Identifier
Identifier
Values
[2] generating graphics... => 2
[1,1] generating graphics... => 1
[3] generating graphics... => 3
[2,1] generating graphics... => 4
[1,1,1] generating graphics... => 1
[4] generating graphics... => 4
[3,1] generating graphics... => 5
[2,2] generating graphics... => 2
[2,1,1] generating graphics... => 5
[1,1,1,1] generating graphics... => 1
[5] generating graphics... => 5
[4,1] generating graphics... => 6
[3,2] generating graphics... => 6
[3,1,1] generating graphics... => 6
[2,2,1] generating graphics... => 4
[2,1,1,1] generating graphics... => 6
[1,1,1,1,1] generating graphics... => 1
[6] generating graphics... => 6
[5,1] generating graphics... => 7
[4,2] generating graphics... => 7
[4,1,1] generating graphics... => 7
[3,3] generating graphics... => 3
[3,2,1] generating graphics... => 9
[3,1,1,1] generating graphics... => 7
[2,2,2] generating graphics... => 2
[2,2,1,1] generating graphics... => 5
[2,1,1,1,1] generating graphics... => 7
[1,1,1,1,1,1] generating graphics... => 1
[7] generating graphics... => 7
[6,1] generating graphics... => 8
[5,2] generating graphics... => 8
[5,1,1] generating graphics... => 8
[4,3] generating graphics... => 8
[4,2,1] generating graphics... => 10
[4,1,1,1] generating graphics... => 8
[3,3,1] generating graphics... => 5
[3,2,2] generating graphics... => 7
[3,2,1,1] generating graphics... => 11
[3,1,1,1,1] generating graphics... => 8
[2,2,2,1] generating graphics... => 4
[2,2,1,1,1] generating graphics... => 6
[2,1,1,1,1,1] generating graphics... => 8
[1,1,1,1,1,1,1] generating graphics... => 1
[8] generating graphics... => 8
[7,1] generating graphics... => 9
[6,2] generating graphics... => 9
[6,1,1] generating graphics... => 9
[5,3] generating graphics... => 9
[5,2,1] generating graphics... => 11
[5,1,1,1] generating graphics... => 9
[4,4] generating graphics... => 4
[4,3,1] generating graphics... => 11
[4,2,2] generating graphics... => 8
[4,2,1,1] generating graphics... => 12
[4,1,1,1,1] generating graphics... => 9
[3,3,2] generating graphics... => 6
[3,3,1,1] generating graphics... => 6
[3,2,2,1] generating graphics... => 10
[3,2,1,1,1] generating graphics... => 13
[3,1,1,1,1,1] generating graphics... => 9
[2,2,2,2] generating graphics... => 2
[2,2,2,1,1] generating graphics... => 5
[2,2,1,1,1,1] generating graphics... => 7
[2,1,1,1,1,1,1] generating graphics... => 9
[1,1,1,1,1,1,1,1] generating graphics... => 1
[9] generating graphics... => 9
[8,1] generating graphics... => 10
[7,2] generating graphics... => 10
[7,1,1] generating graphics... => 10
[6,3] generating graphics... => 10
[6,2,1] generating graphics... => 12
[6,1,1,1] generating graphics... => 10
[5,4] generating graphics... => 10
[5,3,1] generating graphics... => 12
[5,2,2] generating graphics... => 9
[5,2,1,1] generating graphics... => 13
[5,1,1,1,1] generating graphics... => 10
[4,4,1] generating graphics... => 6
[4,3,2] generating graphics... => 12
[4,3,1,1] generating graphics... => 13
[4,2,2,1] generating graphics... => 11
[4,2,1,1,1] generating graphics... => 14
[4,1,1,1,1,1] generating graphics... => 10
[3,3,3] generating graphics... => 3
[3,3,2,1] generating graphics... => 9
[3,3,1,1,1] generating graphics... => 7
[3,2,2,2] generating graphics... => 8
[3,2,2,1,1] generating graphics... => 12
[3,2,1,1,1,1] generating graphics... => 15
[3,1,1,1,1,1,1] generating graphics... => 10
[2,2,2,2,1] generating graphics... => 4
[2,2,2,1,1,1] generating graphics... => 6
[2,2,1,1,1,1,1] generating graphics... => 8
[2,1,1,1,1,1,1,1] generating graphics... => 10
[1,1,1,1,1,1,1,1,1] generating graphics... => 1
[10] generating graphics... => 10
[9,1] generating graphics... => 11
[8,2] generating graphics... => 11
[8,1,1] generating graphics... => 11
[7,3] generating graphics... => 11
