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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, *
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-----------------------------------------------------------------------------
Statistic identifier: St000029
-----------------------------------------------------------------------------
Collection: Permutations
-----------------------------------------------------------------------------
Description: The depth of a permutation.
This is given by
$$\operatorname{dp}(\sigma) = \sum_{\sigma_i>i} (\sigma_i-i) = |\{ i \leq j : \sigma_i > j\}|.$$
The depth is half of the total displacement [4], Problem 5.1.1.28, or Spearman’s disarray [3] $\sum_i |\sigma_i-i|$.
Permutations with depth at most $1$ are called ''almost-increasing'' in [5].
-----------------------------------------------------------------------------
References: [1] Petersen, T. K., Tenner, B. E. The depth of a permutation [[arXiv:1202.4765]]
[2] Bagno, E., Biagioli, R., Novick, M., Woo, A. Depth in classical Coexter groups [[arXiv:1507.01180]]
[3] Diaconis, P., Graham, R. L. Spearman's footrule as a measure of disarray [[MathSciNet:0652736]]
[4] Knuth, D. E. The art of computer programming. Vol. 3 [[MathSciNet:3077154]]
[5] Elizalde, S. The $X$-class and almost-increasing permutations [[arXiv:0710.5168]]
-----------------------------------------------------------------------------
Code:
def statistic(w):
return sum(w[i]-i-1 for i in range(len(w)) if w[i]>i+1)
-----------------------------------------------------------------------------
Statistic values:
[1] => 0
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 2
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 2
[2,1,3,4] => 1
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 3
[2,4,1,3] => 3
[2,4,3,1] => 3
[3,1,2,4] => 2
[3,1,4,2] => 3
[3,2,1,4] => 2
[3,2,4,1] => 3
[3,4,1,2] => 4
[3,4,2,1] => 4
[4,1,2,3] => 3
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 3
[4,3,1,2] => 4
[4,3,2,1] => 4
[1,2,3,4,5] => 0
[1,2,3,5,4] => 1
[1,2,4,3,5] => 1
[1,2,4,5,3] => 2
[1,2,5,3,4] => 2
[1,2,5,4,3] => 2
[1,3,2,4,5] => 1
[1,3,2,5,4] => 2
[1,3,4,2,5] => 2
[1,3,4,5,2] => 3
[1,3,5,2,4] => 3
[1,3,5,4,2] => 3
[1,4,2,3,5] => 2
[1,4,2,5,3] => 3
