- FindStat

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Identifier

St000977: Dyck paths ⟶ ℤ

Values

[1,0,1,0] => 0

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

[1,0,1,0,1,0] => 0

[1,0,1,1,0,0] => 8

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

[1,1,0,1,0,0] => 6

[1,1,1,0,0,0] => 12

[1,0,1,0,1,0,1,0] => 0

[1,0,1,0,1,1,0,0] => 12

[1,0,1,1,0,0,1,0] => 8

[1,0,1,1,0,1,0,0] => 10

[1,0,1,1,1,0,0,0] => 20

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

[1,1,0,0,1,1,0,0] => 16

[1,1,0,1,0,0,1,0] => 6

[1,1,0,1,0,1,0,0] => 8

[1,1,0,1,1,0,0,0] => 18

[1,1,1,0,0,0,1,0] => 12

[1,1,1,0,0,1,0,0] => 14

[1,1,1,0,1,0,0,0] => 16

[1,1,1,1,0,0,0,0] => 24

[1,0,1,0,1,0,1,0,1,0] => 0

[1,0,1,0,1,0,1,1,0,0] => 16

[1,0,1,0,1,1,0,0,1,0] => 12

[1,0,1,0,1,1,0,1,0,0] => 14

[1,0,1,0,1,1,1,0,0,0] => 28

[1,0,1,1,0,0,1,0,1,0] => 8

[1,0,1,1,0,0,1,1,0,0] => 24

[1,0,1,1,0,1,0,0,1,0] => 10

[1,0,1,1,0,1,0,1,0,0] => 12

[1,0,1,1,0,1,1,0,0,0] => 26

[1,0,1,1,1,0,0,0,1,0] => 20

[1,0,1,1,1,0,0,1,0,0] => 22

[1,0,1,1,1,0,1,0,0,0] => 24

[1,0,1,1,1,1,0,0,0,0] => 36

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

[1,1,0,0,1,0,1,1,0,0] => 20

[1,1,0,0,1,1,0,0,1,0] => 16

[1,1,0,0,1,1,0,1,0,0] => 18

[1,1,0,0,1,1,1,0,0,0] => 32

[1,1,0,1,0,0,1,0,1,0] => 6

[1,1,0,1,0,0,1,1,0,0] => 22

[1,1,0,1,0,1,0,0,1,0] => 8

[1,1,0,1,0,1,0,1,0,0] => 10

[1,1,0,1,0,1,1,0,0,0] => 24

[1,1,0,1,1,0,0,0,1,0] => 18

[1,1,0,1,1,0,0,1,0,0] => 20

[1,1,0,1,1,0,1,0,0,0] => 22

[1,1,0,1,1,1,0,0,0,0] => 34

[1,1,1,0,0,0,1,0,1,0] => 12

[1,1,1,0,0,0,1,1,0,0] => 28

[1,1,1,0,0,1,0,0,1,0] => 14

[1,1,1,0,0,1,0,1,0,0] => 16

[1,1,1,0,0,1,1,0,0,0] => 30

[1,1,1,0,1,0,0,0,1,0] => 16

[1,1,1,0,1,0,0,1,0,0] => 18

[1,1,1,0,1,0,1,0,0,0] => 20

[1,1,1,0,1,1,0,0,0,0] => 32

[1,1,1,1,0,0,0,0,1,0] => 24

[1,1,1,1,0,0,0,1,0,0] => 26

[1,1,1,1,0,0,1,0,0,0] => 28

[1,1,1,1,0,1,0,0,0,0] => 30

[1,1,1,1,1,0,0,0,0,0] => 40

[1,0,1,0,1,0,1,0,1,0,1,0] => 0

[1,0,1,0,1,0,1,0,1,1,0,0] => 20

[1,0,1,0,1,0,1,1,0,0,1,0] => 16

[1,0,1,0,1,0,1,1,0,1,0,0] => 18

[1,0,1,0,1,0,1,1,1,0,0,0] => 36

[1,0,1,0,1,1,0,0,1,0,1,0] => 12

[1,0,1,0,1,1,0,0,1,1,0,0] => 32

[1,0,1,0,1,1,0,1,0,0,1,0] => 14

[1,0,1,0,1,1,0,1,0,1,0,0] => 16

[1,0,1,0,1,1,0,1,1,0,0,0] => 34

[1,0,1,0,1,1,1,0,0,0,1,0] => 28

[1,0,1,0,1,1,1,0,0,1,0,0] => 30

[1,0,1,0,1,1,1,0,1,0,0,0] => 32

[1,0,1,0,1,1,1,1,0,0,0,0] => 48

[1,0,1,1,0,0,1,0,1,0,1,0] => 8

[1,0,1,1,0,0,1,0,1,1,0,0] => 28

[1,0,1,1,0,0,1,1,0,0,1,0] => 24

[1,0,1,1,0,0,1,1,0,1,0,0] => 26

[1,0,1,1,0,0,1,1,1,0,0,0] => 44

[1,0,1,1,0,1,0,0,1,0,1,0] => 10

[1,0,1,1,0,1,0,0,1,1,0,0] => 30

[1,0,1,1,0,1,0,1,0,0,1,0] => 12

[1,0,1,1,0,1,0,1,0,1,0,0] => 14

[1,0,1,1,0,1,0,1,1,0,0,0] => 32

[1,0,1,1,0,1,1,0,0,0,1,0] => 26

[1,0,1,1,0,1,1,0,0,1,0,0] => 28

[1,0,1,1,0,1,1,0,1,0,0,0] => 30

[1,0,1,1,0,1,1,1,0,0,0,0] => 46

[1,0,1,1,1,0,0,0,1,0,1,0] => 20

[1,0,1,1,1,0,0,0,1,1,0,0] => 40

[1,0,1,1,1,0,0,1,0,0,1,0] => 22

[1,0,1,1,1,0,0,1,0,1,0,0] => 24

[1,0,1,1,1,0,0,1,1,0,0,0] => 42

[1,0,1,1,1,0,1,0,0,0,1,0] => 24

[1,0,1,1,1,0,1,0,0,1,0,0] => 26

[1,0,1,1,1,0,1,0,1,0,0,0] => 28

[1,0,1,1,1,0,1,1,0,0,0,0] => 44

[1,0,1,1,1,1,0,0,0,0,1,0] => 36

>>> Load all 1200 entries. <<<

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Description

MacMahon's equal index of a Dyck path.
This is the sum of the positions of double (up- or down-)steps of a Dyck path, see [1, p. 135].

References

[1] MacMahon, P. A. Combinatory analysis. Vol. I, II (bound in one volume) MathSciNet:2417935

Code

def statistic(p):
    return sum( i+1 for i in range(len(p)-1) if p[i] == p[i+1] )

Created

Sep 08, 2017 at 12:22 by Christian Stump

Updated

Sep 08, 2017 at 12:22 by Christian Stump