edit this statistic or download as text // json
Identifier
Values
=>
[1]=>1 [1,1]=>2 [2]=>1 [1,1,1]=>3 [1,2]=>2 [2,1]=>1 [3]=>1 [1,1,1,1]=>4 [1,1,2]=>3 [1,2,1]=>2 [1,3]=>2 [2,1,1]=>1 [2,2]=>2 [3,1]=>1 [4]=>1 [1,1,1,1,1]=>5 [1,1,1,2]=>4 [1,1,2,1]=>3 [1,1,3]=>3 [1,2,1,1]=>2 [1,2,2]=>3 [1,3,1]=>2 [1,4]=>2 [2,1,1,1]=>1 [2,1,2]=>2 [2,2,1]=>2 [2,3]=>2 [3,1,1]=>1 [3,2]=>1 [4,1]=>1 [5]=>1 [1,1,1,1,1,1]=>6 [1,1,1,1,2]=>5 [1,1,1,2,1]=>4 [1,1,1,3]=>4 [1,1,2,1,1]=>3 [1,1,2,2]=>4 [1,1,3,1]=>3 [1,1,4]=>3 [1,2,1,1,1]=>2 [1,2,1,2]=>3 [1,2,2,1]=>3 [1,2,3]=>3 [1,3,1,1]=>2 [1,3,2]=>2 [1,4,1]=>2 [1,5]=>2 [2,1,1,1,1]=>1 [2,1,1,2]=>2 [2,1,2,1]=>2 [2,1,3]=>2 [2,2,1,1]=>2 [2,2,2]=>3 [2,3,1]=>2 [2,4]=>2 [3,1,1,1]=>1 [3,1,2]=>1 [3,2,1]=>1 [3,3]=>2 [4,1,1]=>1 [4,2]=>1 [5,1]=>1 [6]=>1 [1,1,1,1,1,1,1]=>7 [1,1,1,1,1,2]=>6 [1,1,1,1,2,1]=>5 [1,1,1,1,3]=>5 [1,1,1,2,1,1]=>4 [1,1,1,2,2]=>5 [1,1,1,3,1]=>4 [1,1,1,4]=>4 [1,1,2,1,1,1]=>3 [1,1,2,1,2]=>4 [1,1,2,2,1]=>4 [1,1,2,3]=>4 [1,1,3,1,1]=>3 [1,1,3,2]=>3 [1,1,4,1]=>3 [1,1,5]=>3 [1,2,1,1,1,1]=>2 [1,2,1,1,2]=>3 [1,2,1,2,1]=>3 [1,2,1,3]=>3 [1,2,2,1,1]=>3 [1,2,2,2]=>4 [1,2,3,1]=>3 [1,2,4]=>3 [1,3,1,1,1]=>2 [1,3,1,2]=>2 [1,3,2,1]=>2 [1,3,3]=>3 [1,4,1,1]=>2 [1,4,2]=>2 [1,5,1]=>2 [1,6]=>2 [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]=>3 [2,1,3,1]=>2 [2,1,4]=>2 [2,2,1,1,1]=>2 [2,2,1,2]=>3 [2,2,2,1]=>3 [2,2,3]=>3 [2,3,1,1]=>2 [2,3,2]=>2 [2,4,1]=>2 [2,5]=>2 [3,1,1,1,1]=>1 [3,1,1,2]=>1 [3,1,2,1]=>1 [3,1,3]=>2 [3,2,1,1]=>1 [3,2,2]=>1 [3,3,1]=>2 [3,4]=>2 [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]=>8 [1,1,1,1,1,1,2]=>7 [1,1,1,1,1,2,1]=>6 [1,1,1,1,1,3]=>6 [1,1,1,1,2,1,1]=>5 [1,1,1,1,2,2]=>6 [1,1,1,1,3,1]=>5 [1,1,1,1,4]=>5 [1,1,1,2,1,1,1]=>4 [1,1,1,2,1,2]=>5 [1,1,1,2,2,1]=>5 [1,1,1,2,3]=>5 [1,1,1,3,1,1]=>4 [1,1,1,3,2]=>4 [1,1,1,4,1]=>4 [1,1,1,5]=>4 [1,1,2,1,1,1,1]=>3 [1,1,2,1,1,2]=>4 [1,1,2,1,2,1]=>4 [1,1,2,1,3]=>4 [1,1,2,2,1,1]=>4 [1,1,2,2,2]=>5 [1,1,2,3,1]=>4 [1,1,2,4]=>4 [1,1,3,1,1,1]=>3 [1,1,3,1,2]=>3 [1,1,3,2,1]=>3 [1,1,3,3]=>4 [1,1,4,1,1]=>3 [1,1,4,2]=>3 [1,1,5,1]=>3 [1,1,6]=>3 [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]=>3 [1,2,1,2,1,1]=>3 [1,2,1,2,2]=>4 [1,2,1,3,1]=>3 [1,2,1,4]=>3 [1,2,2,1,1,1]=>3 [1,2,2,1,2]=>4 [1,2,2,2,1]=>4 [1,2,2,3]=>4 [1,2,3,1,1]=>3 [1,2,3,2]=>3 [1,2,4,1]=>3 [1,2,5]=>3 [1,3,1,1,1,1]=>2 [1,3,1,1,2]=>2 [1,3,1,2,1]=>2 [1,3,1,3]=>3 [1,3,2,1,1]=>2 [1,3,2,2]=>2 [1,3,3,1]=>3 [1,3,4]=>3 [1,4,1,1,1]=>2 [1,4,1,2]=>2 [1,4,2,1]=>2 [1,4,3]=>2 [1,5,1,1]=>2 [1,5,2]=>2 [1,6,1]=>2 [1,7]=>2 [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]=>3 [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]=>3 [2,1,2,3]=>3 [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]=>2 [2,2,1,1,2]=>3 [2,2,1,2,1]=>3 [2,2,1,3]=>3 [2,2,2,1,1]=>3 [2,2,2,2]=>4 [2,2,3,1]=>3 [2,2,4]=>3 [2,3,1,1,1]=>2 [2,3,1,2]=>2 [2,3,2,1]=>2 [2,3,3]=>3 [2,4,1,1]=>2 [2,4,2]=>2 [2,5,1]=>2 [2,6]=>2 [3,1,1,1,1,1]=>1 [3,1,1,1,2]=>1 [3,1,1,2,1]=>1 [3,1,1,3]=>2 [3,1,2,1,1]=>1 [3,1,2,2]=>1 [3,1,3,1]=>2 [3,1,4]=>2 [3,2,1,1,1]=>1 [3,2,1,2]=>1 [3,2,2,1]=>1 [3,2,3]=>2 [3,3,1,1]=>2 [3,3,2]=>2 [3,4,1]=>2 [3,5]=>2 [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]=>2 [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]=>9 [1,1,1,1,1,1,1,2]=>8 [1,1,1,1,1,1,2,1]=>7 [1,1,1,1,1,1,3]=>7 [1,1,1,1,1,2,1,1]=>6 [1,1,1,1,1,2,2]=>7 [1,1,1,1,1,3,1]=>6 [1,1,1,1,1,4]=>6 [1,1,1,1,2,1,1,1]=>5 [1,1,1,1,2,1,2]=>6 [1,1,1,1,2,2,1]=>6 [1,1,1,1,2,3]=>6 [1,1,1,1,3,1,1]=>5 [1,1,1,1,3,2]=>5 [1,1,1,1,4,1]=>5 [1,1,1,1,5]=>5 [1,1,1,2,1,1,1,1]=>4 [1,1,1,2,1,1,2]=>5 [1,1,1,2,1,2,1]=>5 [1,1,1,2,1,3]=>5 [1,1,1,2,2,1,1]=>5 [1,1,1,2,2,2]=>6 [1,1,1,2,3,1]=>5 [1,1,1,2,4]=>5 [1,1,1,3,1,1,1]=>4 [1,1,1,3,1,2]=>4 [1,1,1,3,2,1]=>4 [1,1,1,3,3]=>5 [1,1,1,4,1,1]=>4 [1,1,1,4,2]=>4 [1,1,1,5,1]=>4 [1,1,1,6]=>4 [1,1,2,1,1,1,1,1]=>3 [1,1,2,1,1,1,2]=>4 [1,1,2,1,1,2,1]=>4 [1,1,2,1,1,3]=>4 [1,1,2,1,2,1,1]=>4 [1,1,2,1,2,2]=>5 [1,1,2,1,3,1]=>4 [1,1,2,1,4]=>4 [1,1,2,2,1,1,1]=>4 [1,1,2,2,1,2]=>5 [1,1,2,2,2,1]=>5 [1,1,2,2,3]=>5 [1,1,2,3,1,1]=>4 [1,1,2,3,2]=>4 [1,1,2,4,1]=>4 [1,1,2,5]=>4 [1,1,3,1,1,1,1]=>3 [1,1,3,1,1,2]=>3 [1,1,3,1,2,1]=>3 [1,1,3,1,3]=>4 [1,1,3,2,1,1]=>3 [1,1,3,2,2]=>3 [1,1,3,3,1]=>4 [1,1,3,4]=>4 [1,1,4,1,1,1]=>3 [1,1,4,1,2]=>3 [1,1,4,2,1]=>3 [1,1,4,3]=>3 [1,1,5,1,1]=>3 [1,1,5,2]=>3 [1,1,6,1]=>3 [1,1,7]=>3 [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]=>3 [1,2,1,1,2,1,1]=>3 [1,2,1,1,2,2]=>4 [1,2,1,1,3,1]=>3 [1,2,1,1,4]=>3 [1,2,1,2,1,1,1]=>3 [1,2,1,2,1,2]=>4 [1,2,1,2,2,1]=>4 [1,2,1,2,3]=>4 [1,2,1,3,1,1]=>3 [1,2,1,3,2]=>3 [1,2,1,4,1]=>3 [1,2,1,5]=>3 [1,2,2,1,1,1,1]=>3 [1,2,2,1,1,2]=>4 [1,2,2,1,2,1]=>4 [1,2,2,1,3]=>4 [1,2,2,2,1,1]=>4 [1,2,2,2,2]=>5 [1,2,2,3,1]=>4 [1,2,2,4]=>4 [1,2,3,1,1,1]=>3 [1,2,3,1,2]=>3 [1,2,3,2,1]=>3 [1,2,3,3]=>4 [1,2,4,1,1]=>3 [1,2,4,2]=>3 [1,2,5,1]=>3 [1,2,6]=>3 [1,3,1,1,1,1,1]=>2 [1,3,1,1,1,2]=>2 [1,3,1,1,2,1]=>2 [1,3,1,1,3]=>3 [1,3,1,2,1,1]=>2 [1,3,1,2,2]=>2 [1,3,1,3,1]=>3 [1,3,1,4]=>3 [1,3,2,1,1,1]=>2 [1,3,2,1,2]=>2 [1,3,2,2,1]=>2 [1,3,2,3]=>3 [1,3,3,1,1]=>3 [1,3,3,2]=>3 [1,3,4,1]=>3 [1,3,5]=>3 [1,4,1,1,1,1]=>2 [1,4,1,1,2]=>2 [1,4,1,2,1]=>2 [1,4,1,3]=>2 [1,4,2,1,1]=>2 [1,4,2,2]=>2 [1,4,3,1]=>2 [1,4,4]=>3 [1,5,1,1,1]=>2 [1,5,1,2]=>2 [1,5,2,1]=>2 [1,5,3]=>2 [1,6,1,1]=>2 [1,6,2]=>2 [1,7,1]=>2 [1,8]=>2 [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]=>3 [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]=>3 [2,1,1,2,3]=>3 [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]=>3 [2,1,2,2,2]=>4 [2,1,2,3,1]=>3 [2,1,2,4]=>3 [2,1,3,1,1,1]=>2 [2,1,3,1,2]=>2 [2,1,3,2,1]=>2 [2,1,3,3]=>3 [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]=>2 [2,2,1,1,1,2]=>3 [2,2,1,1,2,1]=>3 [2,2,1,1,3]=>3 [2,2,1,2,1,1]=>3 [2,2,1,2,2]=>4 [2,2,1,3,1]=>3 [2,2,1,4]=>3 [2,2,2,1,1,1]=>3 [2,2,2,1,2]=>4 [2,2,2,2,1]=>4 [2,2,2,3]=>4 [2,2,3,1,1]=>3 [2,2,3,2]=>3 [2,2,4,1]=>3 [2,2,5]=>3 [2,3,1,1,1,1]=>2 [2,3,1,1,2]=>2 [2,3,1,2,1]=>2 [2,3,1,3]=>3 [2,3,2,1,1]=>2 [2,3,2,2]=>2 [2,3,3,1]=>3 [2,3,4]=>3 [2,4,1,1,1]=>2 [2,4,1,2]=>2 [2,4,2,1]=>2 [2,4,3]=>2 [2,5,1,1]=>2 [2,5,2]=>2 [2,6,1]=>2 [2,7]=>2 [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]=>2 [3,1,1,2,1,1]=>1 [3,1,1,2,2]=>1 [3,1,1,3,1]=>2 [3,1,1,4]=>2 [3,1,2,1,1,1]=>1 [3,1,2,1,2]=>1 [3,1,2,2,1]=>1 [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]=>1 [3,2,1,2,1]=>1 [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]=>2 [3,3,1,2]=>2 [3,3,2,1]=>2 [3,3,3]=>3 [3,4,1,1]=>2 [3,4,2]=>2 [3,5,1]=>2 [3,6]=>2 [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]=>2 [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]=>2 [4,5]=>2 [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
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The number of weak records in an integer composition.
A weak record is an element $a_i$ such that $a_i \geq a_j$ for all $j < i$.
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 += 1
    return res
Created
Apr 08, 2017 at 21:58 by Martin Rubey
Updated
Nov 19, 2017 at 22:06 by Christian Stump