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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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-----------------------------------------------------------------------------
Statistic identifier: St000004
-----------------------------------------------------------------------------
Collection: Permutations
-----------------------------------------------------------------------------
Description: The major index of a permutation.
This is the sum of the positions of its descents,
$$\operatorname{maj}(\sigma) = \sum_{\sigma(i) > \sigma(i+1)} i.$$
Its generating function is $[n]_q! = [1]_q \cdot [2]_q \dots [n]_q$ for $[k]_q = 1 + q + q^2 + \dots q^{k-1}$.
A statistic equidistributed with the major index is called '''Mahonian statistic'''.
-----------------------------------------------------------------------------
References: [1] Foata, D. Distributions eulériennes et mahoniennes sur le groupe des permutations [[MathSciNet:0519777]]
[2] Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product_i=0..n-1 (1 + x + ... + x^i), where k ranges from 0 to A000217(n-1). [[OEIS:A008302]]
-----------------------------------------------------------------------------
Code:
def statistic(x):
return x.major_index()
-----------------------------------------------------------------------------
Statistic values:
[] => 0
[1] => 0
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 2
[2,1,3] => 1
[2,3,1] => 2
[3,1,2] => 1
[3,2,1] => 3
[1,2,3,4] => 0
[1,2,4,3] => 3
[1,3,2,4] => 2
[1,3,4,2] => 3
[1,4,2,3] => 2
[1,4,3,2] => 5
[2,1,3,4] => 1
[2,1,4,3] => 4
[2,3,1,4] => 2
[2,3,4,1] => 3
[2,4,1,3] => 2
[2,4,3,1] => 5
[3,1,2,4] => 1
[3,1,4,2] => 4
[3,2,1,4] => 3
[3,2,4,1] => 4
[3,4,1,2] => 2
[3,4,2,1] => 5
[4,1,2,3] => 1
[4,1,3,2] => 4
[4,2,1,3] => 3
[4,2,3,1] => 4
[4,3,1,2] => 3
[4,3,2,1] => 6
[1,2,3,4,5] => 0
[1,2,3,5,4] => 4
[1,2,4,3,5] => 3
[1,2,4,5,3] => 4
[1,2,5,3,4] => 3
[1,2,5,4,3] => 7
[1,3,2,4,5] => 2
[1,3,2,5,4] => 6
[1,3,4,2,5] => 3
[1,3,4,5,2] => 4
[1,3,5,2,4] => 3
[1,3,5,4,2] => 7
[1,4,2,3,5] => 2
[1,4,2,5,3] => 6
[1,4,3,2,5] => 5
[1,4,3,5,2] => 6
[1,4,5,2,3] => 3
[1,4,5,3,2] => 7
[1,5,2,3,4] => 2
[1,5,2,4,3] => 6
[1,5,3,2,4] => 5
[1,5,3,4,2] => 6
[1,5,4,2,3] => 5
