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Identifier
Values
=>
Cc0002;cc-rep
[2]=>1 [1,1]=>-1 [3]=>3 [2,1]=>0 [1,1,1]=>-3 [4]=>6 [3,1]=>2 [2,2]=>0 [2,1,1]=>-2 [1,1,1,1]=>-6 [5]=>10 [4,1]=>5 [3,2]=>2 [3,1,1]=>0 [2,2,1]=>-2 [2,1,1,1]=>-5 [1,1,1,1,1]=>-10 [6]=>15 [5,1]=>9 [4,2]=>5 [4,1,1]=>3 [3,3]=>3 [3,2,1]=>0 [3,1,1,1]=>-3 [2,2,2]=>-3 [2,2,1,1]=>-5 [2,1,1,1,1]=>-9 [1,1,1,1,1,1]=>-15 [7]=>21 [6,1]=>14 [5,2]=>9 [5,1,1]=>7 [4,3]=>6 [4,2,1]=>3 [4,1,1,1]=>0 [3,3,1]=>1 [3,2,2]=>-1 [3,2,1,1]=>-3 [3,1,1,1,1]=>-7 [2,2,2,1]=>-6 [2,2,1,1,1]=>-9 [2,1,1,1,1,1]=>-14 [1,1,1,1,1,1,1]=>-21 [8]=>28 [7,1]=>20 [6,2]=>14 [6,1,1]=>12 [5,3]=>10 [5,2,1]=>7 [5,1,1,1]=>4 [4,4]=>8 [4,3,1]=>4 [4,2,2]=>2 [4,2,1,1]=>0 [4,1,1,1,1]=>-4 [3,3,2]=>0 [3,3,1,1]=>-2 [3,2,2,1]=>-4 [3,2,1,1,1]=>-7 [3,1,1,1,1,1]=>-12 [2,2,2,2]=>-8 [2,2,2,1,1]=>-10 [2,2,1,1,1,1]=>-14 [2,1,1,1,1,1,1]=>-20 [1,1,1,1,1,1,1,1]=>-28 [9]=>36 [8,1]=>27 [7,2]=>20 [7,1,1]=>18 [6,3]=>15 [6,2,1]=>12 [6,1,1,1]=>9 [5,4]=>12 [5,3,1]=>8 [5,2,2]=>6 [5,2,1,1]=>4 [5,1,1,1,1]=>0 [4,4,1]=>6 [4,3,2]=>3 [4,3,1,1]=>1 [4,2,2,1]=>-1 [4,2,1,1,1]=>-4 [4,1,1,1,1,1]=>-9 [3,3,3]=>0 [3,3,2,1]=>-3 [3,3,1,1,1]=>-6 [3,2,2,2]=>-6 [3,2,2,1,1]=>-8 [3,2,1,1,1,1]=>-12 [3,1,1,1,1,1,1]=>-18 [2,2,2,2,1]=>-12 [2,2,2,1,1,1]=>-15 [2,2,1,1,1,1,1]=>-20 [2,1,1,1,1,1,1,1]=>-27 [1,1,1,1,1,1,1,1,1]=>-36 [10]=>45 [9,1]=>35 [8,2]=>27 [8,1,1]=>25 [7,3]=>21 [7,2,1]=>18 [7,1,1,1]=>15 [6,4]=>17 [6,3,1]=>13 [6,2,2]=>11 [6,2,1,1]=>9 [6,1,1,1,1]=>5 [5,5]=>15 [5,4,1]=>10 [5,3,2]=>7 [5,3,1,1]=>5 [5,2,2,1]=>3 [5,2,1,1,1]=>0 [5,1,1,1,1,1]=>-5 [4,4,2]=>5 [4,4,1,1]=>3 [4,3,3]=>3 [4,3,2,1]=>0 [4,3,1,1,1]=>-3 [4,2,2,2]=>-3 [4,2,2,1,1]=>-5 [4,2,1,1,1,1]=>-9 [4,1,1,1,1,1,1]=>-15 [3,3,3,1]=>-3 [3,3,2,2]=>-5 [3,3,2,1,1]=>-7 [3,3,1,1,1,1]=>-11 [3,2,2,2,1]=>-10 [3,2,2,1,1,1]=>-13 [3,2,1,1,1,1,1]=>-18 [3,1,1,1,1,1,1,1]=>-25 [2,2,2,2,2]=>-15 [2,2,2,2,1,1]=>-17 [2,2,2,1,1,1,1]=>-21 [2,2,1,1,1,1,1,1]=>-27 [2,1,1,1,1,1,1,1,1]=>-35 [1,1,1,1,1,1,1,1,1,1]=>-45 [11]=>55 [10,1]=>44 [9,2]=>35 [9,1,1]=>33 [8,3]=>28 [8,2,1]=>25 [8,1,1,1]=>22 [7,4]=>23 [7,3,1]=>19 [7,2,2]=>17 [7,2,1,1]=>15 [7,1,1,1,1]=>11 [6,5]=>20 [6,4,1]=>15 [6,3,2]=>12 [6,3,1,1]=>10 [6,2,2,1]=>8 [6,2,1,1,1]=>5 [6,1,1,1,1,1]=>0 [5,5,1]=>13 [5,4,2]=>9 [5,4,1,1]=>7 [5,3,3]=>7 [5,3,2,1]=>4 [5,3,1,1,1]=>1 [5,2,2,2]=>1 [5,2,2,1,1]=>-1 [5,2,1,1,1,1]=>-5 [5,1,1,1,1,1,1]=>-11 [4,4,3]=>5 [4,4,2,1]=>2 [4,4,1,1,1]=>-1 [4,3,3,1]=>0 [4,3,2,2]=>-2 [4,3,2,1,1]=>-4 [4,3,1,1,1,1]=>-8 [4,2,2,2,1]=>-7 [4,2,2,1,1,1]=>-10 [4,2,1,1,1,1,1]=>-15 [4,1,1,1,1,1,1,1]=>-22 [3,3,3,2]=>-5 [3,3,3,1,1]=>-7 [3,3,2,2,1]=>-9 [3,3,2,1,1,1]=>-12 [3,3,1,1,1,1,1]=>-17 [3,2,2,2,2]=>-13 [3,2,2,2,1,1]=>-15 [3,2,2,1,1,1,1]=>-19 [3,2,1,1,1,1,1,1]=>-25 [3,1,1,1,1,1,1,1,1]=>-33 [2,2,2,2,2,1]=>-20 [2,2,2,2,1,1,1]=>-23 [2,2,2,1,1,1,1,1]=>-28 [2,2,1,1,1,1,1,1,1]=>-35 [2,1,1,1,1,1,1,1,1,1]=>-44 [1,1,1,1,1,1,1,1,1,1,1]=>-55 [12]=>66 [11,1]=>54 [10,2]=>44 [10,1,1]=>42 [9,3]=>36 [9,2,1]=>33 [9,1,1,1]=>30 [8,4]=>30 [8,3,1]=>26 [8,2,2]=>24 [8,2,1,1]=>22 [8,1,1,1,1]=>18 [7,5]=>26 [7,4,1]=>21 [7,3,2]=>18 [7,3,1,1]=>16 [7,2,2,1]=>14 [7,2,1,1,1]=>11 [7,1,1,1,1,1]=>6 [6,6]=>24 [6,5,1]=>18 [6,4,2]=>14 [6,4,1,1]=>12 [6,3,3]=>12 [6,3,2,1]=>9 [6,3,1,1,1]=>6 [6,2,2,2]=>6 [6,2,2,1,1]=>4 [6,2,1,1,1,1]=>0 [6,1,1,1,1,1,1]=>-6 [5,5,2]=>12 [5,5,1,1]=>10 [5,4,3]=>9 [5,4,2,1]=>6 [5,4,1,1,1]=>3 [5,3,3,1]=>4 [5,3,2,2]=>2 [5,3,2,1,1]=>0 [5,3,1,1,1,1]=>-4 [5,2,2,2,1]=>-3 [5,2,2,1,1,1]=>-6 [5,2,1,1,1,1,1]=>-11 [5,1,1,1,1,1,1,1]=>-18 [4,4,4]=>6 [4,4,3,1]=>2 [4,4,2,2]=>0 [4,4,2,1,1]=>-2 [4,4,1,1,1,1]=>-6 [4,3,3,2]=>-2 [4,3,3,1,1]=>-4 [4,3,2,2,1]=>-6 [4,3,2,1,1,1]=>-9 [4,3,1,1,1,1,1]=>-14 [4,2,2,2,2]=>-10 [4,2,2,2,1,1]=>-12 [4,2,2,1,1,1,1]=>-16 [4,2,1,1,1,1,1,1]=>-22 [4,1,1,1,1,1,1,1,1]=>-30 [3,3,3,3]=>-6 [3,3,3,2,1]=>-9 [3,3,3,1,1,1]=>-12 [3,3,2,2,2]=>-12 [3,3,2,2,1,1]=>-14 [3,3,2,1,1,1,1]=>-18 [3,3,1,1,1,1,1,1]=>-24 [3,2,2,2,2,1]=>-18 [3,2,2,2,1,1,1]=>-21 [3,2,2,1,1,1,1,1]=>-26 [3,2,1,1,1,1,1,1,1]=>-33 [3,1,1,1,1,1,1,1,1,1]=>-42 [2,2,2,2,2,2]=>-24 [2,2,2,2,2,1,1]=>-26 [2,2,2,2,1,1,1,1]=>-30 [2,2,2,1,1,1,1,1,1]=>-36 [2,2,1,1,1,1,1,1,1,1]=>-44 [2,1,1,1,1,1,1,1,1,1,1]=>-54 [1,1,1,1,1,1,1,1,1,1,1,1]=>-66
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Description
The diagonal index (content) of a partition.
The diagonal index of the cell at row $r$ and column $c$ of a partition is $c - r$; this is sometimes called the content of the cell. The diagonal index of a partition is the sum of the diagonal index of each cell of the partition.
Code
def statistic(la):
    return sum((j - i) for (i, j) in la.cells())

Created
May 25, 2016 at 20:28 by Franco Saliola
Updated
May 25, 2016 at 20:28 by Franco Saliola