Identifier
Values
=>
[1]=>1
[1,1]=>1
[2]=>2
[1,1,1]=>1
[1,2]=>2
[2,1]=>2
[3]=>3
[1,1,1,1]=>1
[1,1,2]=>2
[1,2,1]=>2
[1,3]=>3
[2,1,1]=>2
[2,2]=>2
[3,1]=>3
[4]=>4
[1,1,1,1,1]=>1
[1,1,1,2]=>2
[1,1,2,1]=>2
[1,1,3]=>3
[1,2,1,1]=>2
[1,2,2]=>2
[1,3,1]=>3
[1,4]=>4
[2,1,1,1]=>2
[2,1,2]=>3
[2,2,1]=>2
[2,3]=>3
[3,1,1]=>3
[3,2]=>3
[4,1]=>4
[5]=>5
[1,1,1,1,1,1]=>1
[1,1,1,1,2]=>2
[1,1,1,2,1]=>2
[1,1,1,3]=>3
[1,1,2,1,1]=>2
[1,1,2,2]=>2
[1,1,3,1]=>3
[1,1,4]=>4
[1,2,1,1,1]=>2
[1,2,1,2]=>3
[1,2,2,1]=>2
[1,2,3]=>3
[1,3,1,1]=>3
[1,3,2]=>3
[1,4,1]=>4
[1,5]=>5
[2,1,1,1,1]=>2
[2,1,1,2]=>3
[2,1,2,1]=>3
[2,1,3]=>4
[2,2,1,1]=>2
[2,2,2]=>2
[2,3,1]=>3
[2,4]=>4
[3,1,1,1]=>3
[3,1,2]=>4
[3,2,1]=>3
[3,3]=>3
[4,1,1]=>4
[4,2]=>4
[5,1]=>5
[6]=>6
[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,2]=>2
[1,1,1,1,2,1]=>2
[1,1,1,1,3]=>3
[1,1,1,2,1,1]=>2
[1,1,1,2,2]=>2
[1,1,1,3,1]=>3
[1,1,1,4]=>4
[1,1,2,1,1,1]=>2
[1,1,2,1,2]=>3
[1,1,2,2,1]=>2
[1,1,2,3]=>3
[1,1,3,1,1]=>3
[1,1,3,2]=>3
[1,1,4,1]=>4
[1,1,5]=>5
[1,2,1,1,1,1]=>2
[1,2,1,1,2]=>3
[1,2,1,2,1]=>3
[1,2,1,3]=>4
[1,2,2,1,1]=>2
[1,2,2,2]=>2
[1,2,3,1]=>3
[1,2,4]=>4
[1,3,1,1,1]=>3
[1,3,1,2]=>4
[1,3,2,1]=>3
[1,3,3]=>3
[1,4,1,1]=>4
[1,4,2]=>4
[1,5,1]=>5
[1,6]=>6
[2,1,1,1,1,1]=>2
[2,1,1,1,2]=>3
[2,1,1,2,1]=>3
[2,1,1,3]=>4
[2,1,2,1,1]=>3
[2,1,2,2]=>3
[2,1,3,1]=>4
[2,1,4]=>5
[2,2,1,1,1]=>2
[2,2,1,2]=>3
[2,2,2,1]=>2
[2,2,3]=>3
[2,3,1,1]=>3
[2,3,2]=>3
[2,4,1]=>4
[2,5]=>5
[3,1,1,1,1]=>3
[3,1,1,2]=>4
[3,1,2,1]=>4
[3,1,3]=>5
[3,2,1,1]=>3
[3,2,2]=>3
[3,3,1]=>3
[3,4]=>4
[4,1,1,1]=>4
[4,1,2]=>5
[4,2,1]=>4
[4,3]=>4
[5,1,1]=>5
[5,2]=>5
[6,1]=>6
[7]=>7
[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,2]=>2
[1,1,1,1,1,2,1]=>2
[1,1,1,1,1,3]=>3
[1,1,1,1,2,1,1]=>2
[1,1,1,1,2,2]=>2
[1,1,1,1,3,1]=>3
[1,1,1,1,4]=>4
[1,1,1,2,1,1,1]=>2
[1,1,1,2,1,2]=>3
[1,1,1,2,2,1]=>2
[1,1,1,2,3]=>3
[1,1,1,3,1,1]=>3
[1,1,1,3,2]=>3
[1,1,1,4,1]=>4
[1,1,1,5]=>5
[1,1,2,1,1,1,1]=>2
[1,1,2,1,1,2]=>3
[1,1,2,1,2,1]=>3
[1,1,2,1,3]=>4
[1,1,2,2,1,1]=>2
[1,1,2,2,2]=>2
[1,1,2,3,1]=>3
[1,1,2,4]=>4
