Identifier
Identifier
Values
[] generating graphics... => 0
[1] generating graphics... => 1
[2] generating graphics... => 3
[1,1] generating graphics... => 3
[3] generating graphics... => 6
[2,1] generating graphics... => 5
[1,1,1] generating graphics... => 6
[4] generating graphics... => 10
[3,1] generating graphics... => 8
[2,2] generating graphics... => 8
[2,1,1] generating graphics... => 8
[1,1,1,1] generating graphics... => 10
[5] generating graphics... => 15
[4,1] generating graphics... => 12
[3,2] generating graphics... => 11
[3,1,1] generating graphics... => 11
[2,2,1] generating graphics... => 11
[2,1,1,1] generating graphics... => 12
[1,1,1,1,1] generating graphics... => 15
[6] generating graphics... => 21
[5,1] generating graphics... => 17
[4,2] generating graphics... => 15
[4,1,1] generating graphics... => 15
[3,3] generating graphics... => 15
[3,2,1] generating graphics... => 14
[3,1,1,1] generating graphics... => 15
[2,2,2] generating graphics... => 15
[2,2,1,1] generating graphics... => 15
[2,1,1,1,1] generating graphics... => 17
[1,1,1,1,1,1] generating graphics... => 21
[7] generating graphics... => 28
[6,1] generating graphics... => 23
[5,2] generating graphics... => 20
[5,1,1] generating graphics... => 20
[4,3] generating graphics... => 19
[4,2,1] generating graphics... => 18
[4,1,1,1] generating graphics... => 19
[3,3,1] generating graphics... => 18
[3,2,2] generating graphics... => 18
[3,2,1,1] generating graphics... => 18
[3,1,1,1,1] generating graphics... => 20
[2,2,2,1] generating graphics... => 19
[2,2,1,1,1] generating graphics... => 20
[2,1,1,1,1,1] generating graphics... => 23
[1,1,1,1,1,1,1] generating graphics... => 28
[8] generating graphics... => 36
[7,1] generating graphics... => 30
[6,2] generating graphics... => 26
[6,1,1] generating graphics... => 26
[5,3] generating graphics... => 24
[5,2,1] generating graphics... => 23
[5,1,1,1] generating graphics... => 24
[4,4] generating graphics... => 24
[4,3,1] generating graphics... => 22
[4,2,2] generating graphics... => 22
[4,2,1,1] generating graphics... => 22
[4,1,1,1,1] generating graphics... => 24
[3,3,2] generating graphics... => 22
[3,3,1,1] generating graphics... => 22
[3,2,2,1] generating graphics... => 22
[3,2,1,1,1] generating graphics... => 23
[3,1,1,1,1,1] generating graphics... => 26
[2,2,2,2] generating graphics... => 24
[2,2,2,1,1] generating graphics... => 24
[2,2,1,1,1,1] generating graphics... => 26
[2,1,1,1,1,1,1] generating graphics... => 30
[1,1,1,1,1,1,1,1] generating graphics... => 36
[9] generating graphics... => 45
[8,1] generating graphics... => 38
[7,2] generating graphics... => 33
[7,1,1] generating graphics... => 33
[6,3] generating graphics... => 30
[6,2,1] generating graphics... => 29
[6,1,1,1] generating graphics... => 30
[5,4] generating graphics... => 29
[5,3,1] generating graphics... => 27
[5,2,2] generating graphics... => 27
[5,2,1,1] generating graphics... => 27
[5,1,1,1,1] generating graphics... => 29
[4,4,1] generating graphics... => 27
[4,3,2] generating graphics... => 26
[4,3,1,1] generating graphics... => 26
[4,2,2,1] generating graphics... => 26
[4,2,1,1,1] generating graphics... => 27
[4,1,1,1,1,1] generating graphics... => 30
[3,3,3] generating graphics... => 27
[3,3,2,1] generating graphics... => 26
[3,3,1,1,1] generating graphics... => 27
[3,2,2,2] generating graphics... => 27
[3,2,2,1,1] generating graphics... => 27
[3,2,1,1,1,1] generating graphics... => 29
[3,1,1,1,1,1,1] generating graphics... => 33
[2,2,2,2,1] generating graphics... => 29
[2,2,2,1,1,1] generating graphics... => 30
[2,2,1,1,1,1,1] generating graphics... => 33
[2,1,1,1,1,1,1,1] generating graphics... => 38
[1,1,1,1,1,1,1,1,1] generating graphics... => 45
[10] generating graphics... => 55
[9,1] generating graphics... => 47
[8,2] generating graphics... => 41
[8,1,1] generating graphics... => 41
[7,3] generating graphics... => 37
[7,2,1] generating graphics... => 36
[7,1,1,1] generating graphics... => 37
[6,4] generating graphics... => 35