[1,4,3,2,5] => 2
[1,4,3,5,2] => 3
[1,4,5,2,3] => 4
[1,4,5,3,2] => 4
[1,5,2,3,4] => 3
[1,5,2,4,3] => 3
[1,5,3,2,4] => 3
[1,5,3,4,2] => 3
[1,5,4,2,3] => 4
[1,5,4,3,2] => 4
[2,1,3,4,5] => 1
[2,1,3,5,4] => 2
[2,1,4,3,5] => 2
[2,1,4,5,3] => 3
[2,1,5,3,4] => 3
[2,1,5,4,3] => 3
[2,3,1,4,5] => 2
[2,3,1,5,4] => 3
[2,3,4,1,5] => 3
[2,3,4,5,1] => 4
[2,3,5,1,4] => 4
[2,3,5,4,1] => 4
[2,4,1,3,5] => 3
[2,4,1,5,3] => 4
[2,4,3,1,5] => 3
[2,4,3,5,1] => 4
[2,4,5,1,3] => 5
[2,4,5,3,1] => 5
[2,5,1,3,4] => 4
[2,5,1,4,3] => 4
[2,5,3,1,4] => 4
[2,5,3,4,1] => 4
[2,5,4,1,3] => 5
[2,5,4,3,1] => 5
[3,1,2,4,5] => 2
[3,1,2,5,4] => 3
[3,1,4,2,5] => 3
[3,1,4,5,2] => 4
[3,1,5,2,4] => 4
[3,1,5,4,2] => 4
[3,2,1,4,5] => 2
[3,2,1,5,4] => 3
[3,2,4,1,5] => 3
[3,2,4,5,1] => 4
[3,2,5,1,4] => 4
[3,2,5,4,1] => 4
[3,4,1,2,5] => 4
[3,4,1,5,2] => 5
[3,4,2,1,5] => 4
[3,4,2,5,1] => 5
[3,4,5,1,2] => 6
[3,4,5,2,1] => 6
[3,5,1,2,4] => 5
[3,5,1,4,2] => 5
[3,5,2,1,4] => 5
[3,5,2,4,1] => 5
[3,5,4,1,2] => 6
[3,5,4,2,1] => 6
[4,1,2,3,5] => 3
[4,1,2,5,3] => 4
[4,1,3,2,5] => 3
[4,1,3,5,2] => 4
[4,1,5,2,3] => 5
[4,1,5,3,2] => 5
[4,2,1,3,5] => 3
[4,2,1,5,3] => 4
[4,2,3,1,5] => 3
[4,2,3,5,1] => 4
[4,2,5,1,3] => 5
[4,2,5,3,1] => 5
[4,3,1,2,5] => 4
[4,3,1,5,2] => 5
[4,3,2,1,5] => 4
[4,3,2,5,1] => 5
[4,3,5,1,2] => 6
[4,3,5,2,1] => 6
[4,5,1,2,3] => 6
[4,5,1,3,2] => 6
[4,5,2,1,3] => 6
[4,5,2,3,1] => 6
[4,5,3,1,2] => 6
[4,5,3,2,1] => 6
[5,1,2,3,4] => 4
[5,1,2,4,3] => 4
[5,1,3,2,4] => 4
[5,1,3,4,2] => 4
[5,1,4,2,3] => 5
[5,1,4,3,2] => 5
[5,2,1,3,4] => 4
[5,2,1,4,3] => 4
[5,2,3,1,4] => 4
[5,2,3,4,1] => 4
[5,2,4,1,3] => 5
[5,2,4,3,1] => 5
[5,3,1,2,4] => 5
[5,3,1,4,2] => 5
[5,3,2,1,4] => 5
[5,3,2,4,1] => 5
[5,3,4,1,2] => 6
[5,3,4,2,1] => 6
[5,4,1,2,3] => 6
[5,4,1,3,2] => 6
[5,4,2,1,3] => 6
[5,4,2,3,1] => 6
[5,4,3,1,2] => 6
[5,4,3,2,1] => 6
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => 1
[1,2,3,5,6,4] => 2
[1,2,3,6,4,5] => 2
[1,2,3,6,5,4] => 2
[1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => 2
[1,2,4,5,3,6] => 2
[1,2,4,5,6,3] => 3
[1,2,4,6,3,5] => 3
[1,2,4,6,5,3] => 3
[1,2,5,3,4,6] => 2
[1,2,5,3,6,4] => 3
[1,2,5,4,3,6] => 2
[1,2,5,4,6,3] => 3
[1,2,5,6,3,4] => 4
[1,2,5,6,4,3] => 4
[1,2,6,3,4,5] => 3
[1,2,6,3,5,4] => 3
[1,2,6,4,3,5] => 3
[1,2,6,4,5,3] => 3
[1,2,6,5,3,4] => 4