[1,1,3,1,1,1]=>3
[1,1,3,1,2]=>4
[1,1,3,2,1]=>3
[1,1,3,3]=>3
[1,1,4,1,1]=>4
[1,1,4,2]=>4
[1,1,5,1]=>5
[1,1,6]=>6
[1,2,1,1,1,1,1]=>2
[1,2,1,1,1,2]=>3
[1,2,1,1,2,1]=>3
[1,2,1,1,3]=>4
[1,2,1,2,1,1]=>3
[1,2,1,2,2]=>3
[1,2,1,3,1]=>4
[1,2,1,4]=>5
[1,2,2,1,1,1]=>2
[1,2,2,1,2]=>3
[1,2,2,2,1]=>2
[1,2,2,3]=>3
[1,2,3,1,1]=>3
[1,2,3,2]=>3
[1,2,4,1]=>4
[1,2,5]=>5
[1,3,1,1,1,1]=>3
[1,3,1,1,2]=>4
[1,3,1,2,1]=>4
[1,3,1,3]=>5
[1,3,2,1,1]=>3
[1,3,2,2]=>3
[1,3,3,1]=>3
[1,3,4]=>4
[1,4,1,1,1]=>4
[1,4,1,2]=>5
[1,4,2,1]=>4
[1,4,3]=>4
[1,5,1,1]=>5
[1,5,2]=>5
[1,6,1]=>6
[1,7]=>7
[2,1,1,1,1,1,1]=>2
[2,1,1,1,1,2]=>3
[2,1,1,1,2,1]=>3
[2,1,1,1,3]=>4
[2,1,1,2,1,1]=>3
[2,1,1,2,2]=>3
[2,1,1,3,1]=>4
[2,1,1,4]=>5
[2,1,2,1,1,1]=>3
[2,1,2,1,2]=>4
[2,1,2,2,1]=>3
[2,1,2,3]=>4
[2,1,3,1,1]=>4
[2,1,3,2]=>4
[2,1,4,1]=>5
[2,1,5]=>6
[2,2,1,1,1,1]=>2
[2,2,1,1,2]=>3
[2,2,1,2,1]=>3
[2,2,1,3]=>4
[2,2,2,1,1]=>2
[2,2,2,2]=>2
[2,2,3,1]=>3
[2,2,4]=>4
[2,3,1,1,1]=>3
[2,3,1,2]=>4
[2,3,2,1]=>3
[2,3,3]=>3
[2,4,1,1]=>4
[2,4,2]=>4
[2,5,1]=>5
[2,6]=>6
[3,1,1,1,1,1]=>3
[3,1,1,1,2]=>4
[3,1,1,2,1]=>4
[3,1,1,3]=>5
[3,1,2,1,1]=>4
[3,1,2,2]=>4
[3,1,3,1]=>5
[3,1,4]=>6
[3,2,1,1,1]=>3
[3,2,1,2]=>4
[3,2,2,1]=>3
[3,2,3]=>4
[3,3,1,1]=>3
[3,3,2]=>3
[3,4,1]=>4
[3,5]=>5
[4,1,1,1,1]=>4
[4,1,1,2]=>5
[4,1,2,1]=>5
[4,1,3]=>6
[4,2,1,1]=>4
[4,2,2]=>4
[4,3,1]=>4
[4,4]=>4
[5,1,1,1]=>5
[5,1,2]=>6
[5,2,1]=>5
[5,3]=>5
[6,1,1]=>6
[6,2]=>6
[7,1]=>7
[8]=>8
[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,2]=>2
[1,1,1,1,1,1,2,1]=>2
[1,1,1,1,1,1,3]=>3
[1,1,1,1,1,2,1,1]=>2
[1,1,1,1,1,2,2]=>2
[1,1,1,1,1,3,1]=>3
[1,1,1,1,1,4]=>4
[1,1,1,1,2,1,1,1]=>2
[1,1,1,1,2,1,2]=>3
[1,1,1,1,2,2,1]=>2
[1,1,1,1,2,3]=>3
[1,1,1,1,3,1,1]=>3
[1,1,1,1,3,2]=>3
[1,1,1,1,4,1]=>4
[1,1,1,1,5]=>5
[1,1,1,2,1,1,1,1]=>2
[1,1,1,2,1,1,2]=>3
[1,1,1,2,1,2,1]=>3
[1,1,1,2,1,3]=>4
[1,1,1,2,2,1,1]=>2
[1,1,1,2,2,2]=>2
[1,1,1,2,3,1]=>3
[1,1,1,2,4]=>4
[1,1,1,3,1,1,1]=>3
[1,1,1,3,1,2]=>4
[1,1,1,3,2,1]=>3
[1,1,1,3,3]=>3
[1,1,1,4,1,1]=>4
[1,1,1,4,2]=>4
[1,1,1,5,1]=>5
[1,1,1,6]=>6
