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Identifier
Values
=>
[1]=>0 [1,1]=>1 [2]=>0 [1,1,1]=>3 [1,2]=>1 [2,1]=>2 [3]=>0 [1,1,1,1]=>6 [1,1,2]=>3 [1,2,1]=>4 [1,3]=>1 [2,1,1]=>5 [2,2]=>2 [3,1]=>3 [4]=>0 [1,1,1,1,1]=>10 [1,1,1,2]=>6 [1,1,2,1]=>7 [1,1,3]=>3 [1,2,1,1]=>8 [1,2,2]=>4 [1,3,1]=>5 [1,4]=>1 [2,1,1,1]=>9 [2,1,2]=>5 [2,2,1]=>6 [2,3]=>2 [3,1,1]=>7 [3,2]=>3 [4,1]=>4 [5]=>0 [1,1,1,1,1,1]=>15 [1,1,1,1,2]=>10 [1,1,1,2,1]=>11 [1,1,1,3]=>6 [1,1,2,1,1]=>12 [1,1,2,2]=>7 [1,1,3,1]=>8 [1,1,4]=>3 [1,2,1,1,1]=>13 [1,2,1,2]=>8 [1,2,2,1]=>9 [1,2,3]=>4 [1,3,1,1]=>10 [1,3,2]=>5 [1,4,1]=>6 [1,5]=>1 [2,1,1,1,1]=>14 [2,1,1,2]=>9 [2,1,2,1]=>10 [2,1,3]=>5 [2,2,1,1]=>11 [2,2,2]=>6 [2,3,1]=>7 [2,4]=>2 [3,1,1,1]=>12 [3,1,2]=>7 [3,2,1]=>8 [3,3]=>3 [4,1,1]=>9 [4,2]=>4 [5,1]=>5 [6]=>0 [1,1,1,1,1,1,1]=>21 [1,1,1,1,1,2]=>15 [1,1,1,1,2,1]=>16 [1,1,1,1,3]=>10 [1,1,1,2,1,1]=>17 [1,1,1,2,2]=>11 [1,1,1,3,1]=>12 [1,1,1,4]=>6 [1,1,2,1,1,1]=>18 [1,1,2,1,2]=>12 [1,1,2,2,1]=>13 [1,1,2,3]=>7 [1,1,3,1,1]=>14 [1,1,3,2]=>8 [1,1,4,1]=>9 [1,1,5]=>3 [1,2,1,1,1,1]=>19 [1,2,1,1,2]=>13 [1,2,1,2,1]=>14 [1,2,1,3]=>8 [1,2,2,1,1]=>15 [1,2,2,2]=>9 [1,2,3,1]=>10 [1,2,4]=>4 [1,3,1,1,1]=>16 [1,3,1,2]=>10 [1,3,2,1]=>11 [1,3,3]=>5 [1,4,1,1]=>12 [1,4,2]=>6 [1,5,1]=>7 [1,6]=>1 [2,1,1,1,1,1]=>20 [2,1,1,1,2]=>14 [2,1,1,2,1]=>15 [2,1,1,3]=>9 [2,1,2,1,1]=>16 [2,1,2,2]=>10 [2,1,3,1]=>11 [2,1,4]=>5 [2,2,1,1,1]=>17 [2,2,1,2]=>11 [2,2,2,1]=>12 [2,2,3]=>6 [2,3,1,1]=>13 [2,3,2]=>7 [2,4,1]=>8 [2,5]=>2 [3,1,1,1,1]=>18 [3,1,1,2]=>12 [3,1,2,1]=>13 [3,1,3]=>7 [3,2,1,1]=>14 [3,2,2]=>8 [3,3,1]=>9 [3,4]=>3 [4,1,1,1]=>15 [4,1,2]=>9 [4,2,1]=>10 [4,3]=>4 [5,1,1]=>11 [5,2]=>5 [6,1]=>6 [7]=>0 [1,1,1,1,1,1,1,1]=>28 [1,1,1,1,1,1,2]=>21 [1,1,1,1,1,2,1]=>22 [1,1,1,1,1,3]=>15 [1,1,1,1,2,1,1]=>23 [1,1,1,1,2,2]=>16 [1,1,1,1,3,1]=>17 [1,1,1,1,4]=>10 [1,1,1,2,1,1,1]=>24 [1,1,1,2,1,2]=>17 [1,1,1,2,2,1]=>18 [1,1,1,2,3]=>11 [1,1,1,3,1,1]=>19 [1,1,1,3,2]=>12 [1,1,1,4,1]=>13 [1,1,1,5]=>6 [1,1,2,1,1,1,1]=>25 [1,1,2,1,1,2]=>18 [1,1,2,1,2,1]=>19 [1,1,2,1,3]=>12 [1,1,2,2,1,1]=>20 [1,1,2,2,2]=>13 [1,1,2,3,1]=>14 [1,1,2,4]=>7 [1,1,3,1,1,1]=>21 [1,1,3,1,2]=>14 [1,1,3,2,1]=>15 [1,1,3,3]=>8 [1,1,4,1,1]=>16 [1,1,4,2]=>9 [1,1,5,1]=>10 [1,1,6]=>3 [1,2,1,1,1,1,1]=>26 [1,2,1,1,1,2]=>19 [1,2,1,1,2,1]=>20 [1,2,1,1,3]=>13 [1,2,1,2,1,1]=>21 [1,2,1,2,2]=>14 [1,2,1,3,1]=>15 [1,2,1,4]=>8 [1,2,2,1,1,1]=>22 [1,2,2,1,2]=>15 [1,2,2,2,1]=>16 [1,2,2,3]=>9 [1,2,3,1,1]=>17 [1,2,3,2]=>10 [1,2,4,1]=>11 [1,2,5]=>4 [1,3,1,1,1,1]=>23 [1,3,1,1,2]=>16 [1,3,1,2,1]=>17 [1,3,1,3]=>10 [1,3,2,1,1]=>18 [1,3,2,2]=>11 [1,3,3,1]=>12 [1,3,4]=>5 [1,4,1,1,1]=>19 [1,4,1,2]=>12 [1,4,2,1]=>13 [1,4,3]=>6 [1,5,1,1]=>14 [1,5,2]=>7 [1,6,1]=>8 [1,7]=>1 [2,1,1,1,1,1,1]=>27 [2,1,1,1,1,2]=>20 [2,1,1,1,2,1]=>21 [2,1,1,1,3]=>14 [2,1,1,2,1,1]=>22 [2,1,1,2,2]=>15 [2,1,1,3,1]=>16 [2,1,1,4]=>9 [2,1,2,1,1,1]=>23 [2,1,2,1,2]=>16 [2,1,2,2,1]=>17 [2,1,2,3]=>10 [2,1,3,1,1]=>18 [2,1,3,2]=>11 [2,1,4,1]=>12 [2,1,5]=>5 [2,2,1,1,1,1]=>24 [2,2,1,1,2]=>17 [2,2,1,2,1]=>18 [2,2,1,3]=>11 [2,2,2,1,1]=>19 [2,2,2,2]=>12 [2,2,3,1]=>13 [2,2,4]=>6 [2,3,1,1,1]=>20 [2,3,1,2]=>13 [2,3,2,1]=>14 [2,3,3]=>7 [2,4,1,1]=>15 [2,4,2]=>8 [2,5,1]=>9 [2,6]=>2 [3,1,1,1,1,1]=>25 [3,1,1,1,2]=>18 [3,1,1,2,1]=>19 [3,1,1,3]=>12 [3,1,2,1,1]=>20 [3,1,2,2]=>13 [3,1,3,1]=>14 [3,1,4]=>7 [3,2,1,1,1]=>21 [3,2,1,2]=>14 [3,2,2,1]=>15 [3,2,3]=>8 [3,3,1,1]=>16 [3,3,2]=>9 [3,4,1]=>10 [3,5]=>3 [4,1,1,1,1]=>22 [4,1,1,2]=>15 [4,1,2,1]=>16 [4,1,3]=>9 [4,2,1,1]=>17 [4,2,2]=>10 [4,3,1]=>11 [4,4]=>4 [5,1,1,1]=>18 [5,1,2]=>11 [5,2,1]=>12 [5,3]=>5 [6,1,1]=>13 [6,2]=>6 [7,1]=>7 [8]=>0 [1,1,1,1,4,1]=>18 [1,1,1,2,3,1]=>19 [1,1,2,1,3,1]=>20 [1,1,6,1]=>11 [1,2,1,1,3,1]=>21 [1,2,1,2,2,1]=>22 [1,2,2,1,2,1]=>23 [1,2,5,1]=>12 [1,3,1,1,2,1]=>24 [1,3,1,2,1,1]=>25 [1,3,2,1,1,1]=>26 [1,3,4,1]=>13 [1,4,1,1,1,1]=>27 [1,4,1,3]=>12 [1,4,2,2]=>13 [1,4,3,1]=>14 [1,5,1,2]=>14 [1,5,2,1]=>15 [1,6,1,1]=>16 [1,6,2]=>8 [1,7,1]=>9 [1,8]=>1 [2,1,5,1]=>13 [2,2,4,1]=>14 [3,1,4,1]=>15 [6,2,1]=>14 [7,1,1]=>15 [8,1]=>8 [1,1,1,1,1,1,1,1,1,1]=>45 [1,1,1,1,1,1,2,2]=>29 [1,1,1,1,2,1,1,2]=>31 [1,1,1,1,2,2,1,1]=>33 [1,1,1,1,3,3]=>17 [1,1,1,1,5,1]=>19 [1,1,2,1,1,1,1,2]=>33 [1,1,2,1,1,2,1,1]=>35 [1,1,2,1,2,3]=>19 [1,1,2,2,1,1,1,1]=>37 [1,1,2,2,2,2]=>21 [1,1,3,1,1,3]=>21 [1,1,3,2,1,2]=>23 [1,1,3,3,1,1]=>25 [1,1,4,4]=>9 [1,1,7,1]=>12 [1,2,1,1,4,1]=>22 [1,2,6,1]=>13 [1,3,1,1,3,1]=>25 [1,3,5,1]=>14 [1,4,1,1,2,1]=>28 [1,4,4,1]=>15 [1,5,1,1,1,1]=>31 [1,5,3,1]=>16 [1,6,1,2]=>16 [1,6,2,1]=>17 [1,7,1,1]=>18 [1,8,1]=>10 [1,9]=>1 [2,1,1,1,1,1,1,2]=>35 [2,1,1,1,1,2,1,1]=>37 [2,1,1,1,2,3]=>21 [2,1,1,2,1,1,1,1]=>39 [2,1,1,2,2,2]=>23 [2,1,2,1,1,3]=>23 [2,1,2,2,1,2]=>25 [2,1,2,3,1,1]=>27 [2,1,3,4]=>11 [2,1,6,1]=>14 [2,2,1,1,1,1,1,1]=>41 [2,2,1,1,2,2]=>25 [2,2,2,1,1,2]=>27 [2,2,2,2,1,1]=>29 [2,2,3,3]=>13 [3,1,1,1,1,3]=>25 [3,1,1,2,1,2]=>27 [3,1,1,3,1,1]=>29 [3,1,2,4]=>13 [3,2,1,1,1,2]=>29 [3,2,1,2,1,1]=>31 [3,2,2,3]=>15 [3,3,1,1,1,1]=>33 [3,3,2,2]=>17 [4,1,1,4]=>15 [4,2,1,3]=>17 [4,3,1,2]=>19 [4,4,1,1]=>21 [5,5]=>5 [8,1,1]=>17 [9,1]=>9 [10,1]=>10 [1,10]=>1 [1,8,1,1]=>20 [1,7,2,1]=>19 [1,6,3,1]=>18 [1,5,4,1]=>17 [1,4,5,1]=>16 [1,3,6,1]=>15 [1,2,7,1]=>14 [1,1,8,1]=>13 [5,5,1,1]=>26 [1,1,5,5]=>10 [1,1,4,1,1,4]=>24 [4,1,1,4,1,1]=>36 [1,1,3,1,2,4]=>22 [1,1,4,2,1,3]=>26 [3,1,2,4,1,1]=>34 [4,2,1,3,1,1]=>38 [1,1,2,1,3,4]=>20 [1,1,3,1,1,1,1,3]=>38 [1,1,4,3,1,2]=>28 [2,2,4,4]=>14 [2,1,3,4,1,1]=>32 [3,1,1,1,1,3,1,1]=>46 [4,4,2,2]=>22 [4,3,1,2,1,1]=>40 [1,1,1,1,4,4]=>18 [1,1,2,1,2,1,1,3]=>36 [1,1,3,2,2,3]=>24 [1,1,3,1,1,2,1,2]=>40 [1,1,4,4,1,1]=>30 [2,2,3,1,1,3]=>30 [2,1,2,1,1,3,1,1]=>44 [3,3,3,3]=>18 [3,2,2,3,1,1]=>36 [3,1,1,3,2,2]=>30 [3,1,1,2,1,2,1,1]=>48 [4,4,1,1,1,1]=>42 [1,1,1,1,3,1,1,3]=>34 [1,1,2,1,1,1,2,3]=>34 [1,1,2,1,2,2,1,2]=>38 [1,1,3,2,1,1,1,2]=>42 [1,1,3,1,1,3,1,1]=>42 [2,2,2,1,2,3]=>28 [2,2,3,2,1,2]=>32 [2,1,1,2,3,3]=>24 [2,1,1,1,2,3,1,1]=>42 [2,1,2,3,2,2]=>28 [2,1,2,2,1,2,1,1]=>46 [3,3,2,1,1,2]=>36 [3,2,1,2,2,2]=>32 [3,2,1,1,1,2,1,1]=>50 [3,1,1,3,1,1,1,1]=>50 [1,1,2,1,1,1,1,1,1,2]=>52 [2,2,1,1,1,1,1,1,1,1]=>62 [1,1,2,2,3,3]=>22 [1,1,1,1,1,1,2,1,1,2]=>48 [1,1,1,1,1,1,1,1,2,2]=>46 [2,2,1,1,2,1,1,2]=>44 [2,2,1,1,1,1,2,2]=>42 [2,1,1,2,2,1,1,2]=>42 [1,1,2,2,2,1,1,2]=>40 [2,1,1,2,1,1,2,2]=>40 [1,1,2,2,1,1,2,2]=>38 [1,1,1,1,3,2,1,2]=>36 [1,1,2,1,1,2,2,2]=>36 [3,3,1,1,2,2]=>34 [1,1,1,1,2,1,1,1,1,2]=>50 [1,1,1,1,2,2,2,2]=>34 [3,2,2,2,1,2]=>34 [2,1,1,1,2,2,1,2]=>40 [1,1,1,1,2,1,2,3]=>32 [3,2,1,1,1,1,1,2]=>48 [2,1,1,1,1,1,1,1,1,2]=>54 [2,1,1,1,1,2,2,2]=>38 [2,2,2,1,1,1,1,2]=>46 [2,2,2,2,2,2]=>30 [1,1,1,1,1,1,3,3]=>30 [3,1,2,3,1,2]=>32 [2,1,3,3,1,2]=>30 [3,1,1,1,1,2,1,2]=>44 [2,1,2,1,1,2,1,2]=>42 [3,1,1,2,1,1,1,2]=>46 [2,1,2,2,1,1,1,2]=>44 [1,1,3,3,2,2]=>26 [2,2,1,1,3,3]=>26 [3,3,1,1,1,1,1,1]=>54 [2,1,2,3,1,1,1,1]=>48 [1,1,3,3,1,1,1,1]=>46 [2,2,3,3,1,1]=>34 [1,1,1,1,3,3,1,1]=>38 [3,1,1,1,1,1,1,3]=>42 [3,1,1,2,2,3]=>28 [3,2,1,1,2,3]=>30 [2,1,1,1,1,1,2,3]=>36 [1,1,2,1,2,3,1,1]=>40 [4,2,1,1,1,3]=>34 [3,2,2,1,1,3]=>32 [4,2,1,2,1,2]=>36 [2,1,2,2,2,3]=>26 [4,3,1,1,1,2]=>38 [3,3,2,2,1,1]=>38 [1,1,2,2,2,2,1,1]=>42 [2,2,1,1,2,2,1,1]=>46 [2,1,1,1,2,1,1,3]=>38 [2,2,2,2,1,1,1,1]=>50 [2,1,1,2,1,1,1,1,1,1]=>60 [2,1,1,1,3,4]=>22 [2,1,1,1,1,1,1,2,1,1]=>56 [2,1,2,1,1,1,1,3]=>40 [2,2,2,1,1,2,1,1]=>48 [2,1,1,1,1,2,1,1,1,1]=>58 [2,1,2,1,2,4]=>24 [2,1,1,2,2,2,1,1]=>44 [2,1,3,2,1,3]=>28 [2,1,3,1,1,4]=>26 [3,1,1,1,2,4]=>26 [1,1,2,1,1,2,1,1,1,1]=>56 [1,1,1,1,2,1,1,2,1,1]=>52 [1,1,2,2,1,1,1,1,1,1]=>58 [1,1,1,1,2,2,1,1,1,1]=>54 [1,1,1,1,1,1,2,2,1,1]=>50 [1,1,1,1,1,1,1,1,1,1,1,1]=>66 [5,4,1,2]=>24 [4,1,1,3,1,2]=>34 [4,3,2,3]=>20 [5,3,1,3]=>22 [4,1,1,2,1,3]=>32 [3,2,1,2,1,1,1,1]=>52 [1,1,3,2,1,2,1,1]=>44 [5,2,1,4]=>20 [5,1,1,5]=>18 [3,1,2,2,1,3]=>30 [4,2,2,4]=>18 [3,1,2,1,1,4]=>28 [4,1,1,1,1,4]=>30 [3,1,3,5]=>14 [6,6]=>6 [4,1,2,5]=>16 [2,1,4,5]=>12 [3,2,3,4]=>16 [1,1,2,1,1,1,1,2,1,1]=>54
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Description
The major index of the composition.
The descents of a composition $[c_1,c_2,\dots,c_k]$ are the partial sums $c_1, c_1+c_2,\dots, c_1+\dots+c_{k-1}$, excluding the sum of all parts. The major index of a composition is the sum of its descents.
For details about the major index see Permutations/Descents-Major.
Code
def statistic(x):
    return x.major_index()
Created
Sep 21, 2011 at 16:41 by Chris Berg
Updated
Jan 26, 2018 at 09:17 by Martin Rubey