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Identifier
Values
=>
[1]=>1 [1,1]=>1 [2]=>1 [1,1,1]=>1 [1,2]=>1 [2,1]=>1 [3]=>1 [1,1,1,1]=>1 [1,1,2]=>1 [1,2,1]=>1 [1,3]=>1 [2,1,1]=>1 [2,2]=>1 [3,1]=>1 [4]=>1 [1,1,1,1,1]=>1 [1,1,1,2]=>1 [1,1,2,1]=>1 [1,1,3]=>1 [1,2,1,1]=>1 [1,2,2]=>1 [1,3,1]=>1 [1,4]=>1 [2,1,1,1]=>1 [2,1,2]=>2 [2,2,1]=>1 [2,3]=>1 [3,1,1]=>1 [3,2]=>1 [4,1]=>1 [5]=>1 [1,1,1,1,1,1]=>1 [1,1,1,1,2]=>1 [1,1,1,2,1]=>1 [1,1,1,3]=>1 [1,1,2,1,1]=>1 [1,1,2,2]=>1 [1,1,3,1]=>1 [1,1,4]=>1 [1,2,1,1,1]=>1 [1,2,1,2]=>2 [1,2,2,1]=>1 [1,2,3]=>1 [1,3,1,1]=>1 [1,3,2]=>1 [1,4,1]=>1 [1,5]=>1 [2,1,1,1,1]=>1 [2,1,1,2]=>2 [2,1,2,1]=>2 [2,1,3]=>2 [2,2,1,1]=>1 [2,2,2]=>1 [2,3,1]=>1 [2,4]=>1 [3,1,1,1]=>1 [3,1,2]=>2 [3,2,1]=>1 [3,3]=>1 [4,1,1]=>1 [4,2]=>1 [5,1]=>1 [6]=>1 [1,1,1,1,1,1,1]=>1 [1,1,1,1,1,2]=>1 [1,1,1,1,2,1]=>1 [1,1,1,1,3]=>1 [1,1,1,2,1,1]=>1 [1,1,1,2,2]=>1 [1,1,1,3,1]=>1 [1,1,1,4]=>1 [1,1,2,1,1,1]=>1 [1,1,2,1,2]=>2 [1,1,2,2,1]=>1 [1,1,2,3]=>1 [1,1,3,1,1]=>1 [1,1,3,2]=>1 [1,1,4,1]=>1 [1,1,5]=>1 [1,2,1,1,1,1]=>1 [1,2,1,1,2]=>2 [1,2,1,2,1]=>2 [1,2,1,3]=>2 [1,2,2,1,1]=>1 [1,2,2,2]=>1 [1,2,3,1]=>1 [1,2,4]=>1 [1,3,1,1,1]=>1 [1,3,1,2]=>2 [1,3,2,1]=>1 [1,3,3]=>1 [1,4,1,1]=>1 [1,4,2]=>1 [1,5,1]=>1 [1,6]=>1 [2,1,1,1,1,1]=>1 [2,1,1,1,2]=>2 [2,1,1,2,1]=>2 [2,1,1,3]=>2 [2,1,2,1,1]=>2 [2,1,2,2]=>2 [2,1,3,1]=>2 [2,1,4]=>2 [2,2,1,1,1]=>1 [2,2,1,2]=>2 [2,2,2,1]=>1 [2,2,3]=>1 [2,3,1,1]=>1 [2,3,2]=>1 [2,4,1]=>1 [2,5]=>1 [3,1,1,1,1]=>1 [3,1,1,2]=>2 [3,1,2,1]=>2 [3,1,3]=>2 [3,2,1,1]=>1 [3,2,2]=>1 [3,3,1]=>1 [3,4]=>1 [4,1,1,1]=>1 [4,1,2]=>2 [4,2,1]=>1 [4,3]=>1 [5,1,1]=>1 [5,2]=>1 [6,1]=>1 [7]=>1 [1,1,1,1,1,1,1,1]=>1 [1,1,1,1,1,1,2]=>1 [1,1,1,1,1,2,1]=>1 [1,1,1,1,1,3]=>1 [1,1,1,1,2,1,1]=>1 [1,1,1,1,2,2]=>1 [1,1,1,1,3,1]=>1 [1,1,1,1,4]=>1 [1,1,1,2,1,1,1]=>1 [1,1,1,2,1,2]=>2 [1,1,1,2,2,1]=>1 [1,1,1,2,3]=>1 [1,1,1,3,1,1]=>1 [1,1,1,3,2]=>1 [1,1,1,4,1]=>1 [1,1,1,5]=>1 [1,1,2,1,1,1,1]=>1 [1,1,2,1,1,2]=>2 [1,1,2,1,2,1]=>2 [1,1,2,1,3]=>2 [1,1,2,2,1,1]=>1 [1,1,2,2,2]=>1 [1,1,2,3,1]=>1 [1,1,2,4]=>1 [1,1,3,1,1,1]=>1 [1,1,3,1,2]=>2 [1,1,3,2,1]=>1 [1,1,3,3]=>1 [1,1,4,1,1]=>1 [1,1,4,2]=>1 [1,1,5,1]=>1 [1,1,6]=>1 [1,2,1,1,1,1,1]=>1 [1,2,1,1,1,2]=>2 [1,2,1,1,2,1]=>2 [1,2,1,1,3]=>2 [1,2,1,2,1,1]=>2 [1,2,1,2,2]=>2 [1,2,1,3,1]=>2 [1,2,1,4]=>2 [1,2,2,1,1,1]=>1 [1,2,2,1,2]=>2 [1,2,2,2,1]=>1 [1,2,2,3]=>1 [1,2,3,1,1]=>1 [1,2,3,2]=>1 [1,2,4,1]=>1 [1,2,5]=>1 [1,3,1,1,1,1]=>1 [1,3,1,1,2]=>2 [1,3,1,2,1]=>2 [1,3,1,3]=>2 [1,3,2,1,1]=>1 [1,3,2,2]=>1 [1,3,3,1]=>1 [1,3,4]=>1 [1,4,1,1,1]=>1 [1,4,1,2]=>2 [1,4,2,1]=>1 [1,4,3]=>1 [1,5,1,1]=>1 [1,5,2]=>1 [1,6,1]=>1 [1,7]=>1 [2,1,1,1,1,1,1]=>1 [2,1,1,1,1,2]=>2 [2,1,1,1,2,1]=>2 [2,1,1,1,3]=>2 [2,1,1,2,1,1]=>2 [2,1,1,2,2]=>2 [2,1,1,3,1]=>2 [2,1,1,4]=>2 [2,1,2,1,1,1]=>2 [2,1,2,1,2]=>3 [2,1,2,2,1]=>2 [2,1,2,3]=>2 [2,1,3,1,1]=>2 [2,1,3,2]=>2 [2,1,4,1]=>2 [2,1,5]=>2 [2,2,1,1,1,1]=>1 [2,2,1,1,2]=>2 [2,2,1,2,1]=>2 [2,2,1,3]=>2 [2,2,2,1,1]=>1 [2,2,2,2]=>1 [2,2,3,1]=>1 [2,2,4]=>1 [2,3,1,1,1]=>1 [2,3,1,2]=>2 [2,3,2,1]=>1 [2,3,3]=>1 [2,4,1,1]=>1 [2,4,2]=>1 [2,5,1]=>1 [2,6]=>1 [3,1,1,1,1,1]=>1 [3,1,1,1,2]=>2 [3,1,1,2,1]=>2 [3,1,1,3]=>2 [3,1,2,1,1]=>2 [3,1,2,2]=>2 [3,1,3,1]=>2 [3,1,4]=>2 [3,2,1,1,1]=>1 [3,2,1,2]=>2 [3,2,2,1]=>1 [3,2,3]=>2 [3,3,1,1]=>1 [3,3,2]=>1 [3,4,1]=>1 [3,5]=>1 [4,1,1,1,1]=>1 [4,1,1,2]=>2 [4,1,2,1]=>2 [4,1,3]=>2 [4,2,1,1]=>1 [4,2,2]=>1 [4,3,1]=>1 [4,4]=>1 [5,1,1,1]=>1 [5,1,2]=>2 [5,2,1]=>1 [5,3]=>1 [6,1,1]=>1 [6,2]=>1 [7,1]=>1 [8]=>1 [1,1,1,1,1,1,1,1,1]=>1 [1,1,1,1,1,1,1,2]=>1 [1,1,1,1,1,1,2,1]=>1 [1,1,1,1,1,1,3]=>1 [1,1,1,1,1,2,1,1]=>1 [1,1,1,1,1,2,2]=>1 [1,1,1,1,1,3,1]=>1 [1,1,1,1,1,4]=>1 [1,1,1,1,2,1,1,1]=>1 [1,1,1,1,2,1,2]=>2 [1,1,1,1,2,2,1]=>1 [1,1,1,1,2,3]=>1 [1,1,1,1,3,1,1]=>1 [1,1,1,1,3,2]=>1 [1,1,1,1,4,1]=>1 [1,1,1,1,5]=>1 [1,1,1,2,1,1,1,1]=>1 [1,1,1,2,1,1,2]=>2 [1,1,1,2,1,2,1]=>2 [1,1,1,2,1,3]=>2 [1,1,1,2,2,1,1]=>1 [1,1,1,2,2,2]=>1 [1,1,1,2,3,1]=>1 [1,1,1,2,4]=>1 [1,1,1,3,1,1,1]=>1 [1,1,1,3,1,2]=>2 [1,1,1,3,2,1]=>1 [1,1,1,3,3]=>1 [1,1,1,4,1,1]=>1 [1,1,1,4,2]=>1 [1,1,1,5,1]=>1 [1,1,1,6]=>1 [1,1,2,1,1,1,1,1]=>1 [1,1,2,1,1,1,2]=>2 [1,1,2,1,1,2,1]=>2 [1,1,2,1,1,3]=>2 [1,1,2,1,2,1,1]=>2 [1,1,2,1,2,2]=>2 [1,1,2,1,3,1]=>2 [1,1,2,1,4]=>2 [1,1,2,2,1,1,1]=>1 [1,1,2,2,1,2]=>2 [1,1,2,2,2,1]=>1 [1,1,2,2,3]=>1 [1,1,2,3,1,1]=>1 [1,1,2,3,2]=>1 [1,1,2,4,1]=>1 [1,1,2,5]=>1 [1,1,3,1,1,1,1]=>1 [1,1,3,1,1,2]=>2 [1,1,3,1,2,1]=>2 [1,1,3,1,3]=>2 [1,1,3,2,1,1]=>1 [1,1,3,2,2]=>1 [1,1,3,3,1]=>1 [1,1,3,4]=>1 [1,1,4,1,1,1]=>1 [1,1,4,1,2]=>2 [1,1,4,2,1]=>1 [1,1,4,3]=>1 [1,1,5,1,1]=>1 [1,1,5,2]=>1 [1,1,6,1]=>1 [1,1,7]=>1 [1,2,1,1,1,1,1,1]=>1 [1,2,1,1,1,1,2]=>2 [1,2,1,1,1,2,1]=>2 [1,2,1,1,1,3]=>2 [1,2,1,1,2,1,1]=>2 [1,2,1,1,2,2]=>2 [1,2,1,1,3,1]=>2 [1,2,1,1,4]=>2 [1,2,1,2,1,1,1]=>2 [1,2,1,2,1,2]=>3 [1,2,1,2,2,1]=>2 [1,2,1,2,3]=>2 [1,2,1,3,1,1]=>2 [1,2,1,3,2]=>2 [1,2,1,4,1]=>2 [1,2,1,5]=>2 [1,2,2,1,1,1,1]=>1 [1,2,2,1,1,2]=>2 [1,2,2,1,2,1]=>2 [1,2,2,1,3]=>2 [1,2,2,2,1,1]=>1 [1,2,2,2,2]=>1 [1,2,2,3,1]=>1 [1,2,2,4]=>1 [1,2,3,1,1,1]=>1 [1,2,3,1,2]=>2 [1,2,3,2,1]=>1 [1,2,3,3]=>1 [1,2,4,1,1]=>1 [1,2,4,2]=>1 [1,2,5,1]=>1 [1,2,6]=>1 [1,3,1,1,1,1,1]=>1 [1,3,1,1,1,2]=>2 [1,3,1,1,2,1]=>2 [1,3,1,1,3]=>2 [1,3,1,2,1,1]=>2 [1,3,1,2,2]=>2 [1,3,1,3,1]=>2 [1,3,1,4]=>2 [1,3,2,1,1,1]=>1 [1,3,2,1,2]=>2 [1,3,2,2,1]=>1 [1,3,2,3]=>2 [1,3,3,1,1]=>1 [1,3,3,2]=>1 [1,3,4,1]=>1 [1,3,5]=>1 [1,4,1,1,1,1]=>1 [1,4,1,1,2]=>2 [1,4,1,2,1]=>2 [1,4,1,3]=>2 [1,4,2,1,1]=>1 [1,4,2,2]=>1 [1,4,3,1]=>1 [1,4,4]=>1 [1,5,1,1,1]=>1 [1,5,1,2]=>2 [1,5,2,1]=>1 [1,5,3]=>1 [1,6,1,1]=>1 [1,6,2]=>1 [1,7,1]=>1 [1,8]=>1 [2,1,1,1,1,1,1,1]=>1 [2,1,1,1,1,1,2]=>2 [2,1,1,1,1,2,1]=>2 [2,1,1,1,1,3]=>2 [2,1,1,1,2,1,1]=>2 [2,1,1,1,2,2]=>2 [2,1,1,1,3,1]=>2 [2,1,1,1,4]=>2 [2,1,1,2,1,1,1]=>2 [2,1,1,2,1,2]=>3 [2,1,1,2,2,1]=>2 [2,1,1,2,3]=>2 [2,1,1,3,1,1]=>2 [2,1,1,3,2]=>2 [2,1,1,4,1]=>2 [2,1,1,5]=>2 [2,1,2,1,1,1,1]=>2 [2,1,2,1,1,2]=>3 [2,1,2,1,2,1]=>3 [2,1,2,1,3]=>3 [2,1,2,2,1,1]=>2 [2,1,2,2,2]=>2 [2,1,2,3,1]=>2 [2,1,2,4]=>2 [2,1,3,1,1,1]=>2 [2,1,3,1,2]=>3 [2,1,3,2,1]=>2 [2,1,3,3]=>2 [2,1,4,1,1]=>2 [2,1,4,2]=>2 [2,1,5,1]=>2 [2,1,6]=>2 [2,2,1,1,1,1,1]=>1 [2,2,1,1,1,2]=>2 [2,2,1,1,2,1]=>2 [2,2,1,1,3]=>2 [2,2,1,2,1,1]=>2 [2,2,1,2,2]=>2 [2,2,1,3,1]=>2 [2,2,1,4]=>2 [2,2,2,1,1,1]=>1 [2,2,2,1,2]=>2 [2,2,2,2,1]=>1 [2,2,2,3]=>1 [2,2,3,1,1]=>1 [2,2,3,2]=>1 [2,2,4,1]=>1 [2,2,5]=>1 [2,3,1,1,1,1]=>1 [2,3,1,1,2]=>2 [2,3,1,2,1]=>2 [2,3,1,3]=>2 [2,3,2,1,1]=>1 [2,3,2,2]=>1 [2,3,3,1]=>1 [2,3,4]=>1 [2,4,1,1,1]=>1 [2,4,1,2]=>2 [2,4,2,1]=>1 [2,4,3]=>1 [2,5,1,1]=>1 [2,5,2]=>1 [2,6,1]=>1 [2,7]=>1 [3,1,1,1,1,1,1]=>1 [3,1,1,1,1,2]=>2 [3,1,1,1,2,1]=>2 [3,1,1,1,3]=>2 [3,1,1,2,1,1]=>2 [3,1,1,2,2]=>2 [3,1,1,3,1]=>2 [3,1,1,4]=>2 [3,1,2,1,1,1]=>2 [3,1,2,1,2]=>3 [3,1,2,2,1]=>2 [3,1,2,3]=>2 [3,1,3,1,1]=>2 [3,1,3,2]=>2 [3,1,4,1]=>2 [3,1,5]=>2 [3,2,1,1,1,1]=>1 [3,2,1,1,2]=>2 [3,2,1,2,1]=>2 [3,2,1,3]=>2 [3,2,2,1,1]=>1 [3,2,2,2]=>1 [3,2,3,1]=>2 [3,2,4]=>2 [3,3,1,1,1]=>1 [3,3,1,2]=>2 [3,3,2,1]=>1 [3,3,3]=>1 [3,4,1,1]=>1 [3,4,2]=>1 [3,5,1]=>1 [3,6]=>1 [4,1,1,1,1,1]=>1 [4,1,1,1,2]=>2 [4,1,1,2,1]=>2 [4,1,1,3]=>2 [4,1,2,1,1]=>2 [4,1,2,2]=>2 [4,1,3,1]=>2 [4,1,4]=>2 [4,2,1,1,1]=>1 [4,2,1,2]=>2 [4,2,2,1]=>1 [4,2,3]=>2 [4,3,1,1]=>1 [4,3,2]=>1 [4,4,1]=>1 [4,5]=>1 [5,1,1,1,1]=>1 [5,1,1,2]=>2 [5,1,2,1]=>2 [5,1,3]=>2 [5,2,1,1]=>1 [5,2,2]=>1 [5,3,1]=>1 [5,4]=>1 [6,1,1,1]=>1 [6,1,2]=>2 [6,2,1]=>1 [6,3]=>1 [7,1,1]=>1 [7,2]=>1 [8,1]=>1 [9]=>1
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Description
The number of peaks of the associated bargraph.
Interpret the composition as the sequence of heights of the bars of a bargraph. This statistic is the number of contiguous subsequences consisting of an up step, a sequence of horizontal steps, and a down step.
References
[1] Deutsch, E., Elizalde, S. A bijection between bargraphs and Dyck paths arXiv:1705.05984
Code
def statistic(c):
    c = [0] + list(c) + [0]
    pk = 0
    found_UH = False
    for i in range(1,len(c)):
        if found_UH:
            if c[i] < c[i-1]:
                found_UH = False
                pk += 1
        else:
            if c[i] > c[i-1]:
                found_UH = True
    return pk
Created
May 18, 2017 at 09:17 by Martin Rubey
Updated
Nov 19, 2017 at 22:05 by Christian Stump