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Identifier
Values
=>
Cc0005;cc-rep
[1,0]=>0 [1,0,1,0]=>1 [1,1,0,0]=>0 [1,0,1,0,1,0]=>3 [1,0,1,1,0,0]=>1 [1,1,0,0,1,0]=>2 [1,1,0,1,0,0]=>1 [1,1,1,0,0,0]=>0 [1,0,1,0,1,0,1,0]=>6 [1,0,1,0,1,1,0,0]=>3 [1,0,1,1,0,0,1,0]=>4 [1,0,1,1,0,1,0,0]=>3 [1,0,1,1,1,0,0,0]=>1 [1,1,0,0,1,0,1,0]=>5 [1,1,0,0,1,1,0,0]=>2 [1,1,0,1,0,0,1,0]=>4 [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]=>3 [1,1,1,0,0,1,0,0]=>2 [1,1,1,0,1,0,0,0]=>1 [1,1,1,1,0,0,0,0]=>0 [1,0,1,0,1,0,1,0,1,0]=>10 [1,0,1,0,1,0,1,1,0,0]=>6 [1,0,1,0,1,1,0,0,1,0]=>7 [1,0,1,0,1,1,0,1,0,0]=>6 [1,0,1,0,1,1,1,0,0,0]=>3 [1,0,1,1,0,0,1,0,1,0]=>8 [1,0,1,1,0,0,1,1,0,0]=>4 [1,0,1,1,0,1,0,0,1,0]=>7 [1,0,1,1,0,1,0,1,0,0]=>4 [1,0,1,1,0,1,1,0,0,0]=>3 [1,0,1,1,1,0,0,0,1,0]=>5 [1,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,1,1,0,1,0,0,0]=>3 [1,0,1,1,1,1,0,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,0]=>9 [1,1,0,0,1,0,1,1,0,0]=>5 [1,1,0,0,1,1,0,0,1,0]=>6 [1,1,0,0,1,1,0,1,0,0]=>5 [1,1,0,0,1,1,1,0,0,0]=>2 [1,1,0,1,0,0,1,0,1,0]=>8 [1,1,0,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,1,0,0,1,0]=>6 [1,1,0,1,0,1,0,1,0,0]=>4 [1,1,0,1,0,1,1,0,0,0]=>2 [1,1,0,1,1,0,0,0,1,0]=>5 [1,1,0,1,1,0,0,1,0,0]=>4 [1,1,0,1,1,0,1,0,0,0]=>2 [1,1,0,1,1,1,0,0,0,0]=>1 [1,1,1,0,0,0,1,0,1,0]=>7 [1,1,1,0,0,0,1,1,0,0]=>3 [1,1,1,0,0,1,0,0,1,0]=>6 [1,1,1,0,0,1,0,1,0,0]=>3 [1,1,1,0,0,1,1,0,0,0]=>2 [1,1,1,0,1,0,0,0,1,0]=>5 [1,1,1,0,1,0,0,1,0,0]=>3 [1,1,1,0,1,0,1,0,0,0]=>2 [1,1,1,0,1,1,0,0,0,0]=>1 [1,1,1,1,0,0,0,0,1,0]=>4 [1,1,1,1,0,0,0,1,0,0]=>3 [1,1,1,1,0,0,1,0,0,0]=>2 [1,1,1,1,0,1,0,0,0,0]=>1 [1,1,1,1,1,0,0,0,0,0]=>0 [1,0,1,0,1,0,1,0,1,0,1,0]=>15 [1,0,1,0,1,0,1,0,1,1,0,0]=>10 [1,0,1,0,1,0,1,1,0,0,1,0]=>11 [1,0,1,0,1,0,1,1,0,1,0,0]=>10 [1,0,1,0,1,0,1,1,1,0,0,0]=>6 [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]=>7 [1,0,1,0,1,1,0,1,0,0,1,0]=>11 [1,0,1,0,1,1,0,1,0,1,0,0]=>7 [1,0,1,0,1,1,0,1,1,0,0,0]=>6 [1,0,1,0,1,1,1,0,0,0,1,0]=>8 [1,0,1,0,1,1,1,0,0,1,0,0]=>7 [1,0,1,0,1,1,1,0,1,0,0,0]=>6 [1,0,1,0,1,1,1,1,0,0,0,0]=>3 [1,0,1,1,0,0,1,0,1,0,1,0]=>13 [1,0,1,1,0,0,1,0,1,1,0,0]=>8 [1,0,1,1,0,0,1,1,0,0,1,0]=>9 [1,0,1,1,0,0,1,1,0,1,0,0]=>8 [1,0,1,1,0,0,1,1,1,0,0,0]=>4 [1,0,1,1,0,1,0,0,1,0,1,0]=>12 [1,0,1,1,0,1,0,0,1,1,0,0]=>7 [1,0,1,1,0,1,0,1,0,0,1,0]=>9 [1,0,1,1,0,1,0,1,0,1,0,0]=>7 [1,0,1,1,0,1,0,1,1,0,0,0]=>4 [1,0,1,1,0,1,1,0,0,0,1,0]=>8 [1,0,1,1,0,1,1,0,0,1,0,0]=>7 [1,0,1,1,0,1,1,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,1,0,0,0,0]=>3 [1,0,1,1,1,0,0,0,1,0,1,0]=>10 [1,0,1,1,1,0,0,0,1,1,0,0]=>5 [1,0,1,1,1,0,0,1,0,0,1,0]=>9 [1,0,1,1,1,0,0,1,0,1,0,0]=>5 [1,0,1,1,1,0,0,1,1,0,0,0]=>4 [1,0,1,1,1,0,1,0,0,0,1,0]=>8 [1,0,1,1,1,0,1,0,0,1,0,0]=>5 [1,0,1,1,1,0,1,0,1,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,0,0,0]=>3 [1,0,1,1,1,1,0,0,0,0,1,0]=>6 [1,0,1,1,1,1,0,0,0,1,0,0]=>5 [1,0,1,1,1,1,0,0,1,0,0,0]=>4 [1,0,1,1,1,1,0,1,0,0,0,0]=>3 [1,0,1,1,1,1,1,0,0,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,0,1,0]=>14 [1,1,0,0,1,0,1,0,1,1,0,0]=>9 [1,1,0,0,1,0,1,1,0,0,1,0]=>10 [1,1,0,0,1,0,1,1,0,1,0,0]=>9 [1,1,0,0,1,0,1,1,1,0,0,0]=>5 [1,1,0,0,1,1,0,0,1,0,1,0]=>11 [1,1,0,0,1,1,0,0,1,1,0,0]=>6 [1,1,0,0,1,1,0,1,0,0,1,0]=>10 [1,1,0,0,1,1,0,1,0,1,0,0]=>6 [1,1,0,0,1,1,0,1,1,0,0,0]=>5 [1,1,0,0,1,1,1,0,0,0,1,0]=>7 [1,1,0,0,1,1,1,0,0,1,0,0]=>6 [1,1,0,0,1,1,1,0,1,0,0,0]=>5 [1,1,0,0,1,1,1,1,0,0,0,0]=>2 [1,1,0,1,0,0,1,0,1,0,1,0]=>13 [1,1,0,1,0,0,1,0,1,1,0,0]=>8 [1,1,0,1,0,0,1,1,0,0,1,0]=>9 [1,1,0,1,0,0,1,1,0,1,0,0]=>8 [1,1,0,1,0,0,1,1,1,0,0,0]=>4 [1,1,0,1,0,1,0,0,1,0,1,0]=>11 [1,1,0,1,0,1,0,0,1,1,0,0]=>6 [1,1,0,1,0,1,0,1,0,0,1,0]=>9 [1,1,0,1,0,1,0,1,0,1,0,0]=>6 [1,1,0,1,0,1,0,1,1,0,0,0]=>4 [1,1,0,1,0,1,1,0,0,0,1,0]=>7 [1,1,0,1,0,1,1,0,0,1,0,0]=>6 [1,1,0,1,0,1,1,0,1,0,0,0]=>4 [1,1,0,1,0,1,1,1,0,0,0,0]=>2 [1,1,0,1,1,0,0,0,1,0,1,0]=>10 [1,1,0,1,1,0,0,0,1,1,0,0]=>5 [1,1,0,1,1,0,0,1,0,0,1,0]=>9 [1,1,0,1,1,0,0,1,0,1,0,0]=>5 [1,1,0,1,1,0,0,1,1,0,0,0]=>4 [1,1,0,1,1,0,1,0,0,0,1,0]=>7 [1,1,0,1,1,0,1,0,0,1,0,0]=>5 [1,1,0,1,1,0,1,0,1,0,0,0]=>4 [1,1,0,1,1,0,1,1,0,0,0,0]=>2 [1,1,0,1,1,1,0,0,0,0,1,0]=>6 [1,1,0,1,1,1,0,0,0,1,0,0]=>5 [1,1,0,1,1,1,0,0,1,0,0,0]=>4 [1,1,0,1,1,1,0,1,0,0,0,0]=>2 [1,1,0,1,1,1,1,0,0,0,0,0]=>1 [1,1,1,0,0,0,1,0,1,0,1,0]=>12 [1,1,1,0,0,0,1,0,1,1,0,0]=>7 [1,1,1,0,0,0,1,1,0,0,1,0]=>8 [1,1,1,0,0,0,1,1,0,1,0,0]=>7 [1,1,1,0,0,0,1,1,1,0,0,0]=>3 [1,1,1,0,0,1,0,0,1,0,1,0]=>11 [1,1,1,0,0,1,0,0,1,1,0,0]=>6 [1,1,1,0,0,1,0,1,0,0,1,0]=>8 [1,1,1,0,0,1,0,1,0,1,0,0]=>6 [1,1,1,0,0,1,0,1,1,0,0,0]=>3 [1,1,1,0,0,1,1,0,0,0,1,0]=>7 [1,1,1,0,0,1,1,0,0,1,0,0]=>6 [1,1,1,0,0,1,1,0,1,0,0,0]=>3 [1,1,1,0,0,1,1,1,0,0,0,0]=>2 [1,1,1,0,1,0,0,0,1,0,1,0]=>10 [1,1,1,0,1,0,0,0,1,1,0,0]=>5 [1,1,1,0,1,0,0,1,0,0,1,0]=>8 [1,1,1,0,1,0,0,1,0,1,0,0]=>5 [1,1,1,0,1,0,0,1,1,0,0,0]=>3 [1,1,1,0,1,0,1,0,0,0,1,0]=>7 [1,1,1,0,1,0,1,0,0,1,0,0]=>5 [1,1,1,0,1,0,1,0,1,0,0,0]=>3 [1,1,1,0,1,0,1,1,0,0,0,0]=>2 [1,1,1,0,1,1,0,0,0,0,1,0]=>6 [1,1,1,0,1,1,0,0,0,1,0,0]=>5 [1,1,1,0,1,1,0,0,1,0,0,0]=>3 [1,1,1,0,1,1,0,1,0,0,0,0]=>2 [1,1,1,0,1,1,1,0,0,0,0,0]=>1 [1,1,1,1,0,0,0,0,1,0,1,0]=>9 [1,1,1,1,0,0,0,0,1,1,0,0]=>4 [1,1,1,1,0,0,0,1,0,0,1,0]=>8 [1,1,1,1,0,0,0,1,0,1,0,0]=>4 [1,1,1,1,0,0,0,1,1,0,0,0]=>3 [1,1,1,1,0,0,1,0,0,0,1,0]=>7 [1,1,1,1,0,0,1,0,0,1,0,0]=>4 [1,1,1,1,0,0,1,0,1,0,0,0]=>3 [1,1,1,1,0,0,1,1,0,0,0,0]=>2 [1,1,1,1,0,1,0,0,0,0,1,0]=>6 [1,1,1,1,0,1,0,0,0,1,0,0]=>4 [1,1,1,1,0,1,0,0,1,0,0,0]=>3 [1,1,1,1,0,1,0,1,0,0,0,0]=>2 [1,1,1,1,0,1,1,0,0,0,0,0]=>1 [1,1,1,1,1,0,0,0,0,0,1,0]=>5 [1,1,1,1,1,0,0,0,0,1,0,0]=>4 [1,1,1,1,1,0,0,0,1,0,0,0]=>3 [1,1,1,1,1,0,0,1,0,0,0,0]=>2 [1,1,1,1,1,0,1,0,0,0,0,0]=>1 [1,1,1,1,1,1,0,0,0,0,0,0]=>0
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Description
The bounce statistic of a Dyck path.
The bounce path $D'$ of a Dyck path $D$ is the Dyck path obtained from $D$ by starting at the end point $(2n,0)$, traveling north-west until hitting $D$, then bouncing back south-west to the $x$-axis, and repeating this procedure until finally reaching the point $(0,0)$.
The points where $D'$ touches the $x$-axis are called bounce points, and a bounce path is uniquely determined by its bounce points.
This statistic is given by the sum of all $i$ for which the bounce path $D'$ of $D$ touches the $x$-axis at $(2i,0)$.
In particular, the bounce statistics of $D$ and $D'$ coincide.
Code
def statistic(x):
    return x.bounce()
Created
Sep 15, 2011 at 15:56 by Chris Berg
Updated
Jun 17, 2019 at 17:01 by Christian Stump