***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St000092 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of outer peaks of a permutation. An outer peak in a permutation $w = [w_1,..., w_n]$ is either a position $i$ such that $w_{i-1} < w_i > w_{i+1}$ or $1$ if $w_1 > w_2$ or $n$ if $w_{n} > w_{n-1}$. In other words, it is a peak in the word $[0,w_1,..., w_n,0]$. ----------------------------------------------------------------------------- References: [1] Claesson, A., Kitaev, S. Classification of bijections between 321- and 132-avoiding permutations [[MathSciNet:2465405]] ----------------------------------------------------------------------------- Code: def statistic(pi): pi = [0] + list(pi) + [0] n = len(pi) return sum( 1 for i in [1 .. n-2] if pi[i-1] < pi[i] > pi[i+1] ) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [1,2] => 1 [2,1] => 1 [1,2,3] => 1 [1,3,2] => 1 [2,1,3] => 2 [2,3,1] => 1 [3,1,2] => 2 [3,2,1] => 1 [1,2,3,4] => 1 [1,2,4,3] => 1 [1,3,2,4] => 2 [1,3,4,2] => 1 [1,4,2,3] => 2 [1,4,3,2] => 1 [2,1,3,4] => 2 [2,1,4,3] => 2 [2,3,1,4] => 2 [2,3,4,1] => 1 [2,4,1,3] => 2 [2,4,3,1] => 1 [3,1,2,4] => 2 [3,1,4,2] => 2 [3,2,1,4] => 2 [3,2,4,1] => 2 [3,4,1,2] => 2 [3,4,2,1] => 1 [4,1,2,3] => 2 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 2 [4,3,1,2] => 2 [4,3,2,1] => 1 [1,2,3,4,5] => 1 [1,2,3,5,4] => 1 [1,2,4,3,5] => 2 [1,2,4,5,3] => 1 [1,2,5,3,4] => 2 [1,2,5,4,3] => 1 [1,3,2,4,5] => 2 [1,3,2,5,4] => 2 [1,3,4,2,5] => 2 [1,3,4,5,2] => 1 [1,3,5,2,4] => 2 [1,3,5,4,2] => 1 [1,4,2,3,5] => 2 [1,4,2,5,3] => 2 [1,4,3,2,5] => 2 [1,4,3,5,2] => 2 [1,4,5,2,3] => 2 [1,4,5,3,2] => 1 [1,5,2,3,4] => 2 [1,5,2,4,3] => 2 [1,5,3,2,4] => 2 [1,5,3,4,2] => 2 [1,5,4,2,3] => 2 [1,5,4,3,2] => 1 [2,1,3,4,5] => 2 [2,1,3,5,4] => 2 [2,1,4,3,5] => 3 [2,1,4,5,3] => 2 [2,1,5,3,4] => 3 [2,1,5,4,3] => 2 [2,3,1,4,5] => 2 [2,3,1,5,4] => 2 [2,3,4,1,5] => 2 [2,3,4,5,1] => 1 [2,3,5,1,4] => 2 [2,3,5,4,1] => 1 [2,4,1,3,5] => 2 [2,4,1,5,3] => 2 [2,4,3,1,5] => 2 [2,4,3,5,1] => 2 [2,4,5,1,3] => 2 [2,4,5,3,1] => 1 [2,5,1,3,4] => 2 [2,5,1,4,3] => 2 [2,5,3,1,4] => 2 [2,5,3,4,1] => 2 [2,5,4,1,3] => 2 [2,5,4,3,1] => 1 [3,1,2,4,5] => 2 [3,1,2,5,4] => 2 [3,1,4,2,5] => 3 [3,1,4,5,2] => 2 [3,1,5,2,4] => 3 [3,1,5,4,2] => 2 [3,2,1,4,5] => 2 [3,2,1,5,4] => 2 [3,2,4,1,5] => 3 [3,2,4,5,1] => 2 [3,2,5,1,4] => 3 [3,2,5,4,1] => 2 [3,4,1,2,5] => 2 [3,4,1,5,2] => 2 [3,4,2,1,5] => 2 [3,4,2,5,1] => 2 [3,4,5,1,2] => 2 [3,4,5,2,1] => 1 [3,5,1,2,4] => 2 [3,5,1,4,2] => 2 [3,5,2,1,4] => 2 [3,5,2,4,1] => 2 [3,5,4,1,2] => 2 [3,5,4,2,1] => 1 [4,1,2,3,5] => 2 [4,1,2,5,3] => 2 [4,1,3,2,5] => 3 [4,1,3,5,2] => 2 [4,1,5,2,3] => 3 [4,1,5,3,2] => 2 [4,2,1,3,5] => 2 [4,2,1,5,3] => 2 [4,2,3,1,5] => 3 [4,2,3,5,1] => 2 [4,2,5,1,3] => 3 [4,2,5,3,1] => 2 [4,3,1,2,5] => 2 [4,3,1,5,2] => 2 [4,3,2,1,5] => 2 [4,3,2,5,1] => 2 [4,3,5,1,2] => 3 [4,3,5,2,1] => 2 [4,5,1,2,3] => 2 [4,5,1,3,2] => 2 [4,5,2,1,3] => 2 [4,5,2,3,1] => 2 [4,5,3,1,2] => 2 [4,5,3,2,1] => 1 [5,1,2,3,4] => 2 [5,1,2,4,3] => 2 [5,1,3,2,4] => 3 [5,1,3,4,2] => 2 [5,1,4,2,3] => 3 [5,1,4,3,2] => 2 [5,2,1,3,4] => 2 [5,2,1,4,3] => 2 [5,2,3,1,4] => 3 [5,2,3,4,1] => 2 [5,2,4,1,3] => 3 [5,2,4,3,1] => 2 [5,3,1,2,4] => 2 [5,3,1,4,2] => 2 [5,3,2,1,4] => 2 [5,3,2,4,1] => 2 [5,3,4,1,2] => 3 [5,3,4,2,1] => 2 [5,4,1,2,3] => 2 [5,4,1,3,2] => 2 [5,4,2,1,3] => 2 [5,4,2,3,1] => 2 [5,4,3,1,2] => 2 [5,4,3,2,1] => 1 [1,2,3,4,5,6] => 1 [1,2,3,4,6,5] => 1 [1,2,3,5,4,6] => 2 [1,2,3,5,6,4] => 1 [1,2,3,6,4,5] => 2 [1,2,3,6,5,4] => 1 [1,2,4,3,5,6] => 2 [1,2,4,3,6,5] => 2 [1,2,4,5,3,6] => 2 [1,2,4,5,6,3] => 1 [1,2,4,6,3,5] => 2 [1,2,4,6,5,3] => 1 [1,2,5,3,4,6] => 2 [1,2,5,3,6,4] => 2 [1,2,5,4,3,6] => 2 [1,2,5,4,6,3] => 2 [1,2,5,6,3,4] => 2 [1,2,5,6,4,3] => 1 [1,2,6,3,4,5] => 2 [1,2,6,3,5,4] => 2 [1,2,6,4,3,5] => 2 [1,2,6,4,5,3] => 2 [1,2,6,5,3,4] => 2 [1,2,6,5,4,3] => 1 [1,3,2,4,5,6] => 2 [1,3,2,4,6,5] => 2 [1,3,2,5,4,6] => 3 [1,3,2,5,6,4] => 2 [1,3,2,6,4,5] => 3 [1,3,2,6,5,4] => 2 [1,3,4,2,5,6] => 2 [1,3,4,2,6,5] => 2 [1,3,4,5,2,6] => 2 [1,3,4,5,6,2] => 1 [1,3,4,6,2,5] => 2 [1,3,4,6,5,2] => 1 [1,3,5,2,4,6] => 2 [1,3,5,2,6,4] => 2 [1,3,5,4,2,6] => 2 [1,3,5,4,6,2] => 2 [1,3,5,6,2,4] => 2 [1,3,5,6,4,2] => 1 [1,3,6,2,4,5] => 2 [1,3,6,2,5,4] => 2 [1,3,6,4,2,5] => 2 [1,3,6,4,5,2] => 2 [1,3,6,5,2,4] => 2 [1,3,6,5,4,2] => 1 [1,4,2,3,5,6] => 2 [1,4,2,3,6,5] => 2 [1,4,2,5,3,6] => 3 [1,4,2,5,6,3] => 2 [1,4,2,6,3,5] => 3 [1,4,2,6,5,3] => 2 [1,4,3,2,5,6] => 2 [1,4,3,2,6,5] => 2 [1,4,3,5,2,6] => 3 [1,4,3,5,6,2] => 2 [1,4,3,6,2,5] => 3 [1,4,3,6,5,2] => 2 [1,4,5,2,3,6] => 2 [1,4,5,2,6,3] => 2 [1,4,5,3,2,6] => 2 [1,4,5,3,6,2] => 2 [1,4,5,6,2,3] => 2 [1,4,5,6,3,2] => 1 [1,4,6,2,3,5] => 2 [1,4,6,2,5,3] => 2 [1,4,6,3,2,5] => 2 [1,4,6,3,5,2] => 2 [1,4,6,5,2,3] => 2 [1,4,6,5,3,2] => 1 [1,5,2,3,4,6] => 2 [1,5,2,3,6,4] => 2 [1,5,2,4,3,6] => 3 [1,5,2,4,6,3] => 2 [1,5,2,6,3,4] => 3 [1,5,2,6,4,3] => 2 [1,5,3,2,4,6] => 2 [1,5,3,2,6,4] => 2 [1,5,3,4,2,6] => 3 [1,5,3,4,6,2] => 2 [1,5,3,6,2,4] => 3 [1,5,3,6,4,2] => 2 [1,5,4,2,3,6] => 2 [1,5,4,2,6,3] => 2 [1,5,4,3,2,6] => 2 [1,5,4,3,6,2] => 2 [1,5,4,6,2,3] => 3 [1,5,4,6,3,2] => 2 [1,5,6,2,3,4] => 2 [1,5,6,2,4,3] => 2 [1,5,6,3,2,4] => 2 [1,5,6,3,4,2] => 2 [1,5,6,4,2,3] => 2 [1,5,6,4,3,2] => 1 [1,6,2,3,4,5] => 2 [1,6,2,3,5,4] => 2 [1,6,2,4,3,5] => 3 [1,6,2,4,5,3] => 2 [1,6,2,5,3,4] => 3 [1,6,2,5,4,3] => 2 [1,6,3,2,4,5] => 2 [1,6,3,2,5,4] => 2 [1,6,3,4,2,5] => 3 [1,6,3,4,5,2] => 2 [1,6,3,5,2,4] => 3 [1,6,3,5,4,2] => 2 [1,6,4,2,3,5] => 2 [1,6,4,2,5,3] => 2 [1,6,4,3,2,5] => 2 [1,6,4,3,5,2] => 2 [1,6,4,5,2,3] => 3 [1,6,4,5,3,2] => 2 [1,6,5,2,3,4] => 2 [1,6,5,2,4,3] => 2 [1,6,5,3,2,4] => 2 [1,6,5,3,4,2] => 2 [1,6,5,4,2,3] => 2 [1,6,5,4,3,2] => 1 [2,1,3,4,5,6] => 2 [2,1,3,4,6,5] => 2 [2,1,3,5,4,6] => 3 [2,1,3,5,6,4] => 2 [2,1,3,6,4,5] => 3 [2,1,3,6,5,4] => 2 [2,1,4,3,5,6] => 3 [2,1,4,3,6,5] => 3 [2,1,4,5,3,6] => 3 [2,1,4,5,6,3] => 2 [2,1,4,6,3,5] => 3 [2,1,4,6,5,3] => 2 [2,1,5,3,4,6] => 3 [2,1,5,3,6,4] => 