Identifier
Identifier
Values
[] generating graphics... => 0
[1] generating graphics... => 1
[2] generating graphics... => 3
[1,1] generating graphics... => 2
[3] generating graphics... => 6
[2,1] generating graphics... => 4
[1,1,1] generating graphics... => 3
[4] generating graphics... => 10
[3,1] generating graphics... => 7
[2,2] generating graphics... => 5
[2,1,1] generating graphics... => 5
[1,1,1,1] generating graphics... => 4
[5] generating graphics... => 15
[4,1] generating graphics... => 11
[3,2] generating graphics... => 8
[3,1,1] generating graphics... => 8
[2,2,1] generating graphics... => 6
[2,1,1,1] generating graphics... => 6
[1,1,1,1,1] generating graphics... => 5
[6] generating graphics... => 21
[5,1] generating graphics... => 16
[4,2] generating graphics... => 12
[4,1,1] generating graphics... => 12
[3,3] generating graphics... => 9
[3,2,1] generating graphics... => 9
[3,1,1,1] generating graphics... => 9
[2,2,2] generating graphics... => 7
[2,2,1,1] generating graphics... => 7
[2,1,1,1,1] generating graphics... => 7
[1,1,1,1,1,1] generating graphics... => 6
[7] generating graphics... => 28
[6,1] generating graphics... => 22
[5,2] generating graphics... => 17
[5,1,1] generating graphics... => 17
[4,3] generating graphics... => 13
[4,2,1] generating graphics... => 13
[4,1,1,1] generating graphics... => 13
[3,3,1] generating graphics... => 10
[3,2,2] generating graphics... => 10
[3,2,1,1] generating graphics... => 10
[3,1,1,1,1] generating graphics... => 10
[2,2,2,1] generating graphics... => 8
[2,2,1,1,1] generating graphics... => 8
[2,1,1,1,1,1] generating graphics... => 8
[1,1,1,1,1,1,1] generating graphics... => 7
[8] generating graphics... => 36
[7,1] generating graphics... => 29
[6,2] generating graphics... => 23
[6,1,1] generating graphics... => 23
[5,3] generating graphics... => 18
[5,2,1] generating graphics... => 18
[5,1,1,1] generating graphics... => 18
[4,4] generating graphics... => 14
[4,3,1] generating graphics... => 14
[4,2,2] generating graphics... => 14
[4,2,1,1] generating graphics... => 14
[4,1,1,1,1] generating graphics... => 14
[3,3,2] generating graphics... => 11
[3,3,1,1] generating graphics... => 11
[3,2,2,1] generating graphics... => 11
[3,2,1,1,1] generating graphics... => 11
[3,1,1,1,1,1] generating graphics... => 11
[2,2,2,2] generating graphics... => 9
[2,2,2,1,1] generating graphics... => 9
[2,2,1,1,1,1] generating graphics... => 9
[2,1,1,1,1,1,1] generating graphics... => 9
[1,1,1,1,1,1,1,1] generating graphics... => 8
[9] generating graphics... => 45
[8,1] generating graphics... => 37
[7,2] generating graphics... => 30
[7,1,1] generating graphics... => 30
[6,3] generating graphics... => 24
[6,2,1] generating graphics... => 24
[6,1,1,1] generating graphics... => 24
[5,4] generating graphics... => 19
[5,3,1] generating graphics... => 19
[5,2,2] generating graphics... => 19
[5,2,1,1] generating graphics... => 19
[5,1,1,1,1] generating graphics... => 19
[4,4,1] generating graphics... => 15
[4,3,2] generating graphics... => 15
[4,3,1,1] generating graphics... => 15
[4,2,2,1] generating graphics... => 15
[4,2,1,1,1] generating graphics... => 15
[4,1,1,1,1,1] generating graphics... => 15
[3,3,3] generating graphics... => 12
[3,3,2,1] generating graphics... => 12
[3,3,1,1,1] generating graphics... => 12
[3,2,2,2] generating graphics... => 12
[3,2,2,1,1] generating graphics... => 12
[3,2,1,1,1,1] generating graphics... => 12
[3,1,1,1,1,1,1] generating graphics... => 12
[2,2,2,2,1] generating graphics... => 10
[2,2,2,1,1,1] generating graphics... => 10
[2,2,1,1,1,1,1] generating graphics... => 10
[2,1,1,1,1,1,1,1] generating graphics... => 10
[1,1,1,1,1,1,1,1,1] generating graphics... => 9
[10] generating graphics... => 55
[9,1] generating graphics... => 46