[1,5,4,3,2] => 9
[2,1,3,4,5] => 1
[2,1,3,5,4] => 5
[2,1,4,3,5] => 4
[2,1,4,5,3] => 5
[2,1,5,3,4] => 4
[2,1,5,4,3] => 8
[2,3,1,4,5] => 2
[2,3,1,5,4] => 6
[2,3,4,1,5] => 3
[2,3,4,5,1] => 4
[2,3,5,1,4] => 3
[2,3,5,4,1] => 7
[2,4,1,3,5] => 2
[2,4,1,5,3] => 6
[2,4,3,1,5] => 5
[2,4,3,5,1] => 6
[2,4,5,1,3] => 3
[2,4,5,3,1] => 7
[2,5,1,3,4] => 2
[2,5,1,4,3] => 6
[2,5,3,1,4] => 5
[2,5,3,4,1] => 6
[2,5,4,1,3] => 5
[2,5,4,3,1] => 9
[3,1,2,4,5] => 1
[3,1,2,5,4] => 5
[3,1,4,2,5] => 4
[3,1,4,5,2] => 5
[3,1,5,2,4] => 4
[3,1,5,4,2] => 8
[3,2,1,4,5] => 3
[3,2,1,5,4] => 7
[3,2,4,1,5] => 4
[3,2,4,5,1] => 5
[3,2,5,1,4] => 4
[3,2,5,4,1] => 8
[3,4,1,2,5] => 2
[3,4,1,5,2] => 6
[3,4,2,1,5] => 5
[3,4,2,5,1] => 6
[3,4,5,1,2] => 3
[3,4,5,2,1] => 7
[3,5,1,2,4] => 2
[3,5,1,4,2] => 6
[3,5,2,1,4] => 5
[3,5,2,4,1] => 6
[3,5,4,1,2] => 5
[3,5,4,2,1] => 9
[4,1,2,3,5] => 1
[4,1,2,5,3] => 5
[4,1,3,2,5] => 4
[4,1,3,5,2] => 5
[4,1,5,2,3] => 4
[4,1,5,3,2] => 8
[4,2,1,3,5] => 3
[4,2,1,5,3] => 7
[4,2,3,1,5] => 4
[4,2,3,5,1] => 5
[4,2,5,1,3] => 4
[4,2,5,3,1] => 8
[4,3,1,2,5] => 3
[4,3,1,5,2] => 7
[4,3,2,1,5] => 6
[4,3,2,5,1] => 7
[4,3,5,1,2] => 4
[4,3,5,2,1] => 8
[4,5,1,2,3] => 2
[4,5,1,3,2] => 6
[4,5,2,1,3] => 5
[4,5,2,3,1] => 6
[4,5,3,1,2] => 5
[4,5,3,2,1] => 9
[5,1,2,3,4] => 1
[5,1,2,4,3] => 5
[5,1,3,2,4] => 4
[5,1,3,4,2] => 5
[5,1,4,2,3] => 4
[5,1,4,3,2] => 8
[5,2,1,3,4] => 3
[5,2,1,4,3] => 7
[5,2,3,1,4] => 4
[5,2,3,4,1] => 5
[5,2,4,1,3] => 4
[5,2,4,3,1] => 8
[5,3,1,2,4] => 3
[5,3,1,4,2] => 7
[5,3,2,1,4] => 6
[5,3,2,4,1] => 7
[5,3,4,1,2] => 4
[5,3,4,2,1] => 8
[5,4,1,2,3] => 3
[5,4,1,3,2] => 7
[5,4,2,1,3] => 6
[5,4,2,3,1] => 7
[5,4,3,1,2] => 6
[5,4,3,2,1] => 10
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 5
[1,2,3,5,4,6] => 4
[1,2,3,5,6,4] => 5
[1,2,3,6,4,5] => 4
[1,2,3,6,5,4] => 9
[1,2,4,3,5,6] => 3
[1,2,4,3,6,5] => 8
[1,2,4,5,3,6] => 4
[1,2,4,5,6,3] => 5
[1,2,4,6,3,5] => 4
[1,2,4,6,5,3] => 9
[1,2,5,3,4,6] => 3
[1,2,5,3,6,4] => 8
[1,2,5,4,3,6] => 7
[1,2,5,4,6,3] => 8
[1,2,5,6,3,4] => 4
[1,2,5,6,4,3] => 9
[1,2,6,3,4,5] => 3
[1,2,6,3,5,4] => 8
[1,2,6,4,3,5] => 7
[1,2,6,4,5,3] => 8
[1,2,6,5,3,4] => 7
[1,2,6,5,4,3] => 12
[1,3,2,4,5,6] => 2
[1,3,2,4,6,5] => 7
[1,3,2,5,4,6] => 6
[1,3,2,5,6,4] => 7
[1,3,2,6,4,5] => 6
[1,3,2,6,5,4] => 11
[1,3,4,2,5,6] => 3