[7,2,1] generating graphics... => 13
[7,1,1,1] generating graphics... => 11
[6,4] generating graphics... => 11
[6,3,1] generating graphics... => 13
[6,2,2] generating graphics... => 10
[6,2,1,1] generating graphics... => 14
[6,1,1,1,1] generating graphics... => 11
[5,5] generating graphics... => 5
[5,4,1] generating graphics... => 13
[5,3,2] generating graphics... => 13
[5,3,1,1] generating graphics... => 14
[5,2,2,1] generating graphics... => 12
[5,2,1,1,1] generating graphics... => 15
[5,1,1,1,1,1] generating graphics... => 11
[4,4,2] generating graphics... => 7
[4,4,1,1] generating graphics... => 7
[4,3,3] generating graphics... => 9
[4,3,2,1] generating graphics... => 16
[4,3,1,1,1] generating graphics... => 15
[4,2,2,2] generating graphics... => 9
[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... => 11
[3,3,3,1] generating graphics... => 5
[3,3,2,2] generating graphics... => 7
[3,3,2,1,1] generating graphics... => 11
[3,3,1,1,1,1] generating graphics... => 8
[3,2,2,2,1] generating graphics... => 11
[3,2,2,1,1,1] generating graphics... => 14
[3,2,1,1,1,1,1] generating graphics... => 17
[3,1,1,1,1,1,1,1] generating graphics... => 11
[2,2,2,2,2] generating graphics... => 2
[2,2,2,2,1,1] generating graphics... => 5
[2,2,2,1,1,1,1] generating graphics... => 7
[2,2,1,1,1,1,1,1] generating graphics... => 9
[2,1,1,1,1,1,1,1,1] generating graphics... => 11
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[11] generating graphics... => 11
[10,1] generating graphics... => 12
[9,2] generating graphics... => 12
[9,1,1] generating graphics... => 12
[8,3] generating graphics... => 12
[8,2,1] generating graphics... => 14
[8,1,1,1] generating graphics... => 12
[7,4] generating graphics... => 12
[7,3,1] generating graphics... => 14
[7,2,2] generating graphics... => 11
[7,2,1,1] generating graphics... => 15
[7,1,1,1,1] generating graphics... => 12
[6,5] generating graphics... => 12
[6,4,1] generating graphics... => 14
[6,3,2] generating graphics... => 14
[6,3,1,1] generating graphics... => 15
[6,2,2,1] generating graphics... => 13
[6,2,1,1,1] generating graphics... => 16
[6,1,1,1,1,1] generating graphics... => 12
[5,5,1] generating graphics... => 7
[5,4,2] generating graphics... => 14
[5,4,1,1] generating graphics... => 15
[5,3,3] generating graphics... => 10
[5,3,2,1] generating graphics... => 17
[5,3,1,1,1] generating graphics... => 16
[5,2,2,2] generating graphics... => 10
[5,2,2,1,1] generating graphics... => 14
[5,2,1,1,1,1] generating graphics... => 17
[5,1,1,1,1,1,1] generating graphics... => 12
[4,4,3] generating graphics... => 8
[4,4,2,1] generating graphics... => 10
[4,4,1,1,1] generating graphics... => 8
[4,3,3,1] generating graphics... => 12
[4,3,2,2] generating graphics... => 14
[4,3,2,1,1] generating graphics... => 19
[4,3,1,1,1,1] generating graphics... => 17
[4,2,2,2,1] generating graphics... => 12
[4,2,2,1,1,1] generating graphics... => 15
[4,2,1,1,1,1,1] generating graphics... => 18
[4,1,1,1,1,1,1,1] generating graphics... => 12
[3,3,3,2] generating graphics... => 6
[3,3,3,1,1] generating graphics... => 6
[3,3,2,2,1] generating graphics... => 10
[3,3,2,1,1,1] generating graphics... => 13
[3,3,1,1,1,1,1] generating graphics... => 9
[3,2,2,2,2] generating graphics... => 9
[3,2,2,2,1,1] generating graphics... => 13
[3,2,2,1,1,1,1] generating graphics... => 16
[3,2,1,1,1,1,1,1] generating graphics... => 19
[3,1,1,1,1,1,1,1,1] generating graphics... => 12
[2,2,2,2,2,1] generating graphics... => 4
[2,2,2,2,1,1,1] generating graphics... => 6
[2,2,2,1,1,1,1,1] generating graphics... => 8
[2,2,1,1,1,1,1,1,1] generating graphics... => 10
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 12
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[12] generating graphics... => 12
