Identifier
Identifier
Values
[] generating graphics... => 1
[1] generating graphics... => 2
[2] generating graphics... => 1
[1,1] generating graphics... => 2
[3] generating graphics... => 1
[2,1] generating graphics... => 3
[1,1,1] generating graphics... => 2
[4] generating graphics... => 1
[3,1] generating graphics... => 2
[2,2] generating graphics... => 1
[2,1,1] generating graphics... => 3
[1,1,1,1] generating graphics... => 2
[5] generating graphics... => 1
[4,1] generating graphics... => 2
[3,2] generating graphics... => 1
[3,1,1] generating graphics... => 2
[2,2,1] generating graphics... => 3
[2,1,1,1] generating graphics... => 3
[1,1,1,1,1] generating graphics... => 2
[6] generating graphics... => 1
[5,1] generating graphics... => 2
[4,2] generating graphics... => 1
[4,1,1] generating graphics... => 2
[3,3] generating graphics... => 1
[3,2,1] generating graphics... => 4
[3,1,1,1] generating graphics... => 2
[2,2,2] generating graphics... => 1
[2,2,1,1] generating graphics... => 3
[2,1,1,1,1] generating graphics... => 3
[1,1,1,1,1,1] generating graphics... => 2
[7] generating graphics... => 1
[6,1] generating graphics... => 2
[5,2] generating graphics... => 1
[5,1,1] generating graphics... => 2
[4,3] generating graphics... => 1
[4,2,1] generating graphics... => 3
[4,1,1,1] generating graphics... => 2
[3,3,1] generating graphics... => 2
[3,2,2] generating graphics... => 1
[3,2,1,1] generating graphics... => 4
[3,1,1,1,1] generating graphics... => 2
[2,2,2,1] generating graphics... => 3
[2,2,1,1,1] generating graphics... => 3
[2,1,1,1,1,1] generating graphics... => 3
[1,1,1,1,1,1,1] generating graphics... => 2
[8] generating graphics... => 1
[7,1] generating graphics... => 2
[6,2] generating graphics... => 1
[6,1,1] generating graphics... => 2
[5,3] generating graphics... => 1
[5,2,1] generating graphics... => 3
[5,1,1,1] generating graphics... => 2
[4,4] generating graphics... => 1
[4,3,1] generating graphics... => 2
[4,2,2] generating graphics... => 1
[4,2,1,1] generating graphics... => 3
[4,1,1,1,1] generating graphics... => 2
[3,3,2] generating graphics... => 1
[3,3,1,1] generating graphics... => 2
[3,2,2,1] generating graphics... => 4
[3,2,1,1,1] generating graphics... => 4
[3,1,1,1,1,1] generating graphics... => 2
[2,2,2,2] generating graphics... => 1
[2,2,2,1,1] generating graphics... => 3
[2,2,1,1,1,1] generating graphics... => 3
[2,1,1,1,1,1,1] generating graphics... => 3
[1,1,1,1,1,1,1,1] generating graphics... => 2
[9] generating graphics... => 1
[8,1] generating graphics... => 2
[7,2] generating graphics... => 1
[7,1,1] generating graphics... => 2
[6,3] generating graphics... => 1
[6,2,1] generating graphics... => 3
[6,1,1,1] generating graphics... => 2
[5,4] generating graphics... => 1
[5,3,1] generating graphics... => 2
[5,2,2] generating graphics... => 1
[5,2,1,1] generating graphics... => 3
[5,1,1,1,1] generating graphics... => 2
[4,4,1] generating graphics... => 2
[4,3,2] generating graphics... => 1
[4,3,1,1] generating graphics... => 2
[4,2,2,1] generating graphics... => 3
[4,2,1,1,1] generating graphics... => 3
[4,1,1,1,1,1] generating graphics... => 2
[3,3,3] generating graphics... => 1
[3,3,2,1] generating graphics... => 4
[3,3,1,1,1] generating graphics... => 2
[3,2,2,2] generating graphics... => 1
[3,2,2,1,1] generating graphics... => 4
[3,2,1,1,1,1] generating graphics... => 4
[3,1,1,1,1,1,1] generating graphics... => 2
[2,2,2,2,1] generating graphics... => 3
[2,2,2,1,1,1] generating graphics... => 3
[2,2,1,1,1,1,1] generating graphics... => 3
[2,1,1,1,1,1,1,1] generating graphics... => 3
[1,1,1,1,1,1,1,1,1] generating graphics... => 2
[10] generating graphics... => 1
[9,1] generating graphics... => 2
[8,2] generating graphics... => 1
[8,1,1] generating graphics... => 2
[7,3] generating graphics... => 1
[7,2,1] generating graphics... => 3
[7,1,1,1] generating graphics... => 2
[6,4] generating graphics... => 1
[6,3,1] generating graphics... => 2