[1,3,4,2,6,5] => 8
[1,3,4,5,2,6] => 4
[1,3,4,5,6,2] => 5
[1,3,4,6,2,5] => 4
[1,3,4,6,5,2] => 9
[1,3,5,2,4,6] => 3
[1,3,5,2,6,4] => 8
[1,3,5,4,2,6] => 7
[1,3,5,4,6,2] => 8
[1,3,5,6,2,4] => 4
[1,3,5,6,4,2] => 9
[1,3,6,2,4,5] => 3
[1,3,6,2,5,4] => 8
[1,3,6,4,2,5] => 7
[1,3,6,4,5,2] => 8
[1,3,6,5,2,4] => 7
[1,3,6,5,4,2] => 12
[1,4,2,3,5,6] => 2
[1,4,2,3,6,5] => 7
[1,4,2,5,3,6] => 6
[1,4,2,5,6,3] => 7
[1,4,2,6,3,5] => 6
[1,4,2,6,5,3] => 11
[1,4,3,2,5,6] => 5
[1,4,3,2,6,5] => 10
[1,4,3,5,2,6] => 6
[1,4,3,5,6,2] => 7
[1,4,3,6,2,5] => 6
[1,4,3,6,5,2] => 11
[1,4,5,2,3,6] => 3
[1,4,5,2,6,3] => 8
[1,4,5,3,2,6] => 7
[1,4,5,3,6,2] => 8
[1,4,5,6,2,3] => 4
[1,4,5,6,3,2] => 9
[1,4,6,2,3,5] => 3
[1,4,6,2,5,3] => 8
[1,4,6,3,2,5] => 7
[1,4,6,3,5,2] => 8
[1,4,6,5,2,3] => 7
[1,4,6,5,3,2] => 12
[1,5,2,3,4,6] => 2
[1,5,2,3,6,4] => 7
[1,5,2,4,3,6] => 6
[1,5,2,4,6,3] => 7
[1,5,2,6,3,4] => 6
[1,5,2,6,4,3] => 11
[1,5,3,2,4,6] => 5
[1,5,3,2,6,4] => 10
[1,5,3,4,2,6] => 6
[1,5,3,4,6,2] => 7
[1,5,3,6,2,4] => 6
[1,5,3,6,4,2] => 11
[1,5,4,2,3,6] => 5
[1,5,4,2,6,3] => 10
[1,5,4,3,2,6] => 9
[1,5,4,3,6,2] => 10
[1,5,4,6,2,3] => 6
[1,5,4,6,3,2] => 11
[1,5,6,2,3,4] => 3
[1,5,6,2,4,3] => 8
[1,5,6,3,2,4] => 7
[1,5,6,3,4,2] => 8
[1,5,6,4,2,3] => 7
[1,5,6,4,3,2] => 12
[1,6,2,3,4,5] => 2
[1,6,2,3,5,4] => 7
[1,6,2,4,3,5] => 6
[1,6,2,4,5,3] => 7
[1,6,2,5,3,4] => 6
[1,6,2,5,4,3] => 11
[1,6,3,2,4,5] => 5
[1,6,3,2,5,4] => 10
[1,6,3,4,2,5] => 6
[1,6,3,4,5,2] => 7
[1,6,3,5,2,4] => 6
[1,6,3,5,4,2] => 11
[1,6,4,2,3,5] => 5
[1,6,4,2,5,3] => 10
[1,6,4,3,2,5] => 9
[1,6,4,3,5,2] => 10
[1,6,4,5,2,3] => 6
[1,6,4,5,3,2] => 11
[1,6,5,2,3,4] => 5
[1,6,5,2,4,3] => 10
[1,6,5,3,2,4] => 9
[1,6,5,3,4,2] => 10
[1,6,5,4,2,3] => 9
[1,6,5,4,3,2] => 14
[2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => 6
[2,1,3,5,4,6] => 5
[2,1,3,5,6,4] => 6
[2,1,3,6,4,5] => 5
[2,1,3,6,5,4] => 10
[2,1,4,3,5,6] => 4
[2,1,4,3,6,5] => 9
[2,1,4,5,3,6] => 5
[2,1,4,5,6,3] => 6
[2,1,4,6,3,5] => 5
[2,1,4,6,5,3] => 10
[2,1,5,3,4,6] => 4
[2,1,5,3,6,4] => 9
[2,1,5,4,3,6] => 8
[2,1,5,4,6,3] => 9
[2,1,5,6,3,4] => 5
[2,1,5,6,4,3] => 10
[2,1,6,3,4,5] => 4
[2,1,6,3,5,4] => 9
[2,1,6,4,3,5] => 8
[2,1,6,4,5,3] => 9
[2,1,6,5,3,4] => 8
[2,1,6,5,4,3] => 13
[2,3,1,4,5,6] => 2
[2,3,1,4,6,5] => 7
[2,3,1,5,4,6] => 6