3 [2,1,5,4,3,6] => 3 [2,1,5,4,6,3] => 3 [2,1,5,6,3,4] => 3 [2,1,5,6,4,3] => 2 [2,1,6,3,4,5] => 3 [2,1,6,3,5,4] => 3 [2,1,6,4,3,5] => 3 [2,1,6,4,5,3] => 3 [2,1,6,5,3,4] => 3 [2,1,6,5,4,3] => 2 [2,3,1,4,5,6] => 2 [2,3,1,4,6,5] => 2 [2,3,1,5,4,6] => 3 [2,3,1,5,6,4] => 2 [2,3,1,6,4,5] => 3 [2,3,1,6,5,4] => 2 [2,3,4,1,5,6] => 2 [2,3,4,1,6,5] => 2 [2,3,4,5,1,6] => 2 [2,3,4,5,6,1] => 1 [2,3,4,6,1,5] => 2 [2,3,4,6,5,1] => 1 [2,3,5,1,4,6] => 2 [2,3,5,1,6,4] => 2 [2,3,5,4,1,6] => 2 [2,3,5,4,6,1] => 2 [2,3,5,6,1,4] => 2 [2,3,5,6,4,1] => 1 [2,3,6,1,4,5] => 2 [2,3,6,1,5,4] => 2 [2,3,6,4,1,5] => 2 [2,3,6,4,5,1] => 2 [2,3,6,5,1,4] => 2 [2,3,6,5,4,1] => 1 [2,4,1,3,5,6] => 2 [2,4,1,3,6,5] => 2 [2,4,1,5,3,6] => 3 [2,4,1,5,6,3] => 2 [2,4,1,6,3,5] => 3 [2,4,1,6,5,3] => 2 [2,4,3,1,5,6] => 2 [2,4,3,1,6,5] => 2 [2,4,3,5,1,6] => 3 [2,4,3,5,6,1] => 2 [2,4,3,6,1,5] => 3 [2,4,3,6,5,1] => 2 [2,4,5,1,3,6] => 2 [2,4,5,1,6,3] => 2 [2,4,5,3,1,6] => 2 [2,4,5,3,6,1] => 2 [2,4,5,6,1,3] => 2 [2,4,5,6,3,1] => 1 [2,4,6,1,3,5] => 2 [2,4,6,1,5,3] => 2 [2,4,6,3,1,5] => 2 [2,4,6,3,5,1] => 2 [2,4,6,5,1,3] => 2 [2,4,6,5,3,1] => 1 [2,5,1,3,4,6] => 2 [2,5,1,3,6,4] => 2 [2,5,1,4,3,6] => 3 [2,5,1,4,6,3] => 2 [2,5,1,6,3,4] => 3 [2,5,1,6,4,3] => 2 [2,5,3,1,4,6] => 2 [2,5,3,1,6,4] => 2 [2,5,3,4,1,6] => 3 [2,5,3,4,6,1] => 2 [2,5,3,6,1,4] => 3 [2,5,3,6,4,1] => 2 [2,5,4,1,3,6] => 2 [2,5,4,1,6,3] => 2 [2,5,4,3,1,6] => 2 [2,5,4,3,6,1] => 2 [2,5,4,6,1,3] => 3 [2,5,4,6,3,1] => 2 [2,5,6,1,3,4] => 2 [2,5,6,1,4,3] => 2 [2,5,6,3,1,4] => 2 [2,5,6,3,4,1] => 2 [2,5,6,4,1,3] => 2 [2,5,6,4,3,1] => 1 [2,6,1,3,4,5] => 2 [2,6,1,3,5,4] => 2 [2,6,1,4,3,5] => 3 [2,6,1,4,5,3] => 2 [2,6,1,5,3,4] => 3 [2,6,1,5,4,3] => 2 [2,6,3,1,4,5] => 2 [2,6,3,1,5,4] => 2 [2,6,3,4,1,5] => 3 [2,6,3,4,5,1] => 2 [2,6,3,5,1,4] => 3 [2,6,3,5,4,1] => 2 [2,6,4,1,3,5] => 2 [2,6,4,1,5,3] => 2 [2,6,4,3,1,5] => 2 [2,6,4,3,5,1] => 2 [2,6,4,5,1,3] => 3 [2,6,4,5,3,1] => 2 [2,6,5,1,3,4] => 2 [2,6,5,1,4,3] => 2 [2,6,5,3,1,4] => 2 [2,6,5,3,4,1] => 2 [2,6,5,4,1,3] => 2 [2,6,5,4,3,1] => 1 [3,1,2,4,5,6] => 2 [3,1,2,4,6,5] => 2 [3,1,2,5,4,6] => 3 [3,1,2,5,6,4] => 2 [3,1,2,6,4,5] => 3 [3,1,2,6,5,4] => 2 [3,1,4,2,5,6] => 3 [3,1,4,2,6,5] => 3 [3,1,4,5,2,6] => 3 [3,1,4,5,6,2] => 2 [3,1,4,6,2,5] => 3 [3,1,4,6,5,2] => 2 [3,1,5,2,4,6] => 3 [3,1,5,2,6,4] => 3 [3,1,5,4,2,6] => 3 [3,1,5,4,6,2] => 3 [3,1,5,6,2,4] => 3 [3,1,5,6,4,2] => 2 [3,1,6,2,4,5] => 3 [3,1,6,2,5,4] => 3 [3,1,6,4,2,5] => 3 [3,1,6,4,5,2] => 3 [3,1,6,5,2,4] => 3 [3,1,6,5,4,2] => 2 [3,2,1,4,5,6] => 2 [3,2,1,4,6,5] => 2 [3,2,1,5,4,6] => 3 [3,2,1,5,6,4] => 2 [3,2,1,6,4,5] => 3 [3,2,1,6,5,4] => 2 [3,2,4,1,5,6] => 3 [3,2,4,1,6,5] => 3 [3,2,4,5,1,6] => 3 [3,2,4,5,6,1] => 2 [3,2,4,6,1,5] => 3 [3,2,4,6,5,1] => 2 [3,2,5,1,4,6] => 3 [3,2,5,1,6,4] => 3 [3,2,5,4,1,6] => 3 [3,2,5,4,6,1] => 3 [3,2,5,6,1,4] => 3 [3,2,5,6,4,1] => 2 [3,2,6,1,4,5] => 3 [3,2,6,1,5,4] => 3 [3,2,6,4,1,5] => 3 [3,2,6,4,5,1] => 3 [3,2,6,5,1,4] => 3 [3,2,6,5,4,1] => 2 [3,4,1,2,5,6] => 2 [3,4,1,2,6,5] => 2 [3,4,1,5,2,6] => 3 [3,4,1,5,6,2] => 2 [3,4,1,6,2,5] => 3 [3,4,1,6,5,2] => 2 [3,4,2,1,5,6] => 2 [3,4,2,1,6,5] => 2 [3,4,2,5,1,6] => 3 [3,4,2,5,6,1] => 2 [3,4,2,6,1,5] => 3 [3,4,2,6,5,1] => 2 [3,4,5,1,2,6] => 2 [3,4,5,1,6,2] => 2 [3,4,5,2,1,6] => 2 [3,4,5,2,6,1] => 2 [3,4,5,6,1,2] => 2 [3,4,5,6,2,1] => 1 [3,4,6,1,2,5] => 2 [3,4,6,1,5,2] => 2 [3,4,6,2,1,5] => 2 [3,4,6,2,5,1] => 2 [3,4,6,5,1,2] => 2 [3,4,6,5,2,1] => 1 [3,5,1,2,4,6] => 2 [3,5,1,2,6,4] => 2 [3,5,1,4,2,6] => 3 [3,5,1,4,6,2] => 2 [3,5,1,6,2,4] => 3 [3,5,1,6,4,2] => 2 [3,5,2,1,4,6] => 2 [3,5,2,1,6,4] => 2 [3,5,2,4,1,6] => 3 [3,5,2,4,6,1] => 2 [3,5,2,6,1,4] => 3 [3,5,2,6,4,1] => 2 [3,5,4,1,2,6] => 2 [3,5,4,1,6,2] => 2 [3,5,4,2,1,6] => 2 [3,5,4,2,6,1] => 2 [3,5,4,6,1,2] => 3 [3,5,4,6,2,1] => 2 [3,5,6,1,2,4] => 2 [3,5,6,1,4,2] => 2 [3,5,6,2,1,4] => 2 [3,5,6,2,4,1] => 2 [3,5,6,4,1,2] => 2 [3,5,6,4,2,1] => 1 [3,6,1,2,4,5] => 2 [3,6,1,2,5,4] => 2 [3,6,1,4,2,5] => 3 [3,6,1,4,5,2] => 2 [3,6,1,5,2,4] => 