Identifier
Values
=>
Cc0002;cc-rep
[1]=>1
[2]=>2
[1,1]=>2
[3]=>3
[2,1]=>3
[1,1,1]=>3
[4]=>4
[3,1]=>4
[2,2]=>3
[2,1,1]=>4
[1,1,1,1]=>4
[5]=>5
[4,1]=>5
[3,2]=>4
[3,1,1]=>5
[2,2,1]=>4
[2,1,1,1]=>5
[1,1,1,1,1]=>5
[6]=>6
[5,1]=>6
[4,2]=>5
[4,1,1]=>6
[3,3]=>8
[3,2,1]=>5
[3,1,1,1]=>6
[2,2,2]=>8
[2,2,1,1]=>5
[2,1,1,1,1]=>6
[1,1,1,1,1,1]=>6
[7]=>7
[6,1]=>7
[5,2]=>6
[5,1,1]=>7
[4,3]=>10
[4,2,1]=>6
[4,1,1,1]=>7
[3,3,1]=>10
[3,2,2]=>10
[3,2,1,1]=>6
[3,1,1,1,1]=>7
[2,2,2,1]=>10
[2,2,1,1,1]=>6
[2,1,1,1,1,1]=>7
[1,1,1,1,1,1,1]=>7
[8]=>8
[7,1]=>8
[6,2]=>7
[6,1,1]=>8
[5,3]=>12
[5,2,1]=>7
[5,1,1,1]=>8
[4,4]=>15
[4,3,1]=>12
[4,2,2]=>12
[4,2,1,1]=>7
[4,1,1,1,1]=>8
[3,3,2]=>15
[3,3,1,1]=>12
[3,2,2,1]=>12
[3,2,1,1,1]=>7
[3,1,1,1,1,1]=>8
[2,2,2,2]=>15
[2,2,2,1,1]=>12
[2,2,1,1,1,1]=>7
[2,1,1,1,1,1,1]=>8
[1,1,1,1,1,1,1,1]=>8
[9]=>9
[8,1]=>9
[7,2]=>8
[7,1,1]=>9
[6,3]=>14
[6,2,1]=>8
[6,1,1,1]=>9
[5,4]=>18
[5,3,1]=>14
[5,2,2]=>14
[5,2,1,1]=>8
[5,1,1,1,1]=>9
[4,4,1]=>18
[4,3,2]=>18
[4,3,1,1]=>14
[4,2,2,1]=>14
[4,2,1,1,1]=>8
[4,1,1,1,1,1]=>9
[3,3,3]=>15
[3,3,2,1]=>18
[3,3,1,1,1]=>14
[3,2,2,2]=>18
[3,2,2,1,1]=>14
[3,2,1,1,1,1]=>8
[3,1,1,1,1,1,1]=>9
[2,2,2,2,1]=>18
[2,2,2,1,1,1]=>14
[2,2,1,1,1,1,1]=>8
[2,1,1,1,1,1,1,1]=>9
[1,1,1,1,1,1,1,1,1]=>9
[10]=>10
[9,1]=>10
[8,2]=>9
[8,1,1]=>10
[7,3]=>16
[7,2,1]=>9
[7,1,1,1]=>10
[6,4]=>21
[6,3,1]=>16
[6,2,2]=>16
[6,2,1,1]=>9
[6,1,1,1,1]=>10
[5,5]=>24
[5,4,1]=>21
[5,3,2]=>21
[5,3,1,1]=>16
[5,2,2,1]=>16
[5,2,1,1,1]=>9
[5,1,1,1,1,1]=>10
[4,4,2]=>24
[4,4,1,1]=>21
[4,3,3]=>18
[4,3,2,1]=>21
[4,3,1,1,1]=>16
[4,2,2,2]=>21
[4,2,2,1,1]=>16
[4,2,1,1,1,1]=>9
[4,1,1,1,1,1,1]=>10
[3,3,3,1]=>18
[3,3,2,2]=>24
[3,3,2,1,1]=>21
[3,3,1,1,1,1]=>16
[3,2,2,2,1]=>21
[3,2,2,1,1,1]=>16
[3,2,1,1,1,1,1]=>9
[3,1,1,1,1,1,1,1]=>10
[2,2,2,2,2]=>24
[2,2,2,2,1,1]=>21
[2,2,2,1,1,1,1]=>16
[2,2,1,1,1,1,1,1]=>9
[2,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,1,1,1,1,1,1]=>10
[11]=>11
[10,1]=>11
[9,2]=>10
[9,1,1]=>11
[8,3]=>18
[8,2,1]=>10
[8,1,1,1]=>11
[7,4]=>24
[7,3,1]=>18
[7,2,2]=>18
[7,2,1,1]=>10
[7,1,1,1,1]=>11
[6,5]=>28
[6,4,1]=>24
[6,3,2]=>24
[6,3,1,1]=>18
[6,2,2,1]=>18
[6,2,1,1,1]=>10
[6,1,1,1,1,1]=>11
[5,5,1]=>28
[5,4,2]=>28
[5,4,1,1]=>24
[5,3,3]=>21
[5,3,2,1]=>24
[5,3,1,1,1]=>18
[5,2,2,2]=>24
[5,2,2,1,1]=>18
[5,2,1,1,1,1]=>10
[5,1,1,1,1,1,1]=>11
[4,4,3]=>24
[4,4,2,1]=>28
[4,4,1,1,1]=>24
[4,3,3,1]=>21
[4,3,2,2]=>28