[6,2,2] generating graphics... => 1
[6,2,1,1] generating graphics... => 3
[6,1,1,1,1] generating graphics... => 2
[5,5] generating graphics... => 1
[5,4,1] generating graphics... => 2
[5,3,2] generating graphics... => 1
[5,3,1,1] generating graphics... => 2
[5,2,2,1] generating graphics... => 3
[5,2,1,1,1] generating graphics... => 3
[5,1,1,1,1,1] generating graphics... => 2
[4,4,2] generating graphics... => 1
[4,4,1,1] generating graphics... => 2
[4,3,3] generating graphics... => 1
[4,3,2,1] generating graphics... => 5
[4,3,1,1,1] generating graphics... => 2
[4,2,2,2] generating graphics... => 1
[4,2,2,1,1] generating graphics... => 3
[4,2,1,1,1,1] generating graphics... => 3
[4,1,1,1,1,1,1] generating graphics... => 2
[3,3,3,1] generating graphics... => 2
[3,3,2,2] generating graphics... => 1
[3,3,2,1,1] generating graphics... => 4
[3,3,1,1,1,1] generating graphics... => 2
[3,2,2,2,1] generating graphics... => 4
[3,2,2,1,1,1] generating graphics... => 4
[3,2,1,1,1,1,1] generating graphics... => 4
[3,1,1,1,1,1,1,1] generating graphics... => 2
[2,2,2,2,2] generating graphics... => 1
[2,2,2,2,1,1] generating graphics... => 3
[2,2,2,1,1,1,1] generating graphics... => 3
[2,2,1,1,1,1,1,1] generating graphics... => 3
[2,1,1,1,1,1,1,1,1] generating graphics... => 3
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 2
[11] generating graphics... => 1
[10,1] generating graphics... => 2
[9,2] generating graphics... => 1
[9,1,1] generating graphics... => 2
[8,3] generating graphics... => 1
[8,2,1] generating graphics... => 3
[8,1,1,1] generating graphics... => 2
[7,4] generating graphics... => 1
[7,3,1] generating graphics... => 2
[7,2,2] generating graphics... => 1
[7,2,1,1] generating graphics... => 3
[7,1,1,1,1] generating graphics... => 2
[6,5] generating graphics... => 1
[6,4,1] generating graphics... => 2
[6,3,2] generating graphics... => 1
[6,3,1,1] generating graphics... => 2
[6,2,2,1] generating graphics... => 3
[6,2,1,1,1] generating graphics... => 3
[6,1,1,1,1,1] generating graphics... => 2
[5,5,1] generating graphics... => 2
[5,4,2] generating graphics... => 1
[5,4,1,1] generating graphics... => 2
[5,3,3] generating graphics... => 1
[5,3,2,1] generating graphics... => 4
[5,3,1,1,1] generating graphics... => 2
[5,2,2,2] generating graphics... => 1
[5,2,2,1,1] generating graphics... => 3
[5,2,1,1,1,1] generating graphics... => 3
[5,1,1,1,1,1,1] generating graphics... => 2
[4,4,3] generating graphics... => 1
[4,4,2,1] generating graphics... => 3
[4,4,1,1,1] generating graphics... => 2
[4,3,3,1] generating graphics... => 2
[4,3,2,2] generating graphics... => 1
[4,3,2,1,1] generating graphics... => 5
[4,3,1,1,1,1] generating graphics... => 2
[4,2,2,2,1] generating graphics... => 3
[4,2,2,1,1,1] generating graphics... => 3
[4,2,1,1,1,1,1] generating graphics... => 3
[4,1,1,1,1,1,1,1] generating graphics... => 2
[3,3,3,2] generating graphics... => 1
[3,3,3,1,1] generating graphics... => 2
[3,3,2,2,1] generating graphics... => 4
[3,3,2,1,1,1] generating graphics... => 4
[3,3,1,1,1,1,1] generating graphics... => 2
[3,2,2,2,2] generating graphics... => 1
[3,2,2,2,1,1] generating graphics... => 4
[3,2,2,1,1,1,1] generating graphics... => 4
[3,2,1,1,1,1,1,1] generating graphics... => 4
[3,1,1,1,1,1,1,1,1] generating graphics... => 2
[2,2,2,2,2,1] generating graphics... => 3
[2,2,2,2,1,1,1] generating graphics... => 3
[2,2,2,1,1,1,1,1] generating graphics... => 3
[2,2,1,1,1,1,1,1,1] generating graphics... => 3
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 3
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 2
[12] generating graphics... => 1
[11,1] generating graphics... => 2
[10,2] generating graphics... => 1
[10,1,1] generating graphics... => 2
[9,3] generating graphics... => 1
[9,2,1] generating graphics... => 3
[9,1,1,1] generating graphics... => 2
[8,4] generating graphics... => 1
[8,3,1] generating graphics... => 2
[8,2,2] generating graphics... => 1
[8,2,1,1] generating graphics... => 3
