Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001910
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Mapping
St001910: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => 1
[1,0,1,0]
 => 0
[1,1,0,0]
 => 2
[1,0,1,0,1,0]
 => 1
[1,0,1,1,0,0]
 => 0
[1,1,0,0,1,0]
 => 0
[1,1,0,1,0,0]
 => 1
[1,1,1,0,0,0]
 => 3
[1,0,1,0,1,0,1,0]
 => 0
[1,0,1,0,1,1,0,0]
 => 1
[1,0,1,1,0,0,1,0]
 => 2
[1,0,1,1,0,1,0,0]
 => 2
[1,0,1,1,1,0,0,0]
 => 0
[1,1,0,0,1,0,1,0]
 => 1
[1,1,0,0,1,1,0,0]
 => 0
[1,1,0,1,0,0,1,0]
 => 2
[1,1,0,1,0,1,0,0]
 => 2
[1,1,0,1,1,0,0,0]
 => 1
[1,1,1,0,0,0,1,0]
 => 0
[1,1,1,0,0,1,0,0]
 => 1
[1,1,1,0,1,0,0,0]
 => 2
[1,1,1,1,0,0,0,0]
 => 4
[1,0,1,0,1,0,1,0,1,0]
 => 1
[1,0,1,0,1,0,1,1,0,0]
 => 0
[1,0,1,0,1,1,0,0,1,0]
 => 0
[1,0,1,0,1,1,0,1,0,0]
 => 0
[1,0,1,0,1,1,1,0,0,0]
 => 1
[1,0,1,1,0,0,1,0,1,0]
 => 0
[1,0,1,1,0,0,1,1,0,0]
 => 2
[1,0,1,1,0,1,0,0,1,0]
 => 1
[1,0,1,1,0,1,0,1,0,0]
 => 1
[1,0,1,1,0,1,1,0,0,0]
 => 2
[1,0,1,1,1,0,0,0,1,0]
 => 3
[1,0,1,1,1,0,0,1,0,0]
 => 3
[1,0,1,1,1,0,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,0,0]
 => 0
[1,1,0,0,1,0,1,0,1,0]
 => 0
[1,1,0,0,1,0,1,1,0,0]
 => 1
[1,1,0,0,1,1,0,0,1,0]
 => 2
[1,1,0,0,1,1,0,1,0,0]
 => 2
[1,1,0,0,1,1,1,0,0,0]
 => 0
[1,1,0,1,0,0,1,0,1,0]
 => 0
[1,1,0,1,0,0,1,1,0,0]
 => 2
[1,1,0,1,0,1,0,0,1,0]
 => 1
[1,1,0,1,0,1,0,1,0,0]
 => 1
[1,1,0,1,0,1,1,0,0,0]
 => 2
[1,1,0,1,1,0,0,0,1,0]
 => 3
[1,1,0,1,1,0,0,1,0,0]
 => 3
[1,1,0,1,1,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => 1
Description
The height of the middle non-run of a Dyck path. A non-run of a Dyck path is a pair of steps which are not both up or both down, that is, which either form a peak or a valley. The number of non-runs is odd. This statistic returns the height of the middle non-run.