Identifier
Identifier
Values
[] generating graphics... => 0
[1] generating graphics... => 0
[2] generating graphics... => 0
[1,1] generating graphics... => 1
[3] generating graphics... => 0
[2,1] generating graphics... => 1
[1,1,1] generating graphics... => 3
[4] generating graphics... => 0
[3,1] generating graphics... => 1
[2,2] generating graphics... => 2
[2,1,1] generating graphics... => 3
[1,1,1,1] generating graphics... => 6
[5] generating graphics... => 0
[4,1] generating graphics... => 1
[3,2] generating graphics... => 2
[3,1,1] generating graphics... => 3
[2,2,1] generating graphics... => 4
[2,1,1,1] generating graphics... => 6
[1,1,1,1,1] generating graphics... => 10
[6] generating graphics... => 0
[5,1] generating graphics... => 1
[4,2] generating graphics... => 2
[4,1,1] generating graphics... => 3
[3,3] generating graphics... => 3
[3,2,1] generating graphics... => 4
[3,1,1,1] generating graphics... => 6
[2,2,2] generating graphics... => 6
[2,2,1,1] generating graphics... => 7
[2,1,1,1,1] generating graphics... => 10
[1,1,1,1,1,1] generating graphics... => 15
[7] generating graphics... => 0
[6,1] generating graphics... => 1
[5,2] generating graphics... => 2
[5,1,1] generating graphics... => 3
[4,3] generating graphics... => 3
[4,2,1] generating graphics... => 4
[4,1,1,1] generating graphics... => 6
[3,3,1] generating graphics... => 5
[3,2,2] generating graphics... => 6
[3,2,1,1] generating graphics... => 7
[3,1,1,1,1] generating graphics... => 10
[2,2,2,1] generating graphics... => 9
[2,2,1,1,1] generating graphics... => 11
[2,1,1,1,1,1] generating graphics... => 15
[1,1,1,1,1,1,1] generating graphics... => 21
[8] generating graphics... => 0
[7,1] generating graphics... => 1
[6,2] generating graphics... => 2
[6,1,1] generating graphics... => 3
[5,3] generating graphics... => 3
[5,2,1] generating graphics... => 4
[5,1,1,1] generating graphics... => 6
[4,4] generating graphics... => 4
[4,3,1] generating graphics... => 5
[4,2,2] generating graphics... => 6
[4,2,1,1] generating graphics... => 7
[4,1,1,1,1] generating graphics... => 10
[3,3,2] generating graphics... => 7
[3,3,1,1] generating graphics... => 8
[3,2,2,1] generating graphics... => 9
[3,2,1,1,1] generating graphics... => 11
[3,1,1,1,1,1] generating graphics... => 15
[2,2,2,2] generating graphics... => 12
[2,2,2,1,1] generating graphics... => 13
[2,2,1,1,1,1] generating graphics... => 16
[2,1,1,1,1,1,1] generating graphics... => 21
[1,1,1,1,1,1,1,1] generating graphics... => 28
[9] generating graphics... => 0
[8,1] generating graphics... => 1
[7,2] generating graphics... => 2
[7,1,1] generating graphics... => 3
[6,3] generating graphics... => 3
[6,2,1] generating graphics... => 4
[6,1,1,1] generating graphics... => 6
[5,4] generating graphics... => 4
[5,3,1] generating graphics... => 5
[5,2,2] generating graphics... => 6
[5,2,1,1] generating graphics... => 7
[5,1,1,1,1] generating graphics... => 10
[4,4,1] generating graphics... => 6
[4,3,2] generating graphics... => 7
[4,3,1,1] generating graphics... => 8
[4,2,2,1] generating graphics... => 9
[4,2,1,1,1] generating graphics... => 11
[4,1,1,1,1,1] generating graphics... => 15
[3,3,3] generating graphics... => 9
[3,3,2,1] generating graphics... => 10
[3,3,1,1,1] generating graphics... => 12
[3,2,2,2] generating graphics... => 12
[3,2,2,1,1] generating graphics... => 13
[3,2,1,1,1,1] generating graphics... => 16
[3,1,1,1,1,1,1] generating graphics... => 21
[2,2,2,2,1] generating graphics... => 16
[2,2,2,1,1,1] generating graphics... => 18
[2,2,1,1,1,1,1] generating graphics... => 22
[2,1,1,1,1,1,1,1] generating graphics... => 28
[1,1,1,1,1,1,1,1,1] generating graphics... => 36
[10] generating graphics... => 0
[9,1] generating graphics... => 1
[8,2] generating graphics... => 2
[8,1,1] generating graphics... => 3
[7,3] generating graphics... => 3
[7,2,1] generating graphics... => 4
[7,1,1,1] generating graphics... => 6
[6,4] generating graphics... => 4
