Identifier
Identifier
Values
[] generating graphics... => 1
[1] generating graphics... => 1
[2] generating graphics... => 2
[1,1] generating graphics... => 1
[3] generating graphics... => 3
[2,1] generating graphics... => 2
[1,1,1] generating graphics... => 1
[4] generating graphics... => 5
[3,1] generating graphics... => 4
[2,2] generating graphics... => 3
[2,1,1] generating graphics... => 2
[1,1,1,1] generating graphics... => 1
[5] generating graphics... => 7
[4,1] generating graphics... => 6
[3,2] generating graphics... => 5
[3,1,1] generating graphics... => 4
[2,2,1] generating graphics... => 3
[2,1,1,1] generating graphics... => 2
[1,1,1,1,1] generating graphics... => 1
[6] generating graphics... => 11
[5,1] generating graphics... => 10
[4,2] generating graphics... => 9
[4,1,1] generating graphics... => 7
[3,3] generating graphics... => 7
[3,2,1] generating graphics... => 6
[3,1,1,1] generating graphics... => 4
[2,2,2] generating graphics... => 4
[2,2,1,1] generating graphics... => 3
[2,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1] generating graphics... => 1
[7] generating graphics... => 15
[6,1] generating graphics... => 14
[5,2] generating graphics... => 13
[5,1,1] generating graphics... => 11
[4,3] generating graphics... => 11
[4,2,1] generating graphics... => 10
[4,1,1,1] generating graphics... => 7
[3,3,1] generating graphics... => 8
[3,2,2] generating graphics... => 7
[3,2,1,1] generating graphics... => 6
[3,1,1,1,1] generating graphics... => 4
[2,2,2,1] generating graphics... => 4
[2,2,1,1,1] generating graphics... => 3
[2,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1] generating graphics... => 1
[8] generating graphics... => 22
[7,1] generating graphics... => 21
[6,2] generating graphics... => 20
[6,1,1] generating graphics... => 17
[5,3] generating graphics... => 18
[5,2,1] generating graphics... => 16
[5,1,1,1] generating graphics... => 12
[4,4] generating graphics... => 15
[4,3,1] generating graphics... => 14
[4,2,2] generating graphics... => 13
[4,2,1,1] generating graphics... => 11
[4,1,1,1,1] generating graphics... => 7
[3,3,2] generating graphics... => 10
[3,3,1,1] generating graphics... => 9
[3,2,2,1] generating graphics... => 8
[3,2,1,1,1] generating graphics... => 6
[3,1,1,1,1,1] generating graphics... => 4
[2,2,2,2] generating graphics... => 5
[2,2,2,1,1] generating graphics... => 4
[2,2,1,1,1,1] generating graphics... => 3
[2,1,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1,1] generating graphics... => 1
[9] generating graphics... => 30
[8,1] generating graphics... => 29
[7,2] generating graphics... => 28
[7,1,1] generating graphics... => 25
[6,3] generating graphics... => 26
[6,2,1] generating graphics... => 24
[6,1,1,1] generating graphics... => 18
[5,4] generating graphics... => 23
[5,3,1] generating graphics... => 22
[5,2,2] generating graphics... => 20
[5,2,1,1] generating graphics... => 17
[5,1,1,1,1] generating graphics... => 12
[4,4,1] generating graphics... => 18
[4,3,2] generating graphics... => 17
[4,3,1,1] generating graphics... => 15
[4,2,2,1] generating graphics... => 14
[4,2,1,1,1] generating graphics... => 11
[4,1,1,1,1,1] generating graphics... => 7
[3,3,3] generating graphics... => 12
[3,3,2,1] generating graphics... => 11
[3,3,1,1,1] generating graphics... => 9
[3,2,2,2] generating graphics... => 9
[3,2,2,1,1] generating graphics... => 8
[3,2,1,1,1,1] generating graphics... => 6
[3,1,1,1,1,1,1] generating graphics... => 4
[2,2,2,2,1] generating graphics... => 5
[2,2,2,1,1,1] generating graphics... => 4
[2,2,1,1,1,1,1] generating graphics... => 3
[2,1,1,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1,1,1] generating graphics... => 1
[10] generating graphics... => 42
[9,1] generating graphics... => 41
[8,2] generating graphics... => 40
[8,1,1] generating graphics... => 36
[7,3] generating graphics... => 38
[7,2,1] generating graphics... => 35
[7,1,1,1] generating graphics... => 28
[6,4] generating graphics... => 35
[6,3,1] generating graphics... => 33
[6,2,2] generating graphics... => 31
[6,2,1,1] generating graphics... => 27
[6,1,1,1,1] generating graphics... => 19
[5,5] generating graphics... => 30
[5,4,1] generating graphics... => 29
[5,3,2] generating graphics... => 28
[5,3,1,1] generating graphics... => 25
[5,2,2,1] generating graphics... => 23
[5,2,1,1,1] generating graphics... => 18
[5,1,1,1,1,1] generating graphics... => 12
[4,4,2] generating graphics... => 23
[4,4,1,1] generating graphics... => 21
[4,3,3] generating graphics... => 21
[4,3,2,1] generating graphics... => 20
[4,3,1,1,1] generating graphics... => 16
[4,2,2,2] generating graphics... => 17
[4,2,2,1,1] generating graphics... => 15
[4,2,1,1,1,1] generating graphics... => 11
[4,1,1,1,1,1,1] generating graphics... => 7
[3,3,3,1] generating graphics... => 14
[3,3,2,2] generating graphics... => 13
[3,3,2,1,1] generating graphics... => 12
[3,3,1,1,1,1] generating graphics... => 9
[3,2,2,2,1] generating graphics... => 10
[3,2,2,1,1,1] generating graphics... => 8
[3,2,1,1,1,1,1] generating graphics... => 6
[3,1,1,1,1,1,1,1] generating graphics... => 4
[2,2,2,2,2] generating graphics... => 6
[2,2,2,2,1,1] generating graphics... => 5
[2,2,2,1,1,1,1] generating graphics... => 4
[2,2,1,1,1,1,1,1] generating graphics... => 3
[2,1,1,1,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
click to show generating function       
Description
The number of integer partitions of n that are dominated by an integer partition.
A partition $\lambda = (\lambda_1,\ldots,\lambda_n) \vdash n$ dominates a partition $\mu = (\mu_1,\ldots,\mu_n) \vdash n$ if $\sum_{i=1}^k (\lambda_i - \mu_i) \geq 0$ for all $k$.
Code
def statistic(L):
    return len(L.dominated_partitions())
Created
Dec 08, 2015 at 16:23 by Christian Stump
Updated
Oct 29, 2017 at 20:53 by Martin Rubey