[8,2] generating graphics... => 38
[8,1,1] generating graphics... => 38
[7,3] generating graphics... => 31
[7,2,1] generating graphics... => 31
[7,1,1,1] generating graphics... => 31
[6,4] generating graphics... => 25
[6,3,1] generating graphics... => 25
[6,2,2] generating graphics... => 25
[6,2,1,1] generating graphics... => 25
[6,1,1,1,1] generating graphics... => 25
[5,5] generating graphics... => 20
[5,4,1] generating graphics... => 20
[5,3,2] generating graphics... => 20
[5,3,1,1] generating graphics... => 20
[5,2,2,1] generating graphics... => 20
[5,2,1,1,1] generating graphics... => 20
[5,1,1,1,1,1] generating graphics... => 20
[4,4,2] generating graphics... => 16
[4,4,1,1] generating graphics... => 16
[4,3,3] generating graphics... => 16
[4,3,2,1] generating graphics... => 16
[4,3,1,1,1] generating graphics... => 16
[4,2,2,2] generating graphics... => 16
[4,2,2,1,1] generating graphics... => 16
[4,2,1,1,1,1] generating graphics... => 16
[4,1,1,1,1,1,1] generating graphics... => 16
[3,3,3,1] generating graphics... => 13
[3,3,2,2] generating graphics... => 13
[3,3,2,1,1] generating graphics... => 13
[3,3,1,1,1,1] generating graphics... => 13
[3,2,2,2,1] generating graphics... => 13
[3,2,2,1,1,1] generating graphics... => 13
[3,2,1,1,1,1,1] generating graphics... => 13
[3,1,1,1,1,1,1,1] generating graphics... => 13
[2,2,2,2,2] generating graphics... => 11
[2,2,2,2,1,1] generating graphics... => 11
[2,2,2,1,1,1,1] generating graphics... => 11
[2,2,1,1,1,1,1,1] generating graphics... => 11
[2,1,1,1,1,1,1,1,1] generating graphics... => 11
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 10
[11] generating graphics... => 66
[10,1] generating graphics... => 56
[9,2] generating graphics... => 47
[9,1,1] generating graphics... => 47
[8,3] generating graphics... => 39
[8,2,1] generating graphics... => 39
[8,1,1,1] generating graphics... => 39
[7,4] generating graphics... => 32
[7,3,1] generating graphics... => 32
[7,2,2] generating graphics... => 32
[7,2,1,1] generating graphics... => 32
[7,1,1,1,1] generating graphics... => 32
[6,5] generating graphics... => 26
[6,4,1] generating graphics... => 26
[6,3,2] generating graphics... => 26
[6,3,1,1] generating graphics... => 26
[6,2,2,1] generating graphics... => 26
[6,2,1,1,1] generating graphics... => 26
[6,1,1,1,1,1] generating graphics... => 26
[5,5,1] generating graphics... => 21
[5,4,2] generating graphics... => 21
[5,4,1,1] generating graphics... => 21
[5,3,3] generating graphics... => 21
[5,3,2,1] generating graphics... => 21
[5,3,1,1,1] generating graphics... => 21
[5,2,2,2] generating graphics... => 21
[5,2,2,1,1] generating graphics... => 21
[5,2,1,1,1,1] generating graphics... => 21
[5,1,1,1,1,1,1] generating graphics... => 21
[4,4,3] generating graphics... => 17
[4,4,2,1] generating graphics... => 17
[4,4,1,1,1] generating graphics... => 17
[4,3,3,1] generating graphics... => 17
[4,3,2,2] generating graphics... => 17
[4,3,2,1,1] generating graphics... => 17
[4,3,1,1,1,1] generating graphics... => 17
[4,2,2,2,1] generating graphics... => 17
[4,2,2,1,1,1] generating graphics... => 17
[4,2,1,1,1,1,1] generating graphics... => 17
[4,1,1,1,1,1,1,1] generating graphics... => 17
[3,3,3,2] generating graphics... => 14
[3,3,3,1,1] generating graphics... => 14
[3,3,2,2,1] generating graphics... => 14
[3,3,2,1,1,1] generating graphics... => 14
[3,3,1,1,1,1,1] generating graphics... => 14
[3,2,2,2,2] generating graphics... => 14
[3,2,2,2,1,1] generating graphics... => 14
[3,2,2,1,1,1,1] generating graphics... => 14
[3,2,1,1,1,1,1,1] generating graphics... => 14
[3,1,1,1,1,1,1,1,1] generating graphics... => 14
[2,2,2,2,2,1] generating graphics... => 12
[2,2,2,2,1,1,1] generating graphics... => 12
[2,2,2,1,1,1,1,1] generating graphics... => 12
[2,2,1,1,1,1,1,1,1] generating graphics... => 12