[6,3,1] generating graphics... => 5
[6,2,2] generating graphics... => 6
[6,2,1,1] generating graphics... => 7
[6,1,1,1,1] generating graphics... => 10
[5,5] generating graphics... => 5
[5,4,1] generating graphics... => 6
[5,3,2] generating graphics... => 7
[5,3,1,1] generating graphics... => 8
[5,2,2,1] generating graphics... => 9
[5,2,1,1,1] generating graphics... => 11
[5,1,1,1,1,1] generating graphics... => 15
[4,4,2] generating graphics... => 8
[4,4,1,1] generating graphics... => 9
[4,3,3] generating graphics... => 9
[4,3,2,1] generating graphics... => 10
[4,3,1,1,1] generating graphics... => 12
[4,2,2,2] generating graphics... => 12
[4,2,2,1,1] generating graphics... => 13
[4,2,1,1,1,1] generating graphics... => 16
[4,1,1,1,1,1,1] generating graphics... => 21
[3,3,3,1] generating graphics... => 12
[3,3,2,2] generating graphics... => 13
[3,3,2,1,1] generating graphics... => 14
[3,3,1,1,1,1] generating graphics... => 17
[3,2,2,2,1] generating graphics... => 16
[3,2,2,1,1,1] generating graphics... => 18
[3,2,1,1,1,1,1] generating graphics... => 22
[3,1,1,1,1,1,1,1] generating graphics... => 28
[2,2,2,2,2] generating graphics... => 20
[2,2,2,2,1,1] generating graphics... => 21
[2,2,2,1,1,1,1] generating graphics... => 24
[2,2,1,1,1,1,1,1] generating graphics... => 29
[2,1,1,1,1,1,1,1,1] generating graphics... => 36
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 45
[5,4,2] generating graphics... => 8
[5,4,1,1] generating graphics... => 9
[5,3,3] generating graphics... => 9
[5,3,2,1] generating graphics... => 10
[5,3,1,1,1] generating graphics... => 12
[5,2,2,2] generating graphics... => 12
[5,2,2,1,1] generating graphics... => 13
[4,4,3] generating graphics... => 10
[4,4,2,1] generating graphics... => 11
[4,4,1,1,1] generating graphics... => 13
[4,3,3,1] generating graphics... => 12
[4,3,2,2] generating graphics... => 13
[4,3,2,1,1] generating graphics... => 14
[4,2,2,2,1] generating graphics... => 16
[3,3,3,2] generating graphics... => 15
[3,3,3,1,1] generating graphics... => 16
[3,3,2,2,1] generating graphics... => 17
[6,4,2] generating graphics... => 8
[5,4,3] generating graphics... => 10
[5,4,2,1] generating graphics... => 11
[5,4,1,1,1] generating graphics... => 13
[5,3,3,1] generating graphics... => 12
[5,3,2,2] generating graphics... => 13
[5,3,2,1,1] generating graphics... => 14
[5,2,2,2,1] generating graphics... => 16
[4,4,3,1] generating graphics... => 13
[4,4,2,2] generating graphics... => 14
[4,4,2,1,1] generating graphics... => 15
[4,3,3,2] generating graphics... => 15
[4,3,3,1,1] generating graphics... => 16
[4,3,2,2,1] generating graphics... => 17
[3,3,3,2,1] generating graphics... => 19
[3,3,2,2,1,1] generating graphics... => 22
[5,4,3,1] generating graphics... => 13
[5,4,2,2] generating graphics... => 14
[5,4,2,1,1] generating graphics... => 15
[5,3,3,2] generating graphics... => 15
[5,3,3,1,1] generating graphics... => 16
[5,3,2,2,1] generating graphics... => 17
[4,4,3,2] generating graphics... => 16
[4,4,3,1,1] generating graphics... => 17
[4,4,2,2,1] generating graphics... => 18
[4,3,3,2,1] generating graphics... => 19
[5,4,3,2] generating graphics... => 16
[5,4,3,1,1] generating graphics... => 17
[5,4,2,2,1] generating graphics... => 18
[5,3,3,2,1] generating graphics... => 19
[4,4,3,2,1] generating graphics... => 20
[5,4,3,2,1] generating graphics... => 20
click to show generating function       
Description
The weighted size of a partition.
Let $\lambda = (\lambda_0\geq\lambda_1 \geq \dots\geq\lambda_m)$ be an integer partition. Then the weighted size of $\lambda$ is
$$\sum_{i=0}^m i \cdot \lambda_i.$$
This also the sum of the leg lengths of the cells in $\lambda$, or
$$ \sum_i \binom{\lambda^{\prime}_i}{2} $$
where $\lambda^{\prime}$ is the conjugate partition of $\lambda$.
Code
def statistic(L):
    return L.weighted_size()
Created
May 07, 2014 at 03:07 by Lahiru Kariyawasam
Updated
Sep 03, 2019 at 16:37 by Martin Rubey