[6,3,1] generating graphics... => 33
[6,2,2] generating graphics... => 33
[6,2,1,1] generating graphics... => 33
[6,1,1,1,1] generating graphics... => 35
[5,5] generating graphics... => 35
[5,4,1] generating graphics... => 32
[5,3,2] generating graphics... => 31
[5,3,1,1] generating graphics... => 31
[5,2,2,1] generating graphics... => 31
[5,2,1,1,1] generating graphics... => 32
[5,1,1,1,1,1] generating graphics... => 35
[4,4,2] generating graphics... => 31
[4,4,1,1] generating graphics... => 31
[4,3,3] generating graphics... => 31
[4,3,2,1] generating graphics... => 30
[4,3,1,1,1] generating graphics... => 31
[4,2,2,2] generating graphics... => 31
[4,2,2,1,1] generating graphics... => 31
[4,2,1,1,1,1] generating graphics... => 33
[4,1,1,1,1,1,1] generating graphics... => 37
[3,3,3,1] generating graphics... => 31
[3,3,2,2] generating graphics... => 31
[3,3,2,1,1] generating graphics... => 31
[3,3,1,1,1,1] generating graphics... => 33
[3,2,2,2,1] generating graphics... => 32
[3,2,2,1,1,1] generating graphics... => 33
[3,2,1,1,1,1,1] generating graphics... => 36
[3,1,1,1,1,1,1,1] generating graphics... => 41
[2,2,2,2,2] generating graphics... => 35
[2,2,2,2,1,1] generating graphics... => 35
[2,2,2,1,1,1,1] generating graphics... => 37
[2,2,1,1,1,1,1,1] generating graphics... => 41
[2,1,1,1,1,1,1,1,1] generating graphics... => 47
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 55
[11] generating graphics... => 66
[10,1] generating graphics... => 57
[9,2] generating graphics... => 50
[9,1,1] generating graphics... => 50
[8,3] generating graphics... => 45
[8,2,1] generating graphics... => 44
[8,1,1,1] generating graphics... => 45
[7,4] generating graphics... => 42
[7,3,1] generating graphics... => 40
[7,2,2] generating graphics... => 40
[7,2,1,1] generating graphics... => 40
[7,1,1,1,1] generating graphics... => 42
[6,5] generating graphics... => 41
[6,4,1] generating graphics... => 38
[6,3,2] generating graphics... => 37
[6,3,1,1] generating graphics... => 37
[6,2,2,1] generating graphics... => 37
[6,2,1,1,1] generating graphics... => 38
[6,1,1,1,1,1] generating graphics... => 41
[5,5,1] generating graphics... => 38
[5,4,2] generating graphics... => 36
[5,4,1,1] generating graphics... => 36
[5,3,3] generating graphics... => 36
[5,3,2,1] generating graphics... => 35
[5,3,1,1,1] generating graphics... => 36
[5,2,2,2] generating graphics... => 36
[5,2,2,1,1] generating graphics... => 36
[5,2,1,1,1,1] generating graphics... => 38
[5,1,1,1,1,1,1] generating graphics... => 42
[4,4,3] generating graphics... => 36
[4,4,2,1] generating graphics... => 35
[4,4,1,1,1] generating graphics... => 36
[4,3,3,1] generating graphics... => 35
[4,3,2,2] generating graphics... => 35
[4,3,2,1,1] generating graphics... => 35
[4,3,1,1,1,1] generating graphics... => 37
[4,2,2,2,1] generating graphics... => 36
[4,2,2,1,1,1] generating graphics... => 37
[4,2,1,1,1,1,1] generating graphics... => 40
[4,1,1,1,1,1,1,1] generating graphics... => 45
[3,3,3,2] generating graphics... => 36
[3,3,3,1,1] generating graphics... => 36
[3,3,2,2,1] generating graphics... => 36
[3,3,2,1,1,1] generating graphics... => 37
[3,3,1,1,1,1,1] generating graphics... => 40
[3,2,2,2,2] generating graphics... => 38
[3,2,2,2,1,1] generating graphics... => 38
[3,2,2,1,1,1,1] generating graphics... => 40
[3,2,1,1,1,1,1,1] generating graphics... => 44
[3,1,1,1,1,1,1,1,1] generating graphics... => 50
[2,2,2,2,2,1] generating graphics... => 41
[2,2,2,2,1,1,1] generating graphics... => 42
[2,2,2,1,1,1,1,1] generating graphics... => 45
[2,2,1,1,1,1,1,1,1] generating graphics... => 50
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 57
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 66
[12] generating graphics... => 78
[11,1] generating graphics... => 68
[10,2] generating graphics... => 60
[10,1,1] generating graphics... => 60
[9,3] generating graphics... => 54
[9,2,1] generating graphics... => 53
[9,1,1,1] generating graphics... => 54
[8,4] generating graphics... => 50
[8,3,1] generating graphics... => 48