[2,3,1,5,6,4] => 7
[2,3,1,6,4,5] => 6
[2,3,1,6,5,4] => 11
[2,3,4,1,5,6] => 3
[2,3,4,1,6,5] => 8
[2,3,4,5,1,6] => 4
[2,3,4,5,6,1] => 5
[2,3,4,6,1,5] => 4
[2,3,4,6,5,1] => 9
[2,3,5,1,4,6] => 3
[2,3,5,1,6,4] => 8
[2,3,5,4,1,6] => 7
[2,3,5,4,6,1] => 8
[2,3,5,6,1,4] => 4
[2,3,5,6,4,1] => 9
[2,3,6,1,4,5] => 3
[2,3,6,1,5,4] => 8
[2,3,6,4,1,5] => 7
[2,3,6,4,5,1] => 8
[2,3,6,5,1,4] => 7
[2,3,6,5,4,1] => 12
[2,4,1,3,5,6] => 2
[2,4,1,3,6,5] => 7
[2,4,1,5,3,6] => 6
[2,4,1,5,6,3] => 7
[2,4,1,6,3,5] => 6
[2,4,1,6,5,3] => 11
[2,4,3,1,5,6] => 5
[2,4,3,1,6,5] => 10
[2,4,3,5,1,6] => 6
[2,4,3,5,6,1] => 7
[2,4,3,6,1,5] => 6
[2,4,3,6,5,1] => 11
[2,4,5,1,3,6] => 3
[2,4,5,1,6,3] => 8
[2,4,5,3,1,6] => 7
[2,4,5,3,6,1] => 8
[2,4,5,6,1,3] => 4
[2,4,5,6,3,1] => 9
[2,4,6,1,3,5] => 3
[2,4,6,1,5,3] => 8
[2,4,6,3,1,5] => 7
[2,4,6,3,5,1] => 8
[2,4,6,5,1,3] => 7
[2,4,6,5,3,1] => 12
[2,5,1,3,4,6] => 2
[2,5,1,3,6,4] => 7
[2,5,1,4,3,6] => 6
[2,5,1,4,6,3] => 7
[2,5,1,6,3,4] => 6
[2,5,1,6,4,3] => 11
[2,5,3,1,4,6] => 5
[2,5,3,1,6,4] => 10
[2,5,3,4,1,6] => 6
[2,5,3,4,6,1] => 7
[2,5,3,6,1,4] => 6
[2,5,3,6,4,1] => 11
[2,5,4,1,3,6] => 5
[2,5,4,1,6,3] => 10
[2,5,4,3,1,6] => 9
[2,5,4,3,6,1] => 10
[2,5,4,6,1,3] => 6
[2,5,4,6,3,1] => 11
[2,5,6,1,3,4] => 3
[2,5,6,1,4,3] => 8
[2,5,6,3,1,4] => 7
[2,5,6,3,4,1] => 8
[2,5,6,4,1,3] => 7
[2,5,6,4,3,1] => 12
[2,6,1,3,4,5] => 2
[2,6,1,3,5,4] => 7
[2,6,1,4,3,5] => 6
[2,6,1,4,5,3] => 7
[2,6,1,5,3,4] => 6
[2,6,1,5,4,3] => 11
[2,6,3,1,4,5] => 5
[2,6,3,1,5,4] => 10
[2,6,3,4,1,5] => 6
[2,6,3,4,5,1] => 7
[2,6,3,5,1,4] => 6
[2,6,3,5,4,1] => 11
[2,6,4,1,3,5] => 5
[2,6,4,1,5,3] => 10
[2,6,4,3,1,5] => 9
[2,6,4,3,5,1] => 10
[2,6,4,5,1,3] => 6
[2,6,4,5,3,1] => 11
[2,6,5,1,3,4] => 5
[2,6,5,1,4,3] => 10
[2,6,5,3,1,4] => 9
[2,6,5,3,4,1] => 10
[2,6,5,4,1,3] => 9
[2,6,5,4,3,1] => 14
[3,1,2,4,5,6] => 1
[3,1,2,4,6,5] => 6
[3,1,2,5,4,6] => 5
[3,1,2,5,6,4] => 6
[3,1,2,6,4,5] => 5
[3,1,2,6,5,4] => 10
[3,1,4,2,5,6] => 4
[3,1,4,2,6,5] => 9
[3,1,4,5,2,6] => 5
[3,1,4,5,6,2] => 6
[3,1,4,6,2,5] => 5
[3,1,4,6,5,2] => 10
[3,1,5,2,4,6] => 4
[3,1,5,2,6,4] => 9
[3,1,5,4,2,6] => 8
[3,1,5,4,6,2] => 9
[3,1,5,6,2,4] => 5
[3,1,5,6,4,2] => 10
[3,1,6,2,4,5] => 4
[3,1,6,2,5,4] => 9
[3,1,6,4,2,5] => 8
[3,1,6,4,5,2] => 9
[3,1,6,5,2,4] => 8
[3,1,6,5,4,2] => 13
[3,2,1,4,5,6] => 3