[1,2,6,5,4,3] => 4
[1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => 2
[1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => 3
[1,3,2,6,4,5] => 3
[1,3,2,6,5,4] => 3
[1,3,4,2,5,6] => 2
[1,3,4,2,6,5] => 3
[1,3,4,5,2,6] => 3
[1,3,4,5,6,2] => 4
[1,3,4,6,2,5] => 4
[1,3,4,6,5,2] => 4
[1,3,5,2,4,6] => 3
[1,3,5,2,6,4] => 4
[1,3,5,4,2,6] => 3
[1,3,5,4,6,2] => 4
[1,3,5,6,2,4] => 5
[1,3,5,6,4,2] => 5
[1,3,6,2,4,5] => 4
[1,3,6,2,5,4] => 4
[1,3,6,4,2,5] => 4
[1,3,6,4,5,2] => 4
[1,3,6,5,2,4] => 5
[1,3,6,5,4,2] => 5
[1,4,2,3,5,6] => 2
[1,4,2,3,6,5] => 3
[1,4,2,5,3,6] => 3
[1,4,2,5,6,3] => 4
[1,4,2,6,3,5] => 4
[1,4,2,6,5,3] => 4
[1,4,3,2,5,6] => 2
[1,4,3,2,6,5] => 3
[1,4,3,5,2,6] => 3
[1,4,3,5,6,2] => 4
[1,4,3,6,2,5] => 4
[1,4,3,6,5,2] => 4
[1,4,5,2,3,6] => 4
[1,4,5,2,6,3] => 5
[1,4,5,3,2,6] => 4
[1,4,5,3,6,2] => 5
[1,4,5,6,2,3] => 6
[1,4,5,6,3,2] => 6
[1,4,6,2,3,5] => 5
[1,4,6,2,5,3] => 5
[1,4,6,3,2,5] => 5
[1,4,6,3,5,2] => 5
[1,4,6,5,2,3] => 6
[1,4,6,5,3,2] => 6
[1,5,2,3,4,6] => 3
[1,5,2,3,6,4] => 4
[1,5,2,4,3,6] => 3
[1,5,2,4,6,3] => 4
[1,5,2,6,3,4] => 5
[1,5,2,6,4,3] => 5
[1,5,3,2,4,6] => 3
[1,5,3,2,6,4] => 4
[1,5,3,4,2,6] => 3
[1,5,3,4,6,2] => 4
[1,5,3,6,2,4] => 5
[1,5,3,6,4,2] => 5
[1,5,4,2,3,6] => 4
[1,5,4,2,6,3] => 5
[1,5,4,3,2,6] => 4
[1,5,4,3,6,2] => 5
[1,5,4,6,2,3] => 6
[1,5,4,6,3,2] => 6
[1,5,6,2,3,4] => 6
[1,5,6,2,4,3] => 6
[1,5,6,3,2,4] => 6
[1,5,6,3,4,2] => 6
[1,5,6,4,2,3] => 6
[1,5,6,4,3,2] => 6
[1,6,2,3,4,5] => 4
[1,6,2,3,5,4] => 4
[1,6,2,4,3,5] => 4
[1,6,2,4,5,3] => 4
[1,6,2,5,3,4] => 5
[1,6,2,5,4,3] => 5
[1,6,3,2,4,5] => 4
[1,6,3,2,5,4] => 4
[1,6,3,4,2,5] => 4
[1,6,3,4,5,2] => 4
[1,6,3,5,2,4] => 5
[1,6,3,5,4,2] => 5
[1,6,4,2,3,5] => 5
[1,6,4,2,5,3] => 5
[1,6,4,3,2,5] => 5
[1,6,4,3,5,2] => 5
[1,6,4,5,2,3] => 6
[1,6,4,5,3,2] => 6
[1,6,5,2,3,4] => 6
[1,6,5,2,4,3] => 6
[1,6,5,3,2,4] => 6
[1,6,5,3,4,2] => 6
[1,6,5,4,2,3] => 6
[1,6,5,4,3,2] => 6
[2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => 2
[2,1,3,5,4,6] => 2
[2,1,3,5,6,4] => 3
[2,1,3,6,4,5] => 3
[2,1,3,6,5,4] => 3
[2,1,4,3,5,6] => 2
[2,1,4,3,6,5] => 3
[2,1,4,5,3,6] => 3
[2,1,4,5,6,3] => 4
[2,1,4,6,3,5] => 4
[2,1,4,6,5,3] => 4
[2,1,5,3,4,6] => 3
[2,1,5,3,6,4] => 4
[2,1,5,4,3,6] => 3
[2,1,5,4,6,3] => 4
[2,1,5,6,3,4] => 5
[2,1,5,6,4,3] => 5
[2,1,6,3,4,5] => 4
