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
>>> Load all 511 entries. <<<
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
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 $j < i$.
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
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!