[3,2,1,4,6,5] => 8
[3,2,1,5,4,6] => 7
[3,2,1,5,6,4] => 8
[3,2,1,6,4,5] => 7
[3,2,1,6,5,4] => 12
[3,2,4,1,5,6] => 4
[3,2,4,1,6,5] => 9
[3,2,4,5,1,6] => 5
[3,2,4,5,6,1] => 6
[3,2,4,6,1,5] => 5
[3,2,4,6,5,1] => 10
[3,2,5,1,4,6] => 4
[3,2,5,1,6,4] => 9
[3,2,5,4,1,6] => 8
[3,2,5,4,6,1] => 9
[3,2,5,6,1,4] => 5
[3,2,5,6,4,1] => 10
[3,2,6,1,4,5] => 4
[3,2,6,1,5,4] => 9
[3,2,6,4,1,5] => 8
[3,2,6,4,5,1] => 9
[3,2,6,5,1,4] => 8
[3,2,6,5,4,1] => 13
[3,4,1,2,5,6] => 2
[3,4,1,2,6,5] => 7
[3,4,1,5,2,6] => 6
[3,4,1,5,6,2] => 7
[3,4,1,6,2,5] => 6
[3,4,1,6,5,2] => 11
[3,4,2,1,5,6] => 5
[3,4,2,1,6,5] => 10
[3,4,2,5,1,6] => 6
[3,4,2,5,6,1] => 7
[3,4,2,6,1,5] => 6
[3,4,2,6,5,1] => 11
[3,4,5,1,2,6] => 3
[3,4,5,1,6,2] => 8
[3,4,5,2,1,6] => 7
[3,4,5,2,6,1] => 8
[3,4,5,6,1,2] => 4
[3,4,5,6,2,1] => 9
[3,4,6,1,2,5] => 3
[3,4,6,1,5,2] => 8
[3,4,6,2,1,5] => 7
[3,4,6,2,5,1] => 8
[3,4,6,5,1,2] => 7
[3,4,6,5,2,1] => 12
[3,5,1,2,4,6] => 2
[3,5,1,2,6,4] => 7
[3,5,1,4,2,6] => 6
[3,5,1,4,6,2] => 7
[3,5,1,6,2,4] => 6
[3,5,1,6,4,2] => 11
[3,5,2,1,4,6] => 5
[3,5,2,1,6,4] => 10
[3,5,2,4,1,6] => 6
[3,5,2,4,6,1] => 7
[3,5,2,6,1,4] => 6
[3,5,2,6,4,1] => 11
[3,5,4,1,2,6] => 5
[3,5,4,1,6,2] => 10
[3,5,4,2,1,6] => 9
[3,5,4,2,6,1] => 10
[3,5,4,6,1,2] => 6
[3,5,4,6,2,1] => 11
[3,5,6,1,2,4] => 3
[3,5,6,1,4,2] => 8
[3,5,6,2,1,4] => 7
[3,5,6,2,4,1] => 8
[3,5,6,4,1,2] => 7
[3,5,6,4,2,1] => 12
[3,6,1,2,4,5] => 2
[3,6,1,2,5,4] => 7
[3,6,1,4,2,5] => 6
[3,6,1,4,5,2] => 7
[3,6,1,5,2,4] => 6
[3,6,1,5,4,2] => 11
[3,6,2,1,4,5] => 5
[3,6,2,1,5,4] => 10
[3,6,2,4,1,5] => 6
[3,6,2,4,5,1] => 7
[3,6,2,5,1,4] => 6
[3,6,2,5,4,1] => 11
[3,6,4,1,2,5] => 5
[3,6,4,1,5,2] => 10
[3,6,4,2,1,5] => 9
[3,6,4,2,5,1] => 10
[3,6,4,5,1,2] => 6
[3,6,4,5,2,1] => 11
[3,6,5,1,2,4] => 5
[3,6,5,1,4,2] => 10
[3,6,5,2,1,4] => 9
[3,6,5,2,4,1] => 10
[3,6,5,4,1,2] => 9
[3,6,5,4,2,1] => 14
[4,1,2,3,5,6] => 1
[4,1,2,3,6,5] => 6
[4,1,2,5,3,6] => 5
[4,1,2,5,6,3] => 6
[4,1,2,6,3,5] => 5
[4,1,2,6,5,3] => 10
[4,1,3,2,5,6] => 4
[4,1,3,2,6,5] => 9
[4,1,3,5,2,6] => 5
[4,1,3,5,6,2] => 6
[4,1,3,6,2,5] => 5
[4,1,3,6,5,2] => 10
[4,1,5,2,3,6] => 4
[4,1,5,2,6,3] => 9
[4,1,5,3,2,6] => 8
[4,1,5,3,6,2] => 9
[4,1,5,6,2,3] => 5
[4,1,5,6,3,2] => 10
[4,1,6,2,3,5] => 4
[4,1,6,2,5,3] => 9
[4,1,6,3,2,5] => 8
[4,1,6,3,5,2] => 9