[1,1,2,1,1,1,1,1]=>2
[1,1,2,1,1,1,2]=>3
[1,1,2,1,1,2,1]=>3
[1,1,2,1,1,3]=>4
[1,1,2,1,2,1,1]=>3
[1,1,2,1,2,2]=>3
[1,1,2,1,3,1]=>4
[1,1,2,1,4]=>5
[1,1,2,2,1,1,1]=>2
[1,1,2,2,1,2]=>3
[1,1,2,2,2,1]=>2
[1,1,2,2,3]=>3
[1,1,2,3,1,1]=>3
[1,1,2,3,2]=>3
[1,1,2,4,1]=>4
[1,1,2,5]=>5
[1,1,3,1,1,1,1]=>3
[1,1,3,1,1,2]=>4
[1,1,3,1,2,1]=>4
[1,1,3,1,3]=>5
[1,1,3,2,1,1]=>3
[1,1,3,2,2]=>3
[1,1,3,3,1]=>3
[1,1,3,4]=>4
[1,1,4,1,1,1]=>4
[1,1,4,1,2]=>5
[1,1,4,2,1]=>4
[1,1,4,3]=>4
[1,1,5,1,1]=>5
[1,1,5,2]=>5
[1,1,6,1]=>6
[1,1,7]=>7
[1,2,1,1,1,1,1,1]=>2
[1,2,1,1,1,1,2]=>3
[1,2,1,1,1,2,1]=>3
[1,2,1,1,1,3]=>4
[1,2,1,1,2,1,1]=>3
[1,2,1,1,2,2]=>3
[1,2,1,1,3,1]=>4
[1,2,1,1,4]=>5
[1,2,1,2,1,1,1]=>3
[1,2,1,2,1,2]=>4
[1,2,1,2,2,1]=>3
[1,2,1,2,3]=>4
[1,2,1,3,1,1]=>4
[1,2,1,3,2]=>4
[1,2,1,4,1]=>5
[1,2,1,5]=>6
[1,2,2,1,1,1,1]=>2
[1,2,2,1,1,2]=>3
[1,2,2,1,2,1]=>3
[1,2,2,1,3]=>4
[1,2,2,2,1,1]=>2
[1,2,2,2,2]=>2
[1,2,2,3,1]=>3
[1,2,2,4]=>4
[1,2,3,1,1,1]=>3
[1,2,3,1,2]=>4
[1,2,3,2,1]=>3
[1,2,3,3]=>3
[1,2,4,1,1]=>4
[1,2,4,2]=>4
[1,2,5,1]=>5
[1,2,6]=>6
[1,3,1,1,1,1,1]=>3
[1,3,1,1,1,2]=>4
[1,3,1,1,2,1]=>4
[1,3,1,1,3]=>5
[1,3,1,2,1,1]=>4
[1,3,1,2,2]=>4
[1,3,1,3,1]=>5
[1,3,1,4]=>6
[1,3,2,1,1,1]=>3
[1,3,2,1,2]=>4
[1,3,2,2,1]=>3
[1,3,2,3]=>4
[1,3,3,1,1]=>3
[1,3,3,2]=>3
[1,3,4,1]=>4
[1,3,5]=>5
[1,4,1,1,1,1]=>4
[1,4,1,1,2]=>5
[1,4,1,2,1]=>5
[1,4,1,3]=>6
[1,4,2,1,1]=>4
[1,4,2,2]=>4
[1,4,3,1]=>4
[1,4,4]=>4
[1,5,1,1,1]=>5
[1,5,1,2]=>6
[1,5,2,1]=>5
[1,5,3]=>5
[1,6,1,1]=>6
[1,6,2]=>6
[1,7,1]=>7
[1,8]=>8
[2,1,1,1,1,1,1,1]=>2
[2,1,1,1,1,1,2]=>3
[2,1,1,1,1,2,1]=>3
[2,1,1,1,1,3]=>4
[2,1,1,1,2,1,1]=>3
[2,1,1,1,2,2]=>3
[2,1,1,1,3,1]=>4
[2,1,1,1,4]=>5
[2,1,1,2,1,1,1]=>3
[2,1,1,2,1,2]=>4
[2,1,1,2,2,1]=>3
[2,1,1,2,3]=>4
[2,1,1,3,1,1]=>4
[2,1,1,3,2]=>4
[2,1,1,4,1]=>5
[2,1,1,5]=>6
[2,1,2,1,1,1,1]=>3
[2,1,2,1,1,2]=>4
[2,1,2,1,2,1]=>4
[2,1,2,1,3]=>5
[2,1,2,2,1,1]=>3
[2,1,2,2,2]=>3
[2,1,2,3,1]=>4
[2,1,2,4]=>5
[2,1,3,1,1,1]=>4
[2,1,3,1,2]=>5
[2,1,3,2,1]=>4
[2,1,3,3]=>4
[2,1,4,1,1]=>5
[2,1,4,2]=>5
[2,1,5,1]=>6
[2,1,6]=>7
[2,2,1,1,1,1,1]=>2