[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... => 11
[12] generating graphics... => 78
[11,1] generating graphics... => 67
[10,2] generating graphics... => 57
[10,1,1] generating graphics... => 57
[9,3] generating graphics... => 48
[9,2,1] generating graphics... => 48
[9,1,1,1] generating graphics... => 48
[8,4] generating graphics... => 40
[8,3,1] generating graphics... => 40
[8,2,2] generating graphics... => 40
[8,2,1,1] generating graphics... => 40
[8,1,1,1,1] generating graphics... => 40
[7,5] generating graphics... => 33
[7,4,1] generating graphics... => 33
[7,3,2] generating graphics... => 33
[7,3,1,1] generating graphics... => 33
[7,2,2,1] generating graphics... => 33
[7,2,1,1,1] generating graphics... => 33
[7,1,1,1,1,1] generating graphics... => 33
[6,6] generating graphics... => 27
[6,5,1] generating graphics... => 27
[6,4,2] generating graphics... => 27
[6,4,1,1] generating graphics... => 27
[6,3,3] generating graphics... => 27
[6,3,2,1] generating graphics... => 27
[6,3,1,1,1] generating graphics... => 27
[6,2,2,2] generating graphics... => 27
[6,2,2,1,1] generating graphics... => 27
[6,2,1,1,1,1] generating graphics... => 27
[6,1,1,1,1,1,1] generating graphics... => 27
[5,5,2] generating graphics... => 22
[5,5,1,1] generating graphics... => 22
[5,4,3] generating graphics... => 22
[5,4,2,1] generating graphics... => 22
[5,4,1,1,1] generating graphics... => 22
[5,3,3,1] generating graphics... => 22
[5,3,2,2] generating graphics... => 22
[5,3,2,1,1] generating graphics... => 22
[5,3,1,1,1,1] generating graphics... => 22
[5,2,2,2,1] generating graphics... => 22
[5,2,2,1,1,1] generating graphics... => 22
[5,2,1,1,1,1,1] generating graphics... => 22
[5,1,1,1,1,1,1,1] generating graphics... => 22
[4,4,4] generating graphics... => 18
[4,4,3,1] generating graphics... => 18
[4,4,2,2] generating graphics... => 18
[4,4,2,1,1] generating graphics... => 18
[4,4,1,1,1,1] generating graphics... => 18
[4,3,3,2] generating graphics... => 18
[4,3,3,1,1] generating graphics... => 18
[4,3,2,2,1] generating graphics... => 18
[4,3,2,1,1,1] generating graphics... => 18
[4,3,1,1,1,1,1] generating graphics... => 18
[4,2,2,2,2] generating graphics... => 18
[4,2,2,2,1,1] generating graphics... => 18
[4,2,2,1,1,1,1] generating graphics... => 18
[4,2,1,1,1,1,1,1] generating graphics... => 18
[4,1,1,1,1,1,1,1,1] generating graphics... => 18
[3,3,3,3] generating graphics... => 15
[3,3,3,2,1] generating graphics... => 15
[3,3,3,1,1,1] generating graphics... => 15
[3,3,2,2,2] generating graphics... => 15
[3,3,2,2,1,1] generating graphics... => 15
[3,3,2,1,1,1,1] generating graphics... => 15
[3,3,1,1,1,1,1,1] generating graphics... => 15
[3,2,2,2,2,1] generating graphics... => 15
[3,2,2,2,1,1,1] generating graphics... => 15
[3,2,2,1,1,1,1,1] generating graphics... => 15
[3,2,1,1,1,1,1,1,1] generating graphics... => 15
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 15
[2,2,2,2,2,2] generating graphics... => 13
[2,2,2,2,2,1,1] generating graphics... => 13
[2,2,2,2,1,1,1,1] generating graphics... => 13
[2,2,2,1,1,1,1,1,1] generating graphics... => 13
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 13
[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... => 12
click to show generating function       
Description
The sum of the hook lengths in the first column of an integer partition.
For a cell in the Ferrers diagram of a partition, the hook length is given by the number of boxes to its right plus the number of boxes below plus one. This statistic is the sum of the hook lengths of the first column of a partition.
Code
def statistic(L):
    return sum( L.hook_length(*c) for c in L.cells() if c[0] == 0 )

Created
Jun 27, 2017 at 09:08 by Christian Stump
Updated
Oct 31, 2017 at 08:14 by Martin Rubey