[4,1,6,5,2,3] => 8
[4,1,6,5,3,2] => 13
[4,2,1,3,5,6] => 3
[4,2,1,3,6,5] => 8
[4,2,1,5,3,6] => 7
[4,2,1,5,6,3] => 8
[4,2,1,6,3,5] => 7
[4,2,1,6,5,3] => 12
[4,2,3,1,5,6] => 4
[4,2,3,1,6,5] => 9
[4,2,3,5,1,6] => 5
[4,2,3,5,6,1] => 6
[4,2,3,6,1,5] => 5
[4,2,3,6,5,1] => 10
[4,2,5,1,3,6] => 4
[4,2,5,1,6,3] => 9
[4,2,5,3,1,6] => 8
[4,2,5,3,6,1] => 9
[4,2,5,6,1,3] => 5
[4,2,5,6,3,1] => 10
[4,2,6,1,3,5] => 4
[4,2,6,1,5,3] => 9
[4,2,6,3,1,5] => 8
[4,2,6,3,5,1] => 9
[4,2,6,5,1,3] => 8
[4,2,6,5,3,1] => 13
[4,3,1,2,5,6] => 3
[4,3,1,2,6,5] => 8
[4,3,1,5,2,6] => 7
[4,3,1,5,6,2] => 8
[4,3,1,6,2,5] => 7
[4,3,1,6,5,2] => 12
[4,3,2,1,5,6] => 6
[4,3,2,1,6,5] => 11
[4,3,2,5,1,6] => 7
[4,3,2,5,6,1] => 8
[4,3,2,6,1,5] => 7
[4,3,2,6,5,1] => 12
[4,3,5,1,2,6] => 4
[4,3,5,1,6,2] => 9
[4,3,5,2,1,6] => 8
[4,3,5,2,6,1] => 9
[4,3,5,6,1,2] => 5
[4,3,5,6,2,1] => 10
[4,3,6,1,2,5] => 4
[4,3,6,1,5,2] => 9
[4,3,6,2,1,5] => 8
[4,3,6,2,5,1] => 9
[4,3,6,5,1,2] => 8
[4,3,6,5,2,1] => 13
[4,5,1,2,3,6] => 2
[4,5,1,2,6,3] => 7
[4,5,1,3,2,6] => 6
[4,5,1,3,6,2] => 7
[4,5,1,6,2,3] => 6
[4,5,1,6,3,2] => 11
[4,5,2,1,3,6] => 5
[4,5,2,1,6,3] => 10
[4,5,2,3,1,6] => 6
[4,5,2,3,6,1] => 7
[4,5,2,6,1,3] => 6
[4,5,2,6,3,1] => 11
[4,5,3,1,2,6] => 5
[4,5,3,1,6,2] => 10
[4,5,3,2,1,6] => 9
[4,5,3,2,6,1] => 10
[4,5,3,6,1,2] => 6
[4,5,3,6,2,1] => 11
[4,5,6,1,2,3] => 3
[4,5,6,1,3,2] => 8
[4,5,6,2,1,3] => 7
[4,5,6,2,3,1] => 8
[4,5,6,3,1,2] => 7
[4,5,6,3,2,1] => 12
[4,6,1,2,3,5] => 2
[4,6,1,2,5,3] => 7
[4,6,1,3,2,5] => 6
[4,6,1,3,5,2] => 7
[4,6,1,5,2,3] => 6
[4,6,1,5,3,2] => 11
[4,6,2,1,3,5] => 5
[4,6,2,1,5,3] => 10
[4,6,2,3,1,5] => 6
[4,6,2,3,5,1] => 7
[4,6,2,5,1,3] => 6
[4,6,2,5,3,1] => 11
[4,6,3,1,2,5] => 5
[4,6,3,1,5,2] => 10
[4,6,3,2,1,5] => 9
[4,6,3,2,5,1] => 10
[4,6,3,5,1,2] => 6
[4,6,3,5,2,1] => 11
[4,6,5,1,2,3] => 5
[4,6,5,1,3,2] => 10
[4,6,5,2,1,3] => 9
[4,6,5,2,3,1] => 10
[4,6,5,3,1,2] => 9
[4,6,5,3,2,1] => 14
[5,1,2,3,4,6] => 1
[5,1,2,3,6,4] => 6
[5,1,2,4,3,6] => 5
[5,1,2,4,6,3] => 6
[5,1,2,6,3,4] => 5
[5,1,2,6,4,3] => 10
[5,1,3,2,4,6] => 4
[5,1,3,2,6,4] => 9
[5,1,3,4,2,6] => 5
[5,1,3,4,6,2] => 6
[5,1,3,6,2,4] => 5
[5,1,3,6,4,2] => 10
[5,1,4,2,3,6] => 4
[5,1,4,2,6,3] => 9
[5,1,4,3,2,6] => 8
[5,1,4,3,6,2] => 9
[5,1,4,6,2,3] => 5
[5,1,4,6,3,2] => 10
[5,1,6,2,3,4] => 4