[2,1,6,3,5,4] => 4
[2,1,6,4,3,5] => 4
[2,1,6,4,5,3] => 4
[2,1,6,5,3,4] => 5
[2,1,6,5,4,3] => 5
[2,3,1,4,5,6] => 2
[2,3,1,4,6,5] => 3
[2,3,1,5,4,6] => 3
[2,3,1,5,6,4] => 4
[2,3,1,6,4,5] => 4
[2,3,1,6,5,4] => 4
[2,3,4,1,5,6] => 3
[2,3,4,1,6,5] => 4
[2,3,4,5,1,6] => 4
[2,3,4,5,6,1] => 5
[2,3,4,6,1,5] => 5
[2,3,4,6,5,1] => 5
[2,3,5,1,4,6] => 4
[2,3,5,1,6,4] => 5
[2,3,5,4,1,6] => 4
[2,3,5,4,6,1] => 5
[2,3,5,6,1,4] => 6
[2,3,5,6,4,1] => 6
[2,3,6,1,4,5] => 5
[2,3,6,1,5,4] => 5
[2,3,6,4,1,5] => 5
[2,3,6,4,5,1] => 5
[2,3,6,5,1,4] => 6
[2,3,6,5,4,1] => 6
[2,4,1,3,5,6] => 3
[2,4,1,3,6,5] => 4
[2,4,1,5,3,6] => 4
[2,4,1,5,6,3] => 5
[2,4,1,6,3,5] => 5
[2,4,1,6,5,3] => 5
[2,4,3,1,5,6] => 3
[2,4,3,1,6,5] => 4
[2,4,3,5,1,6] => 4
[2,4,3,5,6,1] => 5
[2,4,3,6,1,5] => 5
[2,4,3,6,5,1] => 5
[2,4,5,1,3,6] => 5
[2,4,5,1,6,3] => 6
[2,4,5,3,1,6] => 5
[2,4,5,3,6,1] => 6
[2,4,5,6,1,3] => 7
[2,4,5,6,3,1] => 7
[2,4,6,1,3,5] => 6
[2,4,6,1,5,3] => 6
[2,4,6,3,1,5] => 6
[2,4,6,3,5,1] => 6
[2,4,6,5,1,3] => 7
[2,4,6,5,3,1] => 7
[2,5,1,3,4,6] => 4
[2,5,1,3,6,4] => 5
[2,5,1,4,3,6] => 4
[2,5,1,4,6,3] => 5
[2,5,1,6,3,4] => 6
[2,5,1,6,4,3] => 6
[2,5,3,1,4,6] => 4
[2,5,3,1,6,4] => 5
[2,5,3,4,1,6] => 4
[2,5,3,4,6,1] => 5
[2,5,3,6,1,4] => 6
[2,5,3,6,4,1] => 6
[2,5,4,1,3,6] => 5
[2,5,4,1,6,3] => 6
[2,5,4,3,1,6] => 5
[2,5,4,3,6,1] => 6
[2,5,4,6,1,3] => 7
[2,5,4,6,3,1] => 7
[2,5,6,1,3,4] => 7
[2,5,6,1,4,3] => 7
[2,5,6,3,1,4] => 7
[2,5,6,3,4,1] => 7
[2,5,6,4,1,3] => 7
[2,5,6,4,3,1] => 7
[2,6,1,3,4,5] => 5
[2,6,1,3,5,4] => 5
[2,6,1,4,3,5] => 5
[2,6,1,4,5,3] => 5
[2,6,1,5,3,4] => 6
[2,6,1,5,4,3] => 6
[2,6,3,1,4,5] => 5
[2,6,3,1,5,4] => 5
[2,6,3,4,1,5] => 5
[2,6,3,4,5,1] => 5
[2,6,3,5,1,4] => 6
[2,6,3,5,4,1] => 6
[2,6,4,1,3,5] => 6
[2,6,4,1,5,3] => 6
[2,6,4,3,1,5] => 6
[2,6,4,3,5,1] => 6
[2,6,4,5,1,3] => 7
[2,6,4,5,3,1] => 7
[2,6,5,1,3,4] => 7
[2,6,5,1,4,3] => 7
[2,6,5,3,1,4] => 7
[2,6,5,3,4,1] => 7
[2,6,5,4,1,3] => 7
[2,6,5,4,3,1] => 7
[3,1,2,4,5,6] => 2
[3,1,2,4,6,5] => 3
[3,1,2,5,4,6] => 3
[3,1,2,5,6,4] => 4
[3,1,2,6,4,5] => 4
[3,1,2,6,5,4] => 4
[3,1,4,2,5,6] => 3
[3,1,4,2,6,5] => 4
[3,1,4,5,2,6] => 4
[3,1,4,5,6,2] => 5
[3,1,4,6,2,5] => 5
[3,1,4,6,5,2] => 5
[3,1,5,2,4,6] => 4
[3,1,5,2,6,4] => 5
[3,1,5,4,2,6] => 4
[3,1,5,4,6,2] => 5
[3,1,5,6,2,4] => 6
