edit this statistic or download as text // json
Identifier
Values
[2] => 1
[1,1] => 2
[3] => 1
[2,1] => 1
[1,1,1] => 2
[4] => 1
[3,1] => 1
[2,2] => 1
[2,1,1] => 2
[1,1,1,1] => 2
[5] => 1
[4,1] => 1
[3,2] => 1
[3,1,1] => 2
[2,2,1] => 1
[2,1,1,1] => 2
[1,1,1,1,1] => 2
[6] => 1
[5,1] => 1
[4,2] => 1
[4,1,1] => 2
[3,3] => 1
[3,2,1] => 1
[3,1,1,1] => 2
[2,2,2] => 1
[2,2,1,1] => 3
[2,1,1,1,1] => 2
[1,1,1,1,1,1] => 2
[7] => 1
[6,1] => 1
[5,2] => 1
[5,1,1] => 2
[4,3] => 1
[4,2,1] => 1
[4,1,1,1] => 2
[3,3,1] => 1
[3,2,2] => 1
[3,2,1,1] => 2
[3,1,1,1,1] => 2
[2,2,2,1] => 1
[2,2,1,1,1] => 3
[2,1,1,1,1,1] => 2
[1,1,1,1,1,1,1] => 2
[8] => 1
[7,1] => 1
[6,2] => 1
[6,1,1] => 2
[5,3] => 1
[5,2,1] => 1
[5,1,1,1] => 2
[4,4] => 1
[4,3,1] => 1
[4,2,2] => 1
[4,2,1,1] => 2
[4,1,1,1,1] => 2
[3,3,2] => 1
[3,3,1,1] => 2
[3,2,2,1] => 1
[3,2,1,1,1] => 2
[3,1,1,1,1,1] => 2
[2,2,2,2] => 1
[2,2,2,1,1] => 3
[2,2,1,1,1,1] => 3
[2,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1] => 2
[9] => 1
[8,1] => 1
[7,2] => 1
[7,1,1] => 2
[6,3] => 1
[6,2,1] => 1
[6,1,1,1] => 2
[5,4] => 1
[5,3,1] => 1
[5,2,2] => 1
[5,2,1,1] => 2
[5,1,1,1,1] => 2
[4,4,1] => 1
[4,3,2] => 1
[4,3,1,1] => 2
[4,2,2,1] => 1
[4,2,1,1,1] => 2
[4,1,1,1,1,1] => 2
[3,3,3] => 1
[3,3,2,1] => 1
[3,3,1,1,1] => 2
[3,2,2,2] => 1
[3,2,2,1,1] => 3
[3,2,1,1,1,1] => 2
[3,1,1,1,1,1,1] => 2
[2,2,2,2,1] => 1
[2,2,2,1,1,1] => 3
[2,2,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1] => 2
[10] => 1
[9,1] => 1
[8,2] => 1
[8,1,1] => 2
[7,3] => 1
[7,2,1] => 1
>>> Load all 137 entries. <<<
[7,1,1,1] => 2
[6,4] => 1
[6,3,1] => 1
[6,2,2] => 1
[6,2,1,1] => 2
[6,1,1,1,1] => 2
[5,5] => 1
[5,4,1] => 1
[5,3,2] => 1
[5,3,1,1] => 2
[5,2,2,1] => 1
[5,2,1,1,1] => 2
[5,1,1,1,1,1] => 2
[4,4,2] => 1
[4,4,1,1] => 2
[4,3,3] => 1
[4,3,2,1] => 1
[4,3,1,1,1] => 2
[4,2,2,2] => 1
[4,2,2,1,1] => 3
[4,2,1,1,1,1] => 2
[4,1,1,1,1,1,1] => 2
[3,3,3,1] => 1
[3,3,2,2] => 1
[3,3,2,1,1] => 2
[3,3,1,1,1,1] => 2
[3,2,2,2,1] => 1
[3,2,2,1,1,1] => 3
[3,2,1,1,1,1,1] => 2
[3,1,1,1,1,1,1,1] => 2
[2,2,2,2,2] => 1
[2,2,2,2,1,1] => 3
[2,2,2,1,1,1,1] => 3
[2,2,1,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1] => 2
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 smallest positive integer that does not appear twice in the partition.
References
[1] Ballantine, C., Merca, M. Combinatorial Proof of the Minimal Excludant Theorem arXiv:1908.06789
Code
def statistic(x):
    x = list(x)
    for i in range(1, x[0]+2):
        if x.count(i) < 2:
            return i
Created
Jul 15, 2020 at 15:01 by Martin Rubey
Updated
Jul 15, 2020 at 15:01 by Martin Rubey