[5,1,6,2,4,3] => 9
[5,1,6,3,2,4] => 8
[5,1,6,3,4,2] => 9
[5,1,6,4,2,3] => 8
[5,1,6,4,3,2] => 13
[5,2,1,3,4,6] => 3
[5,2,1,3,6,4] => 8
[5,2,1,4,3,6] => 7
[5,2,1,4,6,3] => 8
[5,2,1,6,3,4] => 7
[5,2,1,6,4,3] => 12
[5,2,3,1,4,6] => 4
[5,2,3,1,6,4] => 9
[5,2,3,4,1,6] => 5
[5,2,3,4,6,1] => 6
[5,2,3,6,1,4] => 5
[5,2,3,6,4,1] => 10
[5,2,4,1,3,6] => 4
[5,2,4,1,6,3] => 9
[5,2,4,3,1,6] => 8
[5,2,4,3,6,1] => 9
[5,2,4,6,1,3] => 5
[5,2,4,6,3,1] => 10
[5,2,6,1,3,4] => 4
[5,2,6,1,4,3] => 9
[5,2,6,3,1,4] => 8
[5,2,6,3,4,1] => 9
[5,2,6,4,1,3] => 8
[5,2,6,4,3,1] => 13
[5,3,1,2,4,6] => 3
[5,3,1,2,6,4] => 8
[5,3,1,4,2,6] => 7
[5,3,1,4,6,2] => 8
[5,3,1,6,2,4] => 7
[5,3,1,6,4,2] => 12
[5,3,2,1,4,6] => 6
[5,3,2,1,6,4] => 11
[5,3,2,4,1,6] => 7
[5,3,2,4,6,1] => 8
[5,3,2,6,1,4] => 7
[5,3,2,6,4,1] => 12
[5,3,4,1,2,6] => 4
[5,3,4,1,6,2] => 9
[5,3,4,2,1,6] => 8
[5,3,4,2,6,1] => 9
[5,3,4,6,1,2] => 5
[5,3,4,6,2,1] => 10
[5,3,6,1,2,4] => 4
[5,3,6,1,4,2] => 9
[5,3,6,2,1,4] => 8
[5,3,6,2,4,1] => 9
[5,3,6,4,1,2] => 8
[5,3,6,4,2,1] => 13
[5,4,1,2,3,6] => 3
[5,4,1,2,6,3] => 8
[5,4,1,3,2,6] => 7
[5,4,1,3,6,2] => 8
[5,4,1,6,2,3] => 7
[5,4,1,6,3,2] => 12
[5,4,2,1,3,6] => 6
[5,4,2,1,6,3] => 11
[5,4,2,3,1,6] => 7
[5,4,2,3,6,1] => 8
[5,4,2,6,1,3] => 7
[5,4,2,6,3,1] => 12
[5,4,3,1,2,6] => 6
[5,4,3,1,6,2] => 11
[5,4,3,2,1,6] => 10
[5,4,3,2,6,1] => 11
[5,4,3,6,1,2] => 7
[5,4,3,6,2,1] => 12
[5,4,6,1,2,3] => 4
[5,4,6,1,3,2] => 9
[5,4,6,2,1,3] => 8
[5,4,6,2,3,1] => 9
[5,4,6,3,1,2] => 8
[5,4,6,3,2,1] => 13
[5,6,1,2,3,4] => 2
[5,6,1,2,4,3] => 7
[5,6,1,3,2,4] => 6
[5,6,1,3,4,2] => 7
[5,6,1,4,2,3] => 6
[5,6,1,4,3,2] => 11
[5,6,2,1,3,4] => 5
[5,6,2,1,4,3] => 10
[5,6,2,3,1,4] => 6
[5,6,2,3,4,1] => 7
[5,6,2,4,1,3] => 6
[5,6,2,4,3,1] => 11
[5,6,3,1,2,4] => 5
[5,6,3,1,4,2] => 10
[5,6,3,2,1,4] => 9
[5,6,3,2,4,1] => 10
[5,6,3,4,1,2] => 6
[5,6,3,4,2,1] => 11
[5,6,4,1,2,3] => 5
[5,6,4,1,3,2] => 10
[5,6,4,2,1,3] => 9
[5,6,4,2,3,1] => 10
[5,6,4,3,1,2] => 9
[5,6,4,3,2,1] => 14
[6,1,2,3,4,5] => 1
[6,1,2,3,5,4] => 6
[6,1,2,4,3,5] => 5
[6,1,2,4,5,3] => 6
[6,1,2,5,3,4] => 5
[6,1,2,5,4,3] => 10
[6,1,3,2,4,5] => 4
[6,1,3,2,5,4] => 9
[6,1,3,4,2,5] => 5
[6,1,3,4,5,2] => 6
[6,1,3,5,2,4] => 5
[6,1,3,5,4,2] => 10
[6,1,4,2,3,5] => 4
[6,1,4,2,5,3] => 9
[6,1,4,3,2,5] => 8
[6,1,4,3,5,2] => 9