[3,1,5,6,4,2] => 6
[3,1,6,2,4,5] => 5
[3,1,6,2,5,4] => 5
[3,1,6,4,2,5] => 5
[3,1,6,4,5,2] => 5
[3,1,6,5,2,4] => 6
[3,1,6,5,4,2] => 6
[3,2,1,4,5,6] => 2
[3,2,1,4,6,5] => 3
[3,2,1,5,4,6] => 3
[3,2,1,5,6,4] => 4
[3,2,1,6,4,5] => 4
[3,2,1,6,5,4] => 4
[3,2,4,1,5,6] => 3
[3,2,4,1,6,5] => 4
[3,2,4,5,1,6] => 4
[3,2,4,5,6,1] => 5
[3,2,4,6,1,5] => 5
[3,2,4,6,5,1] => 5
[3,2,5,1,4,6] => 4
[3,2,5,1,6,4] => 5
[3,2,5,4,1,6] => 4
[3,2,5,4,6,1] => 5
[3,2,5,6,1,4] => 6
[3,2,5,6,4,1] => 6
[3,2,6,1,4,5] => 5
[3,2,6,1,5,4] => 5
[3,2,6,4,1,5] => 5
[3,2,6,4,5,1] => 5
[3,2,6,5,1,4] => 6
[3,2,6,5,4,1] => 6
[3,4,1,2,5,6] => 4
[3,4,1,2,6,5] => 5
[3,4,1,5,2,6] => 5
[3,4,1,5,6,2] => 6
[3,4,1,6,2,5] => 6
[3,4,1,6,5,2] => 6
[3,4,2,1,5,6] => 4
[3,4,2,1,6,5] => 5
[3,4,2,5,1,6] => 5
[3,4,2,5,6,1] => 6
[3,4,2,6,1,5] => 6
[3,4,2,6,5,1] => 6
[3,4,5,1,2,6] => 6
[3,4,5,1,6,2] => 7
[3,4,5,2,1,6] => 6
[3,4,5,2,6,1] => 7
[3,4,5,6,1,2] => 8
[3,4,5,6,2,1] => 8
[3,4,6,1,2,5] => 7
[3,4,6,1,5,2] => 7
[3,4,6,2,1,5] => 7
[3,4,6,2,5,1] => 7
[3,4,6,5,1,2] => 8
[3,4,6,5,2,1] => 8
[3,5,1,2,4,6] => 5
[3,5,1,2,6,4] => 6
[3,5,1,4,2,6] => 5
[3,5,1,4,6,2] => 6
[3,5,1,6,2,4] => 7
[3,5,1,6,4,2] => 7
[3,5,2,1,4,6] => 5
[3,5,2,1,6,4] => 6
[3,5,2,4,1,6] => 5
[3,5,2,4,6,1] => 6
[3,5,2,6,1,4] => 7
[3,5,2,6,4,1] => 7
[3,5,4,1,2,6] => 6
[3,5,4,1,6,2] => 7
[3,5,4,2,1,6] => 6
[3,5,4,2,6,1] => 7
[3,5,4,6,1,2] => 8
[3,5,4,6,2,1] => 8
[3,5,6,1,2,4] => 8
[3,5,6,1,4,2] => 8
[3,5,6,2,1,4] => 8
[3,5,6,2,4,1] => 8
[3,5,6,4,1,2] => 8
[3,5,6,4,2,1] => 8
[3,6,1,2,4,5] => 6
[3,6,1,2,5,4] => 6
[3,6,1,4,2,5] => 6
[3,6,1,4,5,2] => 6
[3,6,1,5,2,4] => 7
[3,6,1,5,4,2] => 7
[3,6,2,1,4,5] => 6
[3,6,2,1,5,4] => 6
[3,6,2,4,1,5] => 6
[3,6,2,4,5,1] => 6
[3,6,2,5,1,4] => 7
[3,6,2,5,4,1] => 7
[3,6,4,1,2,5] => 7
[3,6,4,1,5,2] => 7
[3,6,4,2,1,5] => 7
[3,6,4,2,5,1] => 7
[3,6,4,5,1,2] => 8
[3,6,4,5,2,1] => 8
[3,6,5,1,2,4] => 8
[3,6,5,1,4,2] => 8
[3,6,5,2,1,4] => 8
[3,6,5,2,4,1] => 8
[3,6,5,4,1,2] => 8
[3,6,5,4,2,1] => 8
[4,1,2,3,5,6] => 3
[4,1,2,3,6,5] => 4
[4,1,2,5,3,6] => 4
[4,1,2,5,6,3] => 5
[4,1,2,6,3,5] => 5
[4,1,2,6,5,3] => 5
[4,1,3,2,5,6] => 3
[4,1,3,2,6,5] => 4
[4,1,3,5,2,6] => 4
[4,1,3,5,6,2] => 5
[4,1,3,6,2,5] => 5
[4,1,3,6,5,2] => 5
[4,1,5,2,3,6] => 5
[4,1,5,2,6,3] => 6
[4,1,5,3,2,6] => 5
[4,1,5,3,6,2] => 6
