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Identifier

St000305: Permutations ⟶ ℤ

Values

[1] => 0

[1,2] => 0

[2,1] => 1

[1,2,3] => 0

[1,3,2] => 2

[2,1,3] => 1

[2,3,1] => 1

[3,1,2] => 2

[3,2,1] => 3

[1,2,3,4] => 0

[1,2,4,3] => 3

[1,3,2,4] => 2

[1,3,4,2] => 2

[1,4,2,3] => 3

[1,4,3,2] => 5

[2,1,3,4] => 1

[2,1,4,3] => 4

[2,3,1,4] => 1

[2,3,4,1] => 1

[2,4,1,3] => 4

[2,4,3,1] => 4

[3,1,2,4] => 2

[3,1,4,2] => 2

[3,2,1,4] => 3

[3,2,4,1] => 3

[3,4,1,2] => 2

[3,4,2,1] => 3

[4,1,2,3] => 3

[4,1,3,2] => 5

[4,2,1,3] => 4

[4,2,3,1] => 4

[4,3,1,2] => 5

[4,3,2,1] => 6

[1,2,3,4,5] => 0

[1,2,3,5,4] => 4

[1,2,4,3,5] => 3

[1,2,4,5,3] => 3

[1,2,5,3,4] => 4

[1,2,5,4,3] => 7

[1,3,2,4,5] => 2

[1,3,2,5,4] => 6

[1,3,4,2,5] => 2

[1,3,4,5,2] => 2

[1,3,5,2,4] => 6

[1,3,5,4,2] => 6

[1,4,2,3,5] => 3

[1,4,2,5,3] => 3

[1,4,3,2,5] => 5

[1,4,3,5,2] => 5

[1,4,5,2,3] => 3

[1,4,5,3,2] => 5

[1,5,2,3,4] => 4

[1,5,2,4,3] => 7

[1,5,3,2,4] => 6

[1,5,3,4,2] => 6

[1,5,4,2,3] => 7

[1,5,4,3,2] => 9

[2,1,3,4,5] => 1

[2,1,3,5,4] => 5

[2,1,4,3,5] => 4

[2,1,4,5,3] => 4

[2,1,5,3,4] => 5

[2,1,5,4,3] => 8

[2,3,1,4,5] => 1

[2,3,1,5,4] => 5

[2,3,4,1,5] => 1

[2,3,4,5,1] => 1

[2,3,5,1,4] => 5

[2,3,5,4,1] => 5

[2,4,1,3,5] => 4

[2,4,1,5,3] => 4

[2,4,3,1,5] => 4

[2,4,3,5,1] => 4

[2,4,5,1,3] => 4

[2,4,5,3,1] => 4

[2,5,1,3,4] => 5

[2,5,1,4,3] => 8

[2,5,3,1,4] => 5

[2,5,3,4,1] => 5

[2,5,4,1,3] => 8

[2,5,4,3,1] => 8

[3,1,2,4,5] => 2

[3,1,2,5,4] => 6

[3,1,4,2,5] => 2

[3,1,4,5,2] => 2

[3,1,5,2,4] => 6

[3,1,5,4,2] => 6

[3,2,1,4,5] => 3

[3,2,1,5,4] => 7

[3,2,4,1,5] => 3

[3,2,4,5,1] => 3

[3,2,5,1,4] => 7

[3,2,5,4,1] => 7

[3,4,1,2,5] => 2

[3,4,1,5,2] => 2

[3,4,2,1,5] => 3

[3,4,2,5,1] => 3

[3,4,5,1,2] => 2

[3,4,5,2,1] => 3

[3,5,1,2,4] => 6

[3,5,1,4,2] => 6

>>> Load all 873 entries. <<<

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Description

The inverse major index of a permutation.
This is the major index St000004The major index of a permutation. of the inverse permutation Mp00066inverse.

References

[1] Stump, C. More bijective Catalan combinatorics on permutations and on signed permutations MathSciNet:3153083

Code

def statistic(pi):
    return pi.inverse().major_index()

Created

Dec 01, 2015 at 21:22 by Christian Stump

Updated

Dec 02, 2015 at 15:31 by Christian Stump