[2,2,1,1,1,2]=>3
[2,2,1,1,2,1]=>3
[2,2,1,1,3]=>4
[2,2,1,2,1,1]=>3
[2,2,1,2,2]=>3
[2,2,1,3,1]=>4
[2,2,1,4]=>5
[2,2,2,1,1,1]=>2
[2,2,2,1,2]=>3
[2,2,2,2,1]=>2
[2,2,2,3]=>3
[2,2,3,1,1]=>3
[2,2,3,2]=>3
[2,2,4,1]=>4
[2,2,5]=>5
[2,3,1,1,1,1]=>3
[2,3,1,1,2]=>4
[2,3,1,2,1]=>4
[2,3,1,3]=>5
[2,3,2,1,1]=>3
[2,3,2,2]=>3
[2,3,3,1]=>3
[2,3,4]=>4
[2,4,1,1,1]=>4
[2,4,1,2]=>5
[2,4,2,1]=>4
[2,4,3]=>4
[2,5,1,1]=>5
[2,5,2]=>5
[2,6,1]=>6
[2,7]=>7
[3,1,1,1,1,1,1]=>3
[3,1,1,1,1,2]=>4
[3,1,1,1,2,1]=>4
[3,1,1,1,3]=>5
[3,1,1,2,1,1]=>4
[3,1,1,2,2]=>4
[3,1,1,3,1]=>5
[3,1,1,4]=>6
[3,1,2,1,1,1]=>4
[3,1,2,1,2]=>5
[3,1,2,2,1]=>4
[3,1,2,3]=>5
[3,1,3,1,1]=>5
[3,1,3,2]=>5
[3,1,4,1]=>6
[3,1,5]=>7
[3,2,1,1,1,1]=>3
[3,2,1,1,2]=>4
[3,2,1,2,1]=>4
[3,2,1,3]=>5
[3,2,2,1,1]=>3
[3,2,2,2]=>3
[3,2,3,1]=>4
[3,2,4]=>5
[3,3,1,1,1]=>3
[3,3,1,2]=>4
[3,3,2,1]=>3
[3,3,3]=>3
[3,4,1,1]=>4
[3,4,2]=>4
[3,5,1]=>5
[3,6]=>6
[4,1,1,1,1,1]=>4
[4,1,1,1,2]=>5
[4,1,1,2,1]=>5
[4,1,1,3]=>6
[4,1,2,1,1]=>5
[4,1,2,2]=>5
[4,1,3,1]=>6
[4,1,4]=>7
[4,2,1,1,1]=>4
[4,2,1,2]=>5
[4,2,2,1]=>4
[4,2,3]=>5
[4,3,1,1]=>4
[4,3,2]=>4
[4,4,1]=>4
[4,5]=>5
[5,1,1,1,1]=>5
[5,1,1,2]=>6
[5,1,2,1]=>6
[5,1,3]=>7
[5,2,1,1]=>5
[5,2,2]=>5
[5,3,1]=>5
[5,4]=>5
[6,1,1,1]=>6
[6,1,2]=>7
[6,2,1]=>6
[6,3]=>6
[7,1,1]=>7
[7,2]=>7
[8,1]=>8
[9]=>9
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Description
The number of up steps of the associated bargraph.
Interpret the composition as the sequence of heights of the bars of a bargraph. This statistic is the number of up steps.
Interpret the composition as the sequence of heights of the bars of a bargraph. This statistic is the number of up steps.
References
[1] Deutsch, E., Elizalde, S. A bijection between bargraphs and Dyck paths arXiv:1705.05984
Code
def statistic(c):
if len(c) == 0:
return 0
U = c[0]
for i in range(1, len(c)):
if c[i] > c[i-1]:
U += c[i]-c[i-1]
return U
Created
May 18, 2017 at 09:45 by Martin Rubey
Updated
Nov 19, 2017 at 22:04 by Christian Stump
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