[4,1,5,6,2,3] => 7
[4,1,5,6,3,2] => 7
[4,1,6,2,3,5] => 6
[4,1,6,2,5,3] => 6
[4,1,6,3,2,5] => 6
[4,1,6,3,5,2] => 6
[4,1,6,5,2,3] => 7
[4,1,6,5,3,2] => 7
[4,2,1,3,5,6] => 3
[4,2,1,3,6,5] => 4
[4,2,1,5,3,6] => 4
[4,2,1,5,6,3] => 5
[4,2,1,6,3,5] => 5
[4,2,1,6,5,3] => 5
[4,2,3,1,5,6] => 3
[4,2,3,1,6,5] => 4
[4,2,3,5,1,6] => 4
[4,2,3,5,6,1] => 5
[4,2,3,6,1,5] => 5
[4,2,3,6,5,1] => 5
[4,2,5,1,3,6] => 5
[4,2,5,1,6,3] => 6
[4,2,5,3,1,6] => 5
[4,2,5,3,6,1] => 6
[4,2,5,6,1,3] => 7
[4,2,5,6,3,1] => 7
[4,2,6,1,3,5] => 6
[4,2,6,1,5,3] => 6
[4,2,6,3,1,5] => 6
[4,2,6,3,5,1] => 6
[4,2,6,5,1,3] => 7
[4,2,6,5,3,1] => 7
[4,3,1,2,5,6] => 4
[4,3,1,2,6,5] => 5
[4,3,1,5,2,6] => 5
[4,3,1,5,6,2] => 6
[4,3,1,6,2,5] => 6
[4,3,1,6,5,2] => 6
[4,3,2,1,5,6] => 4
[4,3,2,1,6,5] => 5
[4,3,2,5,1,6] => 5
[4,3,2,5,6,1] => 6
[4,3,2,6,1,5] => 6
[4,3,2,6,5,1] => 6
[4,3,5,1,2,6] => 6
[4,3,5,1,6,2] => 7
[4,3,5,2,1,6] => 6
[4,3,5,2,6,1] => 7
[4,3,5,6,1,2] => 8
[4,3,5,6,2,1] => 8
[4,3,6,1,2,5] => 7
[4,3,6,1,5,2] => 7
[4,3,6,2,1,5] => 7
[4,3,6,2,5,1] => 7
[4,3,6,5,1,2] => 8
[4,3,6,5,2,1] => 8
[4,5,1,2,3,6] => 6
[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] => 8
[4,5,1,6,3,2] => 8
[4,5,2,1,3,6] => 6
[4,5,2,1,6,3] => 7
[4,5,2,3,1,6] => 6
[4,5,2,3,6,1] => 7
[4,5,2,6,1,3] => 8
[4,5,2,6,3,1] => 8
[4,5,3,1,2,6] => 6
[4,5,3,1,6,2] => 7
[4,5,3,2,1,6] => 6
[4,5,3,2,6,1] => 7
[4,5,3,6,1,2] => 8
[4,5,3,6,2,1] => 8
[4,5,6,1,2,3] => 9
[4,5,6,1,3,2] => 9
[4,5,6,2,1,3] => 9
[4,5,6,2,3,1] => 9
[4,5,6,3,1,2] => 9
[4,5,6,3,2,1] => 9
[4,6,1,2,3,5] => 7
[4,6,1,2,5,3] => 7
[4,6,1,3,2,5] => 7
[4,6,1,3,5,2] => 7
[4,6,1,5,2,3] => 8
[4,6,1,5,3,2] => 8
[4,6,2,1,3,5] => 7
[4,6,2,1,5,3] => 7
[4,6,2,3,1,5] => 7
[4,6,2,3,5,1] => 7
[4,6,2,5,1,3] => 8
[4,6,2,5,3,1] => 8
[4,6,3,1,2,5] => 7
[4,6,3,1,5,2] => 7
[4,6,3,2,1,5] => 7
[4,6,3,2,5,1] => 7
[4,6,3,5,1,2] => 8
[4,6,3,5,2,1] => 8
[4,6,5,1,2,3] => 9
[4,6,5,1,3,2] => 9
[4,6,5,2,1,3] => 9
[4,6,5,2,3,1] => 9
[4,6,5,3,1,2] => 9
[4,6,5,3,2,1] => 9
[5,1,2,3,4,6] => 4
[5,1,2,3,6,4] => 5
[5,1,2,4,3,6] => 4
[5,1,2,4,6,3] => 5
[5,1,2,6,3,4] => 6
[5,1,2,6,4,3] => 6
[5,1,3,2,4,6] => 4
[5,1,3,2,6,4] => 5
[5,1,3,4,2,6] => 4
[5,1,3,4,6,2] => 5
[5,1,3,6,2,4] => 6
[5,1,3,6,4,2] => 6
[5,1,4,2,3,6] => 5
[5,1,4,2,6,3] => 6
[5,1,4,3,2,6] => 5
[5,1,4,3,6,2] => 6