[11,1] generating graphics... => 13
[10,2] generating graphics... => 13
[10,1,1] generating graphics... => 13
[9,3] generating graphics... => 13
[9,2,1] generating graphics... => 15
[9,1,1,1] generating graphics... => 13
[8,4] generating graphics... => 13
[8,3,1] generating graphics... => 15
[8,2,2] generating graphics... => 12
[8,2,1,1] generating graphics... => 16
[8,1,1,1,1] generating graphics... => 13
[7,5] generating graphics... => 13
[7,4,1] generating graphics... => 15
[7,3,2] generating graphics... => 15
[7,3,1,1] generating graphics... => 16
[7,2,2,1] generating graphics... => 14
[7,2,1,1,1] generating graphics... => 17
[7,1,1,1,1,1] generating graphics... => 13
[6,6] generating graphics... => 6
[6,5,1] generating graphics... => 15
[6,4,2] generating graphics... => 15
[6,4,1,1] generating graphics... => 16
[6,3,3] generating graphics... => 11
[6,3,2,1] generating graphics... => 18
[6,3,1,1,1] generating graphics... => 17
[6,2,2,2] generating graphics... => 11
[6,2,2,1,1] generating graphics... => 15
[6,2,1,1,1,1] generating graphics... => 18
[6,1,1,1,1,1,1] generating graphics... => 13
[5,5,2] generating graphics... => 8
[5,5,1,1] generating graphics... => 8
[5,4,3] generating graphics... => 15
[5,4,2,1] generating graphics... => 18
[5,4,1,1,1] generating graphics... => 17
[5,3,3,1] generating graphics... => 13
[5,3,2,2] generating graphics... => 15
[5,3,2,1,1] generating graphics... => 20
[5,3,1,1,1,1] generating graphics... => 18
[5,2,2,2,1] generating graphics... => 13
[5,2,2,1,1,1] generating graphics... => 16
[5,2,1,1,1,1,1] generating graphics... => 19
[5,1,1,1,1,1,1,1] generating graphics... => 13
[4,4,4] generating graphics... => 4
[4,4,3,1] generating graphics... => 11
[4,4,2,2] generating graphics... => 8
[4,4,2,1,1] generating graphics... => 12
[4,4,1,1,1,1] generating graphics... => 9
[4,3,3,2] generating graphics... => 13
[4,3,3,1,1] generating graphics... => 14
[4,3,2,2,1] generating graphics... => 18
[4,3,2,1,1,1] generating graphics... => 22
[4,3,1,1,1,1,1] generating graphics... => 19
[4,2,2,2,2] generating graphics... => 10
[4,2,2,2,1,1] generating graphics... => 14
[4,2,2,1,1,1,1] generating graphics... => 17
[4,2,1,1,1,1,1,1] generating graphics... => 20
[4,1,1,1,1,1,1,1,1] generating graphics... => 13
[3,3,3,3] generating graphics... => 3
[3,3,3,2,1] generating graphics... => 9
[3,3,3,1,1,1] generating graphics... => 7
[3,3,2,2,2] generating graphics... => 8
[3,3,2,2,1,1] generating graphics... => 12
[3,3,2,1,1,1,1] generating graphics... => 15
[3,3,1,1,1,1,1,1] generating graphics... => 10
[3,2,2,2,2,1] generating graphics... => 12
[3,2,2,2,1,1,1] generating graphics... => 15
[3,2,2,1,1,1,1,1] generating graphics... => 18
[3,2,1,1,1,1,1,1,1] generating graphics... => 21
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 13
[2,2,2,2,2,2] generating graphics... => 2
[2,2,2,2,2,1,1] generating graphics... => 5
[2,2,2,2,1,1,1,1] generating graphics... => 7
[2,2,2,1,1,1,1,1,1] generating graphics... => 9
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 11
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 13
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
click to show generating function       
Description
The major index of an integer partition when read from bottom to top.
This is the sum of the positions of the corners of the shape of an integer partition when reading from bottom to top.
For example, the partition $\lambda = (8,6,6,4,3,3)$ has corners at positions 3,6,9, and 13, giving a major index of 31.
Code
def statistic(L):
    L = list(L) + [0]
    return sum( len(L)-i-2+L[i] for i in range(len(L)-1) if L[i] > L[i+1] )

Created
Apr 10, 2017 at 15:37 by Christian Stump
Updated
Apr 10, 2017 at 15:37 by Christian Stump