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Identifier
Values
=>
[1,1]=>3 [2]=>1 [1,1,1]=>6 [1,2]=>3 [2,1]=>1 [3]=>1 [1,1,1,1]=>10 [1,1,2]=>6 [1,2,1]=>3 [1,3]=>3 [2,1,1]=>1 [2,2]=>3 [3,1]=>1 [4]=>1 [1,1,1,1,1]=>15 [1,1,1,2]=>10 [1,1,2,1]=>6 [1,1,3]=>6 [1,2,1,1]=>3 [1,2,2]=>6 [1,3,1]=>3 [1,4]=>3 [2,1,1,1]=>1 [2,1,2]=>4 [2,2,1]=>3 [2,3]=>3 [3,1,1]=>1 [3,2]=>1 [4,1]=>1 [5]=>1 [1,1,1,1,1,1]=>21 [1,1,1,1,2]=>15 [1,1,1,2,1]=>10 [1,1,1,3]=>10 [1,1,2,1,1]=>6 [1,1,2,2]=>10 [1,1,3,1]=>6 [1,1,4]=>6 [1,2,1,1,1]=>3 [1,2,1,2]=>7 [1,2,2,1]=>6 [1,2,3]=>6 [1,3,1,1]=>3 [1,3,2]=>3 [1,4,1]=>3 [1,5]=>3 [2,1,1,1,1]=>1 [2,1,1,2]=>5 [2,1,2,1]=>4 [2,1,3]=>4 [2,2,1,1]=>3 [2,2,2]=>6 [2,3,1]=>3 [2,4]=>3 [3,1,1,1]=>1 [3,1,2]=>1 [3,2,1]=>1 [3,3]=>3 [4,1,1]=>1 [4,2]=>1 [5,1]=>1 [6]=>1 [1,1,1,1,1,1,1]=>28 [1,1,1,1,1,2]=>21 [1,1,1,1,2,1]=>15 [1,1,1,1,3]=>15 [1,1,1,2,1,1]=>10 [1,1,1,2,2]=>15 [1,1,1,3,1]=>10 [1,1,1,4]=>10 [1,1,2,1,1,1]=>6 [1,1,2,1,2]=>11 [1,1,2,2,1]=>10 [1,1,2,3]=>10 [1,1,3,1,1]=>6 [1,1,3,2]=>6 [1,1,4,1]=>6 [1,1,5]=>6 [1,2,1,1,1,1]=>3 [1,2,1,1,2]=>8 [1,2,1,2,1]=>7 [1,2,1,3]=>7 [1,2,2,1,1]=>6 [1,2,2,2]=>10 [1,2,3,1]=>6 [1,2,4]=>6 [1,3,1,1,1]=>3 [1,3,1,2]=>3 [1,3,2,1]=>3 [1,3,3]=>6 [1,4,1,1]=>3 [1,4,2]=>3 [1,5,1]=>3 [1,6]=>3 [2,1,1,1,1,1]=>1 [2,1,1,1,2]=>6 [2,1,1,2,1]=>5 [2,1,1,3]=>5 [2,1,2,1,1]=>4 [2,1,2,2]=>8 [2,1,3,1]=>4 [2,1,4]=>4 [2,2,1,1,1]=>3 [2,2,1,2]=>7 [2,2,2,1]=>6 [2,2,3]=>6 [2,3,1,1]=>3 [2,3,2]=>3 [2,4,1]=>3 [2,5]=>3 [3,1,1,1,1]=>1 [3,1,1,2]=>1 [3,1,2,1]=>1 [3,1,3]=>4 [3,2,1,1]=>1 [3,2,2]=>1 [3,3,1]=>3 [3,4]=>3 [4,1,1,1]=>1 [4,1,2]=>1 [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]=>36 [1,1,1,1,1,1,2]=>28 [1,1,1,1,1,2,1]=>21 [1,1,1,1,1,3]=>21 [1,1,1,1,2,1,1]=>15 [1,1,1,1,2,2]=>21 [1,1,1,1,3,1]=>15 [1,1,1,1,4]=>15 [1,1,1,2,1,1,1]=>10 [1,1,1,2,1,2]=>16 [1,1,1,2,2,1]=>15 [1,1,1,2,3]=>15 [1,1,1,3,1,1]=>10 [1,1,1,3,2]=>10 [1,1,1,4,1]=>10 [1,1,1,5]=>10 [1,1,2,1,1,1,1]=>6 [1,1,2,1,1,2]=>12 [1,1,2,1,2,1]=>11 [1,1,2,1,3]=>11 [1,1,2,2,1,1]=>10 [1,1,2,2,2]=>15 [1,1,2,3,1]=>10 [1,1,2,4]=>10 [1,1,3,1,1,1]=>6 [1,1,3,1,2]=>6 [1,1,3,2,1]=>6 [1,1,3,3]=>10 [1,1,4,1,1]=>6 [1,1,4,2]=>6 [1,1,5,1]=>6 [1,1,6]=>6 [1,2,1,1,1,1,1]=>3 [1,2,1,1,1,2]=>9 [1,2,1,1,2,1]=>8 [1,2,1,1,3]=>8 [1,2,1,2,1,1]=>7 [1,2,1,2,2]=>12 [1,2,1,3,1]=>7 [1,2,1,4]=>7 [1,2,2,1,1,1]=>6 [1,2,2,1,2]=>11 [1,2,2,2,1]=>10 [1,2,2,3]=>10 [1,2,3,1,1]=>6 [1,2,3,2]=>6 [1,2,4,1]=>6 [1,2,5]=>6 [1,3,1,1,1,1]=>3 [1,3,1,1,2]=>3 [1,3,1,2,1]=>3 [1,3,1,3]=>7 [1,3,2,1,1]=>3 [1,3,2,2]=>3 [1,3,3,1]=>6 [1,3,4]=>6 [1,4,1,1,1]=>3 [1,4,1,2]=>3 [1,4,2,1]=>3 [1,4,3]=>3 [1,5,1,1]=>3 [1,5,2]=>3 [1,6,1]=>3 [1,7]=>3 [2,1,1,1,1,1,1]=>1 [2,1,1,1,1,2]=>7 [2,1,1,1,2,1]=>6 [2,1,1,1,3]=>6 [2,1,1,2,1,1]=>5 [2,1,1,2,2]=>10 [2,1,1,3,1]=>5 [2,1,1,4]=>5 [2,1,2,1,1,1]=>4 [2,1,2,1,2]=>9 [2,1,2,2,1]=>8 [2,1,2,3]=>8 [2,1,3,1,1]=>4 [2,1,3,2]=>4 [2,1,4,1]=>4 [2,1,5]=>4 [2,2,1,1,1,1]=>3 [2,2,1,1,2]=>8 [2,2,1,2,1]=>7 [2,2,1,3]=>7 [2,2,2,1,1]=>6 [2,2,2,2]=>10 [2,2,3,1]=>6 [2,2,4]=>6 [2,3,1,1,1]=>3 [2,3,1,2]=>3 [2,3,2,1]=>3 [2,3,3]=>6 [2,4,1,1]=>3 [2,4,2]=>3 [2,5,1]=>3 [2,6]=>3 [3,1,1,1,1,1]=>1 [3,1,1,1,2]=>1 [3,1,1,2,1]=>1 [3,1,1,3]=>5 [3,1,2,1,1]=>1 [3,1,2,2]=>1 [3,1,3,1]=>4 [3,1,4]=>4 [3,2,1,1,1]=>1 [3,2,1,2]=>1 [3,2,2,1]=>1 [3,2,3]=>4 [3,3,1,1]=>3 [3,3,2]=>3 [3,4,1]=>3 [3,5]=>3 [4,1,1,1,1]=>1 [4,1,1,2]=>1 [4,1,2,1]=>1 [4,1,3]=>1 [4,2,1,1]=>1 [4,2,2]=>1 [4,3,1]=>1 [4,4]=>3 [5,1,1,1]=>1 [5,1,2]=>1 [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]=>45 [1,1,1,1,1,1,1,2]=>36 [1,1,1,1,1,1,2,1]=>28 [1,1,1,1,1,1,3]=>28 [1,1,1,1,1,2,1,1]=>21 [1,1,1,1,1,2,2]=>28 [1,1,1,1,1,3,1]=>21 [1,1,1,1,1,4]=>21 [1,1,1,1,2,1,1,1]=>15 [1,1,1,1,2,1,2]=>22 [1,1,1,1,2,2,1]=>21 [1,1,1,1,2,3]=>21 [1,1,1,1,3,1,1]=>15 [1,1,1,1,3,2]=>15 [1,1,1,1,4,1]=>15 [1,1,1,1,5]=>15 [1,1,1,2,1,1,1,1]=>10 [1,1,1,2,1,1,2]=>17 [1,1,1,2,1,2,1]=>16 [1,1,1,2,1,3]=>16 [1,1,1,2,2,1,1]=>15 [1,1,1,2,2,2]=>21 [1,1,1,2,3,1]=>15 [1,1,1,2,4]=>15 [1,1,1,3,1,1,1]=>10 [1,1,1,3,1,2]=>10 [1,1,1,3,2,1]=>10 [1,1,1,3,3]=>15 [1,1,1,4,1,1]=>10 [1,1,1,4,2]=>10 [1,1,1,5,1]=>10 [1,1,1,6]=>10 [1,1,2,1,1,1,1,1]=>6 [1,1,2,1,1,1,2]=>13 [1,1,2,1,1,2,1]=>12 [1,1,2,1,1,3]=>12 [1,1,2,1,2,1,1]=>11 [1,1,2,1,2,2]=>17 [1,1,2,1,3,1]=>11 [1,1,2,1,4]=>11 [1,1,2,2,1,1,1]=>10 [1,1,2,2,1,2]=>16 [1,1,2,2,2,1]=>15 [1,1,2,2,3]=>15 [1,1,2,3,1,1]=>10 [1,1,2,3,2]=>10 [1,1,2,4,1]=>10 [1,1,2,5]=>10 [1,1,3,1,1,1,1]=>6 [1,1,3,1,1,2]=>6 [1,1,3,1,2,1]=>6 [1,1,3,1,3]=>11 [1,1,3,2,1,1]=>6 [1,1,3,2,2]=>6 [1,1,3,3,1]=>10 [1,1,3,4]=>10 [1,1,4,1,1,1]=>6 [1,1,4,1,2]=>6 [1,1,4,2,1]=>6 [1,1,4,3]=>6 [1,1,5,1,1]=>6 [1,1,5,2]=>6 [1,1,6,1]=>6 [1,1,7]=>6 [1,2,1,1,1,1,1,1]=>3 [1,2,1,1,1,1,2]=>10 [1,2,1,1,1,2,1]=>9 [1,2,1,1,1,3]=>9 [1,2,1,1,2,1,1]=>8 [1,2,1,1,2,2]=>14 [1,2,1,1,3,1]=>8 [1,2,1,1,4]=>8 [1,2,1,2,1,1,1]=>7 [1,2,1,2,1,2]=>13 [1,2,1,2,2,1]=>12 [1,2,1,2,3]=>12 [1,2,1,3,1,1]=>7 [1,2,1,3,2]=>7 [1,2,1,4,1]=>7 [1,2,1,5]=>7 [1,2,2,1,1,1,1]=>6 [1,2,2,1,1,2]=>12 [1,2,2,1,2,1]=>11 [1,2,2,1,3]=>11 [1,2,2,2,1,1]=>10 [1,2,2,2,2]=>15 [1,2,2,3,1]=>10 [1,2,2,4]=>10 [1,2,3,1,1,1]=>6 [1,2,3,1,2]=>6 [1,2,3,2,1]=>6 [1,2,3,3]=>10 [1,2,4,1,1]=>6 [1,2,4,2]=>6 [1,2,5,1]=>6 [1,2,6]=>6 [1,3,1,1,1,1,1]=>3 [1,3,1,1,1,2]=>3 [1,3,1,1,2,1]=>3 [1,3,1,1,3]=>8 [1,3,1,2,1,1]=>3 [1,3,1,2,2]=>3 [1,3,1,3,1]=>7 [1,3,1,4]=>7 [1,3,2,1,1,1]=>3 [1,3,2,1,2]=>3 [1,3,2,2,1]=>3 [1,3,2,3]=>7 [1,3,3,1,1]=>6 [1,3,3,2]=>6 [1,3,4,1]=>6 [1,3,5]=>6 [1,4,1,1,1,1]=>3 [1,4,1,1,2]=>3 [1,4,1,2,1]=>3 [1,4,1,3]=>3 [1,4,2,1,1]=>3 [1,4,2,2]=>3 [1,4,3,1]=>3 [1,4,4]=>6 [1,5,1,1,1]=>3 [1,5,1,2]=>3 [1,5,2,1]=>3 [1,5,3]=>3 [1,6,1,1]=>3 [1,6,2]=>3 [1,7,1]=>3 [1,8]=>3 [2,1,1,1,1,1,1,1]=>1 [2,1,1,1,1,1,2]=>8 [2,1,1,1,1,2,1]=>7 [2,1,1,1,1,3]=>7 [2,1,1,1,2,1,1]=>6 [2,1,1,1,2,2]=>12 [2,1,1,1,3,1]=>6 [2,1,1,1,4]=>6 [2,1,1,2,1,1,1]=>5 [2,1,1,2,1,2]=>11 [2,1,1,2,2,1]=>10 [2,1,1,2,3]=>10 [2,1,1,3,1,1]=>5 [2,1,1,3,2]=>5 [2,1,1,4,1]=>5 [2,1,1,5]=>5 [2,1,2,1,1,1,1]=>4 [2,1,2,1,1,2]=>10 [2,1,2,1,2,1]=>9 [2,1,2,1,3]=>9 [2,1,2,2,1,1]=>8 [2,1,2,2,2]=>13 [2,1,2,3,1]=>8 [2,1,2,4]=>8 [2,1,3,1,1,1]=>4 [2,1,3,1,2]=>4 [2,1,3,2,1]=>4 [2,1,3,3]=>8 [2,1,4,1,1]=>4 [2,1,4,2]=>4 [2,1,5,1]=>4 [2,1,6]=>4 [2,2,1,1,1,1,1]=>3 [2,2,1,1,1,2]=>9 [2,2,1,1,2,1]=>8 [2,2,1,1,3]=>8 [2,2,1,2,1,1]=>7 [2,2,1,2,2]=>12 [2,2,1,3,1]=>7 [2,2,1,4]=>7 [2,2,2,1,1,1]=>6 [2,2,2,1,2]=>11 [2,2,2,2,1]=>10 [2,2,2,3]=>10 [2,2,3,1,1]=>6 [2,2,3,2]=>6 [2,2,4,1]=>6 [2,2,5]=>6 [2,3,1,1,1,1]=>3 [2,3,1,1,2]=>3 [2,3,1,2,1]=>3 [2,3,1,3]=>7 [2,3,2,1,1]=>3 [2,3,2,2]=>3 [2,3,3,1]=>6 [2,3,4]=>6 [2,4,1,1,1]=>3 [2,4,1,2]=>3 [2,4,2,1]=>3 [2,4,3]=>3 [2,5,1,1]=>3 [2,5,2]=>3 [2,6,1]=>3 [2,7]=>3 [3,1,1,1,1,1,1]=>1 [3,1,1,1,1,2]=>1 [3,1,1,1,2,1]=>1 [3,1,1,1,3]=>6 [3,1,1,2,1,1]=>1 [3,1,1,2,2]=>1 [3,1,1,3,1]=>5 [3,1,1,4]=>5 [3,1,2,1,1,1]=>1 [3,1,2,1,2]=>1 [3,1,2,2,1]=>1 [3,1,2,3]=>5 [3,1,3,1,1]=>4 [3,1,3,2]=>4 [3,1,4,1]=>4 [3,1,5]=>4 [3,2,1,1,1,1]=>1 [3,2,1,1,2]=>1 [3,2,1,2,1]=>1 [3,2,1,3]=>5 [3,2,2,1,1]=>1 [3,2,2,2]=>1 [3,2,3,1]=>4 [3,2,4]=>4 [3,3,1,1,1]=>3 [3,3,1,2]=>3 [3,3,2,1]=>3 [3,3,3]=>6 [3,4,1,1]=>3 [3,4,2]=>3 [3,5,1]=>3 [3,6]=>3 [4,1,1,1,1,1]=>1 [4,1,1,1,2]=>1 [4,1,1,2,1]=>1 [4,1,1,3]=>1 [4,1,2,1,1]=>1 [4,1,2,2]=>1 [4,1,3,1]=>1 [4,1,4]=>4 [4,2,1,1,1]=>1 [4,2,1,2]=>1 [4,2,2,1]=>1 [4,2,3]=>1 [4,3,1,1]=>1 [4,3,2]=>1 [4,4,1]=>3 [4,5]=>3 [5,1,1,1,1]=>1 [5,1,1,2]=>1 [5,1,2,1]=>1 [5,1,3]=>1 [5,2,1,1]=>1 [5,2,2]=>1 [5,3,1]=>1 [5,4]=>1 [6,1,1,1]=>1 [6,1,2]=>1 [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 sum of the positions of the weak records of an integer composition.
A weak record is an element $a_i$ such that $a_i \geq a_j$ for all $j < i$. This statistic is the sum of their positions.
References
[1] Knopfmacher, A., Mansour, T. Record statistics in integer compositions MathSciNet:2721540
Code
def statistic(pi):
    pi = list(pi)
    i = 0
    res = 0
    for j in range(len(pi)):
        if pi[j] >= i:
            i = pi[j] 
            res += j+1
    return res

Created
Apr 08, 2017 at 22:01 by Martin Rubey
Updated
Apr 08, 2017 at 22:01 by Martin Rubey