[5,1,4,6,2,3] => 7
[5,1,4,6,3,2] => 7
[5,1,6,2,3,4] => 7
[5,1,6,2,4,3] => 7
[5,1,6,3,2,4] => 7
[5,1,6,3,4,2] => 7
[5,1,6,4,2,3] => 7
[5,1,6,4,3,2] => 7
[5,2,1,3,4,6] => 4
[5,2,1,3,6,4] => 5
[5,2,1,4,3,6] => 4
[5,2,1,4,6,3] => 5
[5,2,1,6,3,4] => 6
[5,2,1,6,4,3] => 6
[5,2,3,1,4,6] => 4
[5,2,3,1,6,4] => 5
[5,2,3,4,1,6] => 4
[5,2,3,4,6,1] => 5
[5,2,3,6,1,4] => 6
[5,2,3,6,4,1] => 6
[5,2,4,1,3,6] => 5
[5,2,4,1,6,3] => 6
[5,2,4,3,1,6] => 5
[5,2,4,3,6,1] => 6
[5,2,4,6,1,3] => 7
[5,2,4,6,3,1] => 7
[5,2,6,1,3,4] => 7
[5,2,6,1,4,3] => 7
[5,2,6,3,1,4] => 7
[5,2,6,3,4,1] => 7
[5,2,6,4,1,3] => 7
[5,2,6,4,3,1] => 7
[5,3,1,2,4,6] => 5
[5,3,1,2,6,4] => 6
[5,3,1,4,2,6] => 5
[5,3,1,4,6,2] => 6
[5,3,1,6,2,4] => 7
[5,3,1,6,4,2] => 7
[5,3,2,1,4,6] => 5
[5,3,2,1,6,4] => 6
[5,3,2,4,1,6] => 5
[5,3,2,4,6,1] => 6
[5,3,2,6,1,4] => 7
[5,3,2,6,4,1] => 7
[5,3,4,1,2,6] => 6
[5,3,4,1,6,2] => 7
[5,3,4,2,1,6] => 6
[5,3,4,2,6,1] => 7
[5,3,4,6,1,2] => 8
[5,3,4,6,2,1] => 8
[5,3,6,1,2,4] => 8
[5,3,6,1,4,2] => 8
[5,3,6,2,1,4] => 8
[5,3,6,2,4,1] => 8
[5,3,6,4,1,2] => 8
[5,3,6,4,2,1] => 8
[5,4,1,2,3,6] => 6
[5,4,1,2,6,3] => 7
[5,4,1,3,2,6] => 6
[5,4,1,3,6,2] => 7
[5,4,1,6,2,3] => 8
[5,4,1,6,3,2] => 8
[5,4,2,1,3,6] => 6
[5,4,2,1,6,3] => 7
[5,4,2,3,1,6] => 6
[5,4,2,3,6,1] => 7
[5,4,2,6,1,3] => 8
[5,4,2,6,3,1] => 8
[5,4,3,1,2,6] => 6
[5,4,3,1,6,2] => 7
[5,4,3,2,1,6] => 6
[5,4,3,2,6,1] => 7
[5,4,3,6,1,2] => 8
[5,4,3,6,2,1] => 8
[5,4,6,1,2,3] => 9
[5,4,6,1,3,2] => 9
[5,4,6,2,1,3] => 9
[5,4,6,2,3,1] => 9
[5,4,6,3,1,2] => 9
[5,4,6,3,2,1] => 9
[5,6,1,2,3,4] => 8
[5,6,1,2,4,3] => 8
[5,6,1,3,2,4] => 8
[5,6,1,3,4,2] => 8
[5,6,1,4,2,3] => 8
[5,6,1,4,3,2] => 8
[5,6,2,1,3,4] => 8
[5,6,2,1,4,3] => 8
[5,6,2,3,1,4] => 8
[5,6,2,3,4,1] => 8
[5,6,2,4,1,3] => 8
[5,6,2,4,3,1] => 8
[5,6,3,1,2,4] => 8
[5,6,3,1,4,2] => 8
[5,6,3,2,1,4] => 8
[5,6,3,2,4,1] => 8
[5,6,3,4,1,2] => 8
[5,6,3,4,2,1] => 8
[5,6,4,1,2,3] => 9
[5,6,4,1,3,2] => 9
[5,6,4,2,1,3] => 9
[5,6,4,2,3,1] => 9
[5,6,4,3,1,2] => 9
[5,6,4,3,2,1] => 9
[6,1,2,3,4,5] => 5
[6,1,2,3,5,4] => 5
[6,1,2,4,3,5] => 5
[6,1,2,4,5,3] => 5
[6,1,2,5,3,4] => 6
[6,1,2,5,4,3] => 6
[6,1,3,2,4,5] => 5
[6,1,3,2,5,4] => 5
[6,1,3,4,2,5] => 5
[6,1,3,4,5,2] => 5
[6,1,3,5,2,4] => 6
[6,1,3,5,4,2] => 6
[6,1,4,2,3,5] => 6
[6,1,4,2,5,3] => 6
[6,1,4,3,2,5] => 6