[6,1,4,5,2,3] => 5
[6,1,4,5,3,2] => 10
[6,1,5,2,3,4] => 4
[6,1,5,2,4,3] => 9
[6,1,5,3,2,4] => 8
[6,1,5,3,4,2] => 9
[6,1,5,4,2,3] => 8
[6,1,5,4,3,2] => 13
[6,2,1,3,4,5] => 3
[6,2,1,3,5,4] => 8
[6,2,1,4,3,5] => 7
[6,2,1,4,5,3] => 8
[6,2,1,5,3,4] => 7
[6,2,1,5,4,3] => 12
[6,2,3,1,4,5] => 4
[6,2,3,1,5,4] => 9
[6,2,3,4,1,5] => 5
[6,2,3,4,5,1] => 6
[6,2,3,5,1,4] => 5
[6,2,3,5,4,1] => 10
[6,2,4,1,3,5] => 4
[6,2,4,1,5,3] => 9
[6,2,4,3,1,5] => 8
[6,2,4,3,5,1] => 9
[6,2,4,5,1,3] => 5
[6,2,4,5,3,1] => 10
[6,2,5,1,3,4] => 4
[6,2,5,1,4,3] => 9
[6,2,5,3,1,4] => 8
[6,2,5,3,4,1] => 9
[6,2,5,4,1,3] => 8
[6,2,5,4,3,1] => 13
[6,3,1,2,4,5] => 3
[6,3,1,2,5,4] => 8
[6,3,1,4,2,5] => 7
[6,3,1,4,5,2] => 8
[6,3,1,5,2,4] => 7
[6,3,1,5,4,2] => 12
[6,3,2,1,4,5] => 6
[6,3,2,1,5,4] => 11
[6,3,2,4,1,5] => 7
[6,3,2,4,5,1] => 8
[6,3,2,5,1,4] => 7
[6,3,2,5,4,1] => 12
[6,3,4,1,2,5] => 4
[6,3,4,1,5,2] => 9
[6,3,4,2,1,5] => 8
[6,3,4,2,5,1] => 9
[6,3,4,5,1,2] => 5
[6,3,4,5,2,1] => 10
[6,3,5,1,2,4] => 4
[6,3,5,1,4,2] => 9
[6,3,5,2,1,4] => 8
[6,3,5,2,4,1] => 9
[6,3,5,4,1,2] => 8
[6,3,5,4,2,1] => 13
[6,4,1,2,3,5] => 3
[6,4,1,2,5,3] => 8
[6,4,1,3,2,5] => 7
[6,4,1,3,5,2] => 8
[6,4,1,5,2,3] => 7
[6,4,1,5,3,2] => 12
[6,4,2,1,3,5] => 6
[6,4,2,1,5,3] => 11
[6,4,2,3,1,5] => 7
[6,4,2,3,5,1] => 8
[6,4,2,5,1,3] => 7
[6,4,2,5,3,1] => 12
[6,4,3,1,2,5] => 6
[6,4,3,1,5,2] => 11
[6,4,3,2,1,5] => 10
[6,4,3,2,5,1] => 11
[6,4,3,5,1,2] => 7
[6,4,3,5,2,1] => 12
[6,4,5,1,2,3] => 4
[6,4,5,1,3,2] => 9
[6,4,5,2,1,3] => 8
[6,4,5,2,3,1] => 9
[6,4,5,3,1,2] => 8
[6,4,5,3,2,1] => 13
[6,5,1,2,3,4] => 3
[6,5,1,2,4,3] => 8
[6,5,1,3,2,4] => 7
[6,5,1,3,4,2] => 8
[6,5,1,4,2,3] => 7
[6,5,1,4,3,2] => 12
[6,5,2,1,3,4] => 6
[6,5,2,1,4,3] => 11
[6,5,2,3,1,4] => 7
[6,5,2,3,4,1] => 8
[6,5,2,4,1,3] => 7
[6,5,2,4,3,1] => 12
[6,5,3,1,2,4] => 6
[6,5,3,1,4,2] => 11
[6,5,3,2,1,4] => 10
[6,5,3,2,4,1] => 11
[6,5,3,4,1,2] => 7
[6,5,3,4,2,1] => 12
[6,5,4,1,2,3] => 6
[6,5,4,1,3,2] => 11
[6,5,4,2,1,3] => 10
[6,5,4,2,3,1] => 11
[6,5,4,3,1,2] => 10
[6,5,4,3,2,1] => 15
-----------------------------------------------------------------------------
Created: Sep 15, 2011 at 15:51 by Chris Berg
-----------------------------------------------------------------------------
Last Updated: Feb 07, 2020 at 09:49 by Christian Stump