[8,2,2] generating graphics... => 48
[8,2,1,1] generating graphics... => 48
[8,1,1,1,1] generating graphics... => 50
[7,5] generating graphics... => 48
[7,4,1] generating graphics... => 45
[7,3,2] generating graphics... => 44
[7,3,1,1] generating graphics... => 44
[7,2,2,1] generating graphics... => 44
[7,2,1,1,1] generating graphics... => 45
[7,1,1,1,1,1] generating graphics... => 48
[6,6] generating graphics... => 48
[6,5,1] generating graphics... => 44
[6,4,2] generating graphics... => 42
[6,4,1,1] generating graphics... => 42
[6,3,3] generating graphics... => 42
[6,3,2,1] generating graphics... => 41
[6,3,1,1,1] generating graphics... => 42
[6,2,2,2] generating graphics... => 42
[6,2,2,1,1] generating graphics... => 42
[6,2,1,1,1,1] generating graphics... => 44
[6,1,1,1,1,1,1] generating graphics... => 48
[5,5,2] generating graphics... => 42
[5,5,1,1] generating graphics... => 42
[5,4,3] generating graphics... => 41
[5,4,2,1] generating graphics... => 40
[5,4,1,1,1] generating graphics... => 41
[5,3,3,1] generating graphics... => 40
[5,3,2,2] generating graphics... => 40
[5,3,2,1,1] generating graphics... => 40
[5,3,1,1,1,1] generating graphics... => 42
[5,2,2,2,1] generating graphics... => 41
[5,2,2,1,1,1] generating graphics... => 42
[5,2,1,1,1,1,1] generating graphics... => 45
[5,1,1,1,1,1,1,1] generating graphics... => 50
[4,4,4] generating graphics... => 42
[4,4,3,1] generating graphics... => 40
[4,4,2,2] generating graphics... => 40
[4,4,2,1,1] generating graphics... => 40
[4,4,1,1,1,1] generating graphics... => 42
[4,3,3,2] generating graphics... => 40
[4,3,3,1,1] generating graphics... => 40
[4,3,2,2,1] generating graphics... => 40
[4,3,2,1,1,1] generating graphics... => 41
[4,3,1,1,1,1,1] generating graphics... => 44
[4,2,2,2,2] generating graphics... => 42
[4,2,2,2,1,1] generating graphics... => 42
[4,2,2,1,1,1,1] generating graphics... => 44
[4,2,1,1,1,1,1,1] generating graphics... => 48
[4,1,1,1,1,1,1,1,1] generating graphics... => 54
[3,3,3,3] generating graphics... => 42
[3,3,3,2,1] generating graphics... => 41
[3,3,3,1,1,1] generating graphics... => 42
[3,3,2,2,2] generating graphics... => 42
[3,3,2,2,1,1] generating graphics... => 42
[3,3,2,1,1,1,1] generating graphics... => 44
[3,3,1,1,1,1,1,1] generating graphics... => 48
[3,2,2,2,2,1] generating graphics... => 44
[3,2,2,2,1,1,1] generating graphics... => 45
[3,2,2,1,1,1,1,1] generating graphics... => 48
[3,2,1,1,1,1,1,1,1] generating graphics... => 53
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 60
[2,2,2,2,2,2] generating graphics... => 48
[2,2,2,2,2,1,1] generating graphics... => 48
[2,2,2,2,1,1,1,1] generating graphics... => 50
[2,2,2,1,1,1,1,1,1] generating graphics... => 54
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 60
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 68
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 78
[5,4,3,1] generating graphics... => 45
[5,4,2,2] generating graphics... => 45
[5,4,2,1,1] generating graphics... => 45
[5,3,3,2] generating graphics... => 45
[5,3,3,1,1] generating graphics... => 45
[5,3,2,2,1] generating graphics... => 45
[4,4,3,2] generating graphics... => 45
[4,4,3,1,1] generating graphics... => 45
[4,4,2,2,1] generating graphics... => 45
[4,3,3,2,1] generating graphics... => 45
[5,4,3,2] generating graphics... => 50
[5,4,3,1,1] generating graphics... => 50
[5,4,2,2,1] generating graphics... => 50
[5,3,3,2,1] generating graphics... => 50
[4,4,3,2,1] generating graphics... => 50
[5,4,3,2,1] generating graphics... => 55
click to show generating function       
Description
The sum of the hook lengths 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 + 1. This statistic is the sum of all hook lengths of a partition.
References
[1] Amdeberhan, T. Average on sum of hooks in a rectangle MathOverflow:273095
Code
def statistic(L):
    return sum( L.hook_length(*c) for c in L.cells() )

Created
Jun 27, 2017 at 09:02 by Christian Stump
Updated
Apr 26, 2018 at 07:39 by Martin Rubey