[8,1,1,1,1] generating graphics... => 2
[7,5] generating graphics... => 1
[7,4,1] generating graphics... => 2
[7,3,2] generating graphics... => 1
[7,3,1,1] generating graphics... => 2
[7,2,2,1] generating graphics... => 3
[7,2,1,1,1] generating graphics... => 3
[7,1,1,1,1,1] generating graphics... => 2
[6,6] generating graphics... => 1
[6,5,1] generating graphics... => 2
[6,4,2] generating graphics... => 1
[6,4,1,1] generating graphics... => 2
[6,3,3] generating graphics... => 1
[6,3,2,1] generating graphics... => 4
[6,3,1,1,1] generating graphics... => 2
[6,2,2,2] generating graphics... => 1
[6,2,2,1,1] generating graphics... => 3
[6,2,1,1,1,1] generating graphics... => 3
[6,1,1,1,1,1,1] generating graphics... => 2
[5,5,2] generating graphics... => 1
[5,5,1,1] generating graphics... => 2
[5,4,3] generating graphics... => 1
[5,4,2,1] generating graphics... => 3
[5,4,1,1,1] generating graphics... => 2
[5,3,3,1] generating graphics... => 2
[5,3,2,2] generating graphics... => 1
[5,3,2,1,1] generating graphics... => 4
[5,3,1,1,1,1] generating graphics... => 2
[5,2,2,2,1] generating graphics... => 3
[5,2,2,1,1,1] generating graphics... => 3
[5,2,1,1,1,1,1] generating graphics... => 3
[5,1,1,1,1,1,1,1] generating graphics... => 2
[4,4,4] generating graphics... => 1
[4,4,3,1] generating graphics... => 2
[4,4,2,2] generating graphics... => 1
[4,4,2,1,1] generating graphics... => 3
[4,4,1,1,1,1] generating graphics... => 2
[4,3,3,2] generating graphics... => 1
[4,3,3,1,1] generating graphics... => 2
[4,3,2,2,1] generating graphics... => 5
[4,3,2,1,1,1] generating graphics... => 5
[4,3,1,1,1,1,1] generating graphics... => 2
[4,2,2,2,2] generating graphics... => 1
[4,2,2,2,1,1] generating graphics... => 3
[4,2,2,1,1,1,1] generating graphics... => 3
[4,2,1,1,1,1,1,1] generating graphics... => 3
[4,1,1,1,1,1,1,1,1] generating graphics... => 2
[3,3,3,3] generating graphics... => 1
[3,3,3,2,1] generating graphics... => 4
[3,3,3,1,1,1] generating graphics... => 2
[3,3,2,2,2] generating graphics... => 1
[3,3,2,2,1,1] generating graphics... => 4
[3,3,2,1,1,1,1] generating graphics... => 4
[3,3,1,1,1,1,1,1] generating graphics... => 2
[3,2,2,2,2,1] generating graphics... => 4
[3,2,2,2,1,1,1] generating graphics... => 4
[3,2,2,1,1,1,1,1] generating graphics... => 4
[3,2,1,1,1,1,1,1,1] generating graphics... => 4
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 2
[2,2,2,2,2,2] generating graphics... => 1
[2,2,2,2,2,1,1] generating graphics... => 3
[2,2,2,2,1,1,1,1] generating graphics... => 3
[2,2,2,1,1,1,1,1,1] generating graphics... => 3
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 3
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 3
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 2
[5,4,3,1] generating graphics... => 2
[5,4,2,2] generating graphics... => 1
[5,4,2,1,1] generating graphics... => 3
[5,3,3,2] generating graphics... => 1
[5,3,3,1,1] generating graphics... => 2
[5,3,2,2,1] generating graphics... => 4
[4,4,3,2] generating graphics... => 1
[4,4,3,1,1] generating graphics... => 2
[4,4,2,2,1] generating graphics... => 3
[4,3,3,2,1] generating graphics... => 5
[5,4,3,2] generating graphics... => 1
[5,4,3,1,1] generating graphics... => 2
[5,4,2,2,1] generating graphics... => 3
[5,3,3,2,1] generating graphics... => 4
[4,4,3,2,1] generating graphics... => 5
[5,4,3,2,1] generating graphics... => 6
click to show generating function       
Description
The smallest missing part in an integer partition.
For compositions, this is studied in [sec.3.2., 1].
References
[1] Hitczenko, PaweĊ‚, Louchard, G. Distinctness of compositions of an integer: a probabilistic analysis MathSciNet:1871561
[2] Triangle read by rows: T(n,k) is the number of partitions of n having least gap k. OEIS:A264401
Code
def statistic(pi):
    return min(set(range(1,len(pi)+2)).difference(set(pi)))
Created
Apr 08, 2017 at 22:40 by Martin Rubey
Updated
Dec 31, 2017 at 14:09 by Martin Rubey