,1,1,1,3]=>38
[1,1,3,1,2,4]=>22
[1,1,4,4,1,1]=>30
[1,1,4,3,1,2]=>28
[1,1,4,2,1,3]=>26
[1,1,4,1,1,4]=>24
[1,1,5,5]=>10
[2,2,1,1,1,1,1,1,1,1]=>62
[2,2,1,1,1,1,2,2]=>42
[2,2,1,1,2,2,1,1]=>46
[2,2,1,1,2,1,1,2]=>44
[2,2,1,1,3,3]=>26
[2,2,2,2,1,1,1,1]=>50
[2,2,2,2,2,2]=>30
[2,2,2,1,1,2,1,1]=>48
[2,2,2,1,1,1,1,2]=>46
[2,2,2,1,2,3]=>28
[2,2,3,3,1,1]=>34
[2,2,3,2,1,2]=>32
[2,2,3,1,1,3]=>30
[2,2,4,4]=>14
[2,1,1,2,1,1,1,1,1,1]=>60
[2,1,1,2,1,1,2,2]=>40
[2,1,1,2,2,2,1,1]=>44
[2,1,1,2,2,1,1,2]=>42
[2,1,1,2,3,3]=>24
[2,1,1,1,1,2,1,1,1,1]=>58
[2,1,1,1,1,2,2,2]=>38
[2,1,1,1,1,1,1,2,1,1]=>56
[2,1,1,1,1,1,1,1,1,2]=>54
[2,1,1,1,1,1,2,3]=>36
[2,1,1,1,2,3,1,1]=>42
[2,1,1,1,2,2,1,2]=>40
[2,1,1,1,2,1,1,3]=>38
[2,1,1,1,3,4]=>22
[2,1,2,3,1,1,1,1]=>48
[2,1,2,3,2,2]=>28
[2,1,2,2,1,2,1,1]=>46
[2,1,2,2,1,1,1,2]=>44
[2,1,2,2,2,3]=>26
[2,1,2,1,1,3,1,1]=>44
[2,1,2,1,1,2,1,2]=>42
[2,1,2,1,1,1,1,3]=>40
[2,1,2,1,2,4]=>24
[2,1,3,4,1,1]=>32
[2,1,3,3,1,2]=>30
[2,1,3,2,1,3]=>28
[2,1,3,1,1,4]=>26
[2,1,4,5]=>12
[3,3,1,1,1,1,1,1]=>54
[3,3,1,1,2,2]=>34
[3,3,2,2,1,1]=>38
[3,3,2,1,1,2]=>36
[3,3,3,3]=>18
[3,2,1,2,1,1,1,1]=>52
[3,2,1,2,2,2]=>32
[3,2,1,1,1,2,1,1]=>50
[3,2,1,1,1,1,1,2]=>48
[3,2,1,1,2,3]=>30
[3,2,2,3,1,1]=>36
[3,2,2,2,1,2]=>34
[3,2,2,1,1,3]=>32
[3,2,3,4]=>16
[3,1,1,3,1,1,1,1]=>50
[3,1,1,3,2,2]=>30
[3,1,1,2,1,2,1,1]=>48
[3,1,1,2,1,1,1,2]=>46
[3,1,1,2,2,3]=>28
[3,1,1,1,1,3,1,1]=>46
[3,1,1,1,1,2,1,2]=>44
[3,1,1,1,1,1,1,3]=>42
[3,1,1,1,2,4]=>26
[3,1,2,4,1,1]=>34
[3,1,2,3,1,2]=>32
[3,1,2,2,1,3]=>30
[3,1,2,1,1,4]=>28
[3,1,3,5]=>14
[4,4,1,1,1,1]=>42
[4,4,2,2]=>22
[4,3,1,2,1,1]=>40
[4,3,1,1,1,2]=>38
[4,3,2,3]=>20
[4,2,1,3,1,1]=>38
[4,2,1,2,1,2]=>36
[4,2,1,1,1,3]=>34
[4,2,2,4]=>18
[4,1,1,4,1,1]=>36
[4,1,1,3,1,2]=>34
[4,1,1,2,1,3]=>32
[4,1,1,1,1,4]=>30
[4,1,2,5]=>16
[5,5,1,1]=>26
[5,4,1,2]=>24
[5,3,1,3]=>22
[5,2,1,4]=>20
[5,1,1,5]=>18
[6,6]=>6
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The major index of the composition.
The descents of a composition $[c_1,c_2,\dots,c_k]$ are the partial sums $c_1, c_1+c_2,\dots, c_1+\dots+c_{k-1}$, excluding the sum of all parts. The major index of a composition is the sum of its descents.
For details about the major index see Permutations/Descents-Major.
The descents of a composition $[c_1,c_2,\dots,c_k]$ are the partial sums $c_1, c_1+c_2,\dots, c_1+\dots+c_{k-1}$, excluding the sum of all parts. The major index of a composition is the sum of its descents.
For details about the major index see Permutations/Descents-Major.
Code
def statistic(x):
return x.major_index()
Created
Sep 21, 2011 at 16:41 by Chris Berg
Updated
Jan 26, 2018 at 09:17 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!