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Identifier

St000008: Integer compositions ⟶ ℤ

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

>>> Load all 485 entries. <<<

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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.

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