[4,3,2,1,1]=>24
[4,3,1,1,1,1]=>18
[4,2,2,2,1]=>24
[4,2,2,1,1,1]=>18
[4,2,1,1,1,1,1]=>10
[4,1,1,1,1,1,1,1]=>11
[3,3,3,2]=>24
[3,3,3,1,1]=>21
[3,3,2,2,1]=>28
[3,3,2,1,1,1]=>24
[3,3,1,1,1,1,1]=>18
[3,2,2,2,2]=>28
[3,2,2,2,1,1]=>24
[3,2,2,1,1,1,1]=>18
[3,2,1,1,1,1,1,1]=>10
[3,1,1,1,1,1,1,1,1]=>11
[2,2,2,2,2,1]=>28
[2,2,2,2,1,1,1]=>24
[2,2,2,1,1,1,1,1]=>18
[2,2,1,1,1,1,1,1,1]=>10
[2,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,1,1,1,1,1,1,1]=>11
[12]=>12
[11,1]=>12
[10,2]=>11
[10,1,1]=>12
[9,3]=>20
[9,2,1]=>11
[9,1,1,1]=>12
[8,4]=>27
[8,3,1]=>20
[8,2,2]=>20
[8,2,1,1]=>11
[8,1,1,1,1]=>12
[7,5]=>32
[7,4,1]=>27
[7,3,2]=>27
[7,3,1,1]=>20
[7,2,2,1]=>20
[7,2,1,1,1]=>11
[7,1,1,1,1,1]=>12
[6,6]=>35
[6,5,1]=>32
[6,4,2]=>32
[6,4,1,1]=>27
[6,3,3]=>24
[6,3,2,1]=>27
[6,3,1,1,1]=>20
[6,2,2,2]=>27
[6,2,2,1,1]=>20
[6,2,1,1,1,1]=>11
[6,1,1,1,1,1,1]=>12
[5,5,2]=>35
[5,5,1,1]=>32
[5,4,3]=>28
[5,4,2,1]=>32
[5,4,1,1,1]=>27
[5,3,3,1]=>24
[5,3,2,2]=>32
[5,3,2,1,1]=>27
[5,3,1,1,1,1]=>20
[5,2,2,2,1]=>27
[5,2,2,1,1,1]=>20
[5,2,1,1,1,1,1]=>11
[5,1,1,1,1,1,1,1]=>12
[4,4,4]=>48
[4,4,3,1]=>28
[4,4,2,2]=>35
[4,4,2,1,1]=>32
[4,4,1,1,1,1]=>27
[4,3,3,2]=>28
[4,3,3,1,1]=>24
[4,3,2,2,1]=>32
[4,3,2,1,1,1]=>27
[4,3,1,1,1,1,1]=>20
[4,2,2,2,2]=>32
[4,2,2,2,1,1]=>27
[4,2,2,1,1,1,1]=>20
[4,2,1,1,1,1,1,1]=>11
[4,1,1,1,1,1,1,1,1]=>12
[3,3,3,3]=>48
[3,3,3,2,1]=>28
[3,3,3,1,1,1]=>24
[3,3,2,2,2]=>35
[3,3,2,2,1,1]=>32
[3,3,2,1,1,1,1]=>27
[3,3,1,1,1,1,1,1]=>20
[3,2,2,2,2,1]=>32
[3,2,2,2,1,1,1]=>27
[3,2,2,1,1,1,1,1]=>20
[3,2,1,1,1,1,1,1,1]=>11
[3,1,1,1,1,1,1,1,1,1]=>12
[2,2,2,2,2,2]=>35
[2,2,2,2,2,1,1]=>32
[2,2,2,2,1,1,1,1]=>27
[2,2,2,1,1,1,1,1,1]=>20
[2,2,1,1,1,1,1,1,1,1]=>11
[2,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,1,1,1,1,1,1,1,1]=>12
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Description
The product of the hook lengths of the diagonal cells in 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 product of the hook lengths of the diagonal cells $(i,i)$ of a 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 product of the hook lengths of the diagonal cells $(i,i)$ of a partition.
Code
def statistic(L):
return prod( L.hook_length(*c) for c in L.cells() if c[0] == c[1] )
Created
Jun 27, 2017 at 09:05 by Christian Stump
Updated
Jul 06, 2021 at 07:55 by Martin Rubey
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