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Identifier
Values
=>
Cc0005;cc-rep
[1,0]=>1 [1,0,1,0]=>2 [1,1,0,0]=>2 [1,0,1,0,1,0]=>3 [1,0,1,1,0,0]=>3 [1,1,0,0,1,0]=>3 [1,1,0,1,0,0]=>2 [1,1,1,0,0,0]=>3 [1,0,1,0,1,0,1,0]=>4 [1,0,1,0,1,1,0,0]=>4 [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]=>4 [1,1,0,0,1,0,1,0]=>4 [1,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,0]=>3 [1,1,0,1,0,1,0,0]=>3 [1,1,0,1,1,0,0,0]=>3 [1,1,1,0,0,0,1,0]=>4 [1,1,1,0,0,1,0,0]=>3 [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]=>5 [1,0,1,0,1,0,1,1,0,0]=>5 [1,0,1,0,1,1,0,0,1,0]=>5 [1,0,1,0,1,1,0,1,0,0]=>4 [1,0,1,0,1,1,1,0,0,0]=>5 [1,0,1,1,0,0,1,0,1,0]=>5 [1,0,1,1,0,0,1,1,0,0]=>5 [1,0,1,1,0,1,0,0,1,0]=>4 [1,0,1,1,0,1,0,1,0,0]=>4 [1,0,1,1,0,1,1,0,0,0]=>4 [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]=>5 [1,1,0,0,1,0,1,0,1,0]=>5 [1,1,0,0,1,0,1,1,0,0]=>5 [1,1,0,0,1,1,0,0,1,0]=>5 [1,1,0,0,1,1,0,1,0,0]=>4 [1,1,0,0,1,1,1,0,0,0]=>5 [1,1,0,1,0,0,1,0,1,0]=>4 [1,1,0,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,1,0,0,1,0]=>4 [1,1,0,1,0,1,0,1,0,0]=>4 [1,1,0,1,0,1,1,0,0,0]=>4 [1,1,0,1,1,0,0,0,1,0]=>4 [1,1,0,1,1,0,0,1,0,0]=>4 [1,1,0,1,1,0,1,0,0,0]=>3 [1,1,0,1,1,1,0,0,0,0]=>4 [1,1,1,0,0,0,1,0,1,0]=>5 [1,1,1,0,0,0,1,1,0,0]=>5 [1,1,1,0,0,1,0,0,1,0]=>4 [1,1,1,0,0,1,0,1,0,0]=>4 [1,1,1,0,0,1,1,0,0,0]=>4 [1,1,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,0,0,1,0,0]=>3 [1,1,1,0,1,0,1,0,0,0]=>3 [1,1,1,0,1,1,0,0,0,0]=>3 [1,1,1,1,0,0,0,0,1,0]=>5 [1,1,1,1,0,0,0,1,0,0]=>4 [1,1,1,1,0,0,1,0,0,0]=>3 [1,1,1,1,0,1,0,0,0,0]=>2 [1,1,1,1,1,0,0,0,0,0]=>5 [1,0,1,0,1,0,1,0,1,0,1,0]=>6 [1,0,1,0,1,0,1,0,1,1,0,0]=>6 [1,0,1,0,1,0,1,1,0,0,1,0]=>6 [1,0,1,0,1,0,1,1,0,1,0,0]=>5 [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]=>6 [1,0,1,0,1,1,0,0,1,1,0,0]=>6 [1,0,1,0,1,1,0,1,0,0,1,0]=>5 [1,0,1,0,1,1,0,1,0,1,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,0,0]=>5 [1,0,1,0,1,1,1,0,0,0,1,0]=>6 [1,0,1,0,1,1,1,0,0,1,0,0]=>5 [1,0,1,0,1,1,1,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,1,0,0,0,0]=>6 [1,0,1,1,0,0,1,0,1,0,1,0]=>6 [1,0,1,1,0,0,1,0,1,1,0,0]=>6 [1,0,1,1,0,0,1,1,0,0,1,0]=>6 [1,0,1,1,0,0,1,1,0,1,0,0]=>5 [1,0,1,1,0,0,1,1,1,0,0,0]=>6 [1,0,1,1,0,1,0,0,1,0,1,0]=>5 [1,0,1,1,0,1,0,0,1,1,0,0]=>5 [1,0,1,1,0,1,0,1,0,0,1,0]=>5 [1,0,1,1,0,1,0,1,0,1,0,0]=>5 [1,0,1,1,0,1,0,1,1,0,0,0]=>5 [1,0,1,1,0,1,1,0,0,0,1,0]=>5 [1,0,1,1,0,1,1,0,0,1,0,0]=>5 [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]=>5 [1,0,1,1,1,0,0,0,1,0,1,0]=>6 [1,0,1,1,1,0,0,0,1,1,0,0]=>6 [1,0,1,1,1,0,0,1,0,0,1,0]=>5 [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]=>5 [1,0,1,1,1,0,1,0,0,0,1,0]=>4 [1,0,1,1,1,0,1,0,0,1,0,0]=>4 [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]=>4 [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]=>6 [1,1,0,0,1,0,1,0,1,0,1,0]=>6 [1,1,0,0,1,0,1,0,1,1,0,0]=>6 [1,1,0,0,1,0,1,1,0,0,1,0]=>6 [1,1,0,0,1,0,1,1,0,1,0,0]=>5 [1,1,0,0,1,0,1,1,1,0,0,0]=>6 [1,1,0,0,1,1,0,0,1,0,1,0]=>6 [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]=>5 [1,1,0,0,1,1,0,1,0,1,0,0]=>5 [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]=>6 [1,1,0,0,1,1,1,0,0,1,0,0]=>5 [1,1,0,0,1,1,1,0,1,0,0,0]=>4 [1,1,0,0,1,1,1,1,0,0,0,0]=>6 [1,1,0,1,0,0,1,0,1,0,1,0]=>5 [1,1,0,1,0,0,1,0,1,1,0,0]=>5 [1,1,0,1,0,0,1,1,0,0,1,0]=>5 [1,1,0,1,0,0,1,1,0,1,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,0,0]=>5 [1,1,0,1,0,1,0,0,1,0,1,0]=>5 [1,1,0,1,0,1,0,0,1,1,0,0]=>5 [1,1,0,1,0,1,0,1,0,0,1,0]=>5 [1,1,0,1,0,1,0,1,0,1,0,0]=>5 [1,1,0,1,0,1,0,1,1,0,0,0]=>5 [1,1,0,1,0,1,1,0,0,0,1,0]=>5 [1,1,0,1,0,1,1,0,0,1,0,0]=>5 [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]=>5 [1,1,0,1,1,0,0,0,1,0,1,0]=>5 [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]=>5 [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]=>5 [1,1,0,1,1,0,1,0,0,0,1,0]=>4 [1,1,0,1,1,0,1,0,0,1,0,0]=>4 [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]=>4 [1,1,0,1,1,1,0,0,0,0,1,0]=>5 [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]=>3 [1,1,0,1,1,1,1,0,0,0,0,0]=>5 [1,1,1,0,0,0,1,0,1,0,1,0]=>6 [1,1,1,0,0,0,1,0,1,1,0,0]=>6 [1,1,1,0,0,0,1,1,0,0,1,0]=>6 [1,1,1,0,0,0,1,1,0,1,0,0]=>5 [1,1,1,0,0,0,1,1,1,0,0,0]=>6 [1,1,1,0,0,1,0,0,1,0,1,0]=>5 [1,1,1,0,0,1,0,0,1,1,0,0]=>5 [1,1,1,0,0,1,0,1,0,0,1,0]=>5 [1,1,1,0,0,1,0,1,0,1,0,0]=>5 [1,1,1,0,0,1,0,1,1,0,0,0]=>5 [1,1,1,0,0,1,1,0,0,0,1,0]=>5 [1,1,1,0,0,1,1,0,0,1,0,0]=>5 [1,1,1,0,0,1,1,0,1,0,0,0]=>4 [1,1,1,0,0,1,1,1,0,0,0,0]=>5 [1,1,1,0,1,0,0,0,1,0,1,0]=>4 [1,1,1,0,1,0,0,0,1,1,0,0]=>4 [1,1,1,0,1,0,0,1,0,0,1,0]=>4 [1,1,1,0,1,0,0,1,0,1,0,0]=>4 [1,1,1,0,1,0,0,1,1,0,0,0]=>4 [1,1,1,0,1,0,1,0,0,0,1,0]=>4 [1,1,1,0,1,0,1,0,0,1,0,0]=>4 [1,1,1,0,1,0,1,0,1,0,0,0]=>4 [1,1,1,0,1,0,1,1,0,0,0,0]=>4 [1,1,1,0,1,1,0,0,0,0,1,0]=>4 [1,1,1,0,1,1,0,0,0,1,0,0]=>4 [1,1,1,0,1,1,0,0,1,0,0,0]=>4 [1,1,1,0,1,1,0,1,0,0,0,0]=>3 [1,1,1,0,1,1,1,0,0,0,0,0]=>4 [1,1,1,1,0,0,0,0,1,0,1,0]=>6 [1,1,1,1,0,0,0,0,1,1,0,0]=>6 [1,1,1,1,0,0,0,1,0,0,1,0]=>5 [1,1,1,1,0,0,0,1,0,1,0,0]=>5 [1,1,1,1,0,0,0,1,1,0,0,0]=>5 [1,1,1,1,0,0,1,0,0,0,1,0]=>4 [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]=>4 [1,1,1,1,0,0,1,1,0,0,0,0]=>4 [1,1,1,1,0,1,0,0,0,0,1,0]=>3 [1,1,1,1,0,1,0,0,0,1,0,0]=>3 [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]=>3 [1,1,1,1,0,1,1,0,0,0,0,0]=>3 [1,1,1,1,1,0,0,0,0,0,1,0]=>6 [1,1,1,1,1,0,0,0,0,1,0,0]=>5 [1,1,1,1,1,0,0,0,1,0,0,0]=>4 [1,1,1,1,1,0,0,1,0,0,0,0]=>3 [1,1,1,1,1,0,1,0,0,0,0,0]=>2 [1,1,1,1,1,1,0,0,0,0,0,0]=>6
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Description
The pyramid weight of the Dyck path.
The pyramid weight of a Dyck path is the sum of the lengths of the maximal pyramids (maximal sequences of the form $1^h0^h$) in the path.
Maximal pyramids are called lower interactions by Le Borgne [2], see St000331The number of upper interactions of a Dyck path. and St000335The difference of lower and upper interactions. for related statistics.
References
[1] Denise, A., Simion, R. Two combinatorial statistics on Dyck paths MathSciNet:1312450
[2] Le Borgne, Y. Counting upper interactions in Dyck paths MathSciNet:2196524
Code
def statistic(x):
    return x.pyramid_weight()
Created
Jul 01, 2013 at 12:03 by Olivier Mallet
Updated
Apr 07, 2016 at 08:33 by Martin Rubey