[6,1,4,3,5,2] => 6
[6,1,4,5,2,3] => 7
[6,1,4,5,3,2] => 7
[6,1,5,2,3,4] => 7
[6,1,5,2,4,3] => 7
[6,1,5,3,2,4] => 7
[6,1,5,3,4,2] => 7
[6,1,5,4,2,3] => 7
[6,1,5,4,3,2] => 7
[6,2,1,3,4,5] => 5
[6,2,1,3,5,4] => 5
[6,2,1,4,3,5] => 5
[6,2,1,4,5,3] => 5
[6,2,1,5,3,4] => 6
[6,2,1,5,4,3] => 6
[6,2,3,1,4,5] => 5
[6,2,3,1,5,4] => 5
[6,2,3,4,1,5] => 5
[6,2,3,4,5,1] => 5
[6,2,3,5,1,4] => 6
[6,2,3,5,4,1] => 6
[6,2,4,1,3,5] => 6
[6,2,4,1,5,3] => 6
[6,2,4,3,1,5] => 6
[6,2,4,3,5,1] => 6
[6,2,4,5,1,3] => 7
[6,2,4,5,3,1] => 7
[6,2,5,1,3,4] => 7
[6,2,5,1,4,3] => 7
[6,2,5,3,1,4] => 7
[6,2,5,3,4,1] => 7
[6,2,5,4,1,3] => 7
[6,2,5,4,3,1] => 7
[6,3,1,2,4,5] => 6
[6,3,1,2,5,4] => 6
[6,3,1,4,2,5] => 6
[6,3,1,4,5,2] => 6
[6,3,1,5,2,4] => 7
[6,3,1,5,4,2] => 7
[6,3,2,1,4,5] => 6
[6,3,2,1,5,4] => 6
[6,3,2,4,1,5] => 6
[6,3,2,4,5,1] => 6
[6,3,2,5,1,4] => 7
[6,3,2,5,4,1] => 7
[6,3,4,1,2,5] => 7
[6,3,4,1,5,2] => 7
[6,3,4,2,1,5] => 7
[6,3,4,2,5,1] => 7
[6,3,4,5,1,2] => 8
[6,3,4,5,2,1] => 8
[6,3,5,1,2,4] => 8
[6,3,5,1,4,2] => 8
[6,3,5,2,1,4] => 8
[6,3,5,2,4,1] => 8
[6,3,5,4,1,2] => 8
[6,3,5,4,2,1] => 8
[6,4,1,2,3,5] => 7
[6,4,1,2,5,3] => 7
[6,4,1,3,2,5] => 7
[6,4,1,3,5,2] => 7
[6,4,1,5,2,3] => 8
[6,4,1,5,3,2] => 8
[6,4,2,1,3,5] => 7
[6,4,2,1,5,3] => 7
[6,4,2,3,1,5] => 7
[6,4,2,3,5,1] => 7
[6,4,2,5,1,3] => 8
[6,4,2,5,3,1] => 8
[6,4,3,1,2,5] => 7
[6,4,3,1,5,2] => 7
[6,4,3,2,1,5] => 7
[6,4,3,2,5,1] => 7
[6,4,3,5,1,2] => 8
[6,4,3,5,2,1] => 8
[6,4,5,1,2,3] => 9
[6,4,5,1,3,2] => 9
[6,4,5,2,1,3] => 9
[6,4,5,2,3,1] => 9
[6,4,5,3,1,2] => 9
[6,4,5,3,2,1] => 9
[6,5,1,2,3,4] => 8
[6,5,1,2,4,3] => 8
[6,5,1,3,2,4] => 8
[6,5,1,3,4,2] => 8
[6,5,1,4,2,3] => 8
[6,5,1,4,3,2] => 8
[6,5,2,1,3,4] => 8
[6,5,2,1,4,3] => 8
[6,5,2,3,1,4] => 8
[6,5,2,3,4,1] => 8
[6,5,2,4,1,3] => 8
[6,5,2,4,3,1] => 8
[6,5,3,1,2,4] => 8
[6,5,3,1,4,2] => 8
[6,5,3,2,1,4] => 8
[6,5,3,2,4,1] => 8
[6,5,3,4,1,2] => 8
[6,5,3,4,2,1] => 8
[6,5,4,1,2,3] => 9
[6,5,4,1,3,2] => 9
[6,5,4,2,1,3] => 9
[6,5,4,2,3,1] => 9
[6,5,4,3,1,2] => 9
[6,5,4,3,2,1] => 9
-----------------------------------------------------------------------------
Created: Nov 30, 2012 at 21:09 by Chris Berg
-----------------------------------------------------------------------------
Last Updated: Jan 15, 2017 at 10:37 by Christian Stump