3 [3,6,1,5,4,2] => 2 [3,6,2,1,4,5] => 2 [3,6,2,1,5,4] => 2 [3,6,2,4,1,5] => 3 [3,6,2,4,5,1] => 2 [3,6,2,5,1,4] => 3 [3,6,2,5,4,1] => 2 [3,6,4,1,2,5] => 2 [3,6,4,1,5,2] => 2 [3,6,4,2,1,5] => 2 [3,6,4,2,5,1] => 2 [3,6,4,5,1,2] => 3 [3,6,4,5,2,1] => 2 [3,6,5,1,2,4] => 2 [3,6,5,1,4,2] => 2 [3,6,5,2,1,4] => 2 [3,6,5,2,4,1] => 2 [3,6,5,4,1,2] => 2 [3,6,5,4,2,1] => 1 [4,1,2,3,5,6] => 2 [4,1,2,3,6,5] => 2 [4,1,2,5,3,6] => 3 [4,1,2,5,6,3] => 2 [4,1,2,6,3,5] => 3 [4,1,2,6,5,3] => 2 [4,1,3,2,5,6] => 3 [4,1,3,2,6,5] => 3 [4,1,3,5,2,6] => 3 [4,1,3,5,6,2] => 2 [4,1,3,6,2,5] => 3 [4,1,3,6,5,2] => 2 [4,1,5,2,3,6] => 3 [4,1,5,2,6,3] => 3 [4,1,5,3,2,6] => 3 [4,1,5,3,6,2] => 3 [4,1,5,6,2,3] => 3 [4,1,5,6,3,2] => 2 [4,1,6,2,3,5] => 3 [4,1,6,2,5,3] => 3 [4,1,6,3,2,5] => 3 [4,1,6,3,5,2] => 3 [4,1,6,5,2,3] => 3 [4,1,6,5,3,2] => 2 [4,2,1,3,5,6] => 2 [4,2,1,3,6,5] => 2 [4,2,1,5,3,6] => 3 [4,2,1,5,6,3] => 2 [4,2,1,6,3,5] => 3 [4,2,1,6,5,3] => 2 [4,2,3,1,5,6] => 3 [4,2,3,1,6,5] => 3 [4,2,3,5,1,6] => 3 [4,2,3,5,6,1] => 2 [4,2,3,6,1,5] => 3 [4,2,3,6,5,1] => 2 [4,2,5,1,3,6] => 3 [4,2,5,1,6,3] => 3 [4,2,5,3,1,6] => 3 [4,2,5,3,6,1] => 3 [4,2,5,6,1,3] => 3 [4,2,5,6,3,1] => 2 [4,2,6,1,3,5] => 3 [4,2,6,1,5,3] => 3 [4,2,6,3,1,5] => 3 [4,2,6,3,5,1] => 3 [4,2,6,5,1,3] => 3 [4,2,6,5,3,1] => 2 [4,3,1,2,5,6] => 2 [4,3,1,2,6,5] => 2 [4,3,1,5,2,6] => 3 [4,3,1,5,6,2] => 2 [4,3,1,6,2,5] => 3 [4,3,1,6,5,2] => 2 [4,3,2,1,5,6] => 2 [4,3,2,1,6,5] => 2 [4,3,2,5,1,6] => 3 [4,3,2,5,6,1] => 2 [4,3,2,6,1,5] => 3 [4,3,2,6,5,1] => 2 [4,3,5,1,2,6] => 3 [4,3,5,1,6,2] => 3 [4,3,5,2,1,6] => 3 [4,3,5,2,6,1] => 3 [4,3,5,6,1,2] => 3 [4,3,5,6,2,1] => 2 [4,3,6,1,2,5] => 3 [4,3,6,1,5,2] => 3 [4,3,6,2,1,5] => 3 [4,3,6,2,5,1] => 3 [4,3,6,5,1,2] => 3 [4,3,6,5,2,1] => 2 [4,5,1,2,3,6] => 2 [4,5,1,2,6,3] => 2 [4,5,1,3,2,6] => 3 [4,5,1,3,6,2] => 2 [4,5,1,6,2,3] => 3 [4,5,1,6,3,2] => 2 [4,5,2,1,3,6] => 2 [4,5,2,1,6,3] => 2 [4,5,2,3,1,6] => 3 [4,5,2,3,6,1] => 2 [4,5,2,6,1,3] => 3 [4,5,2,6,3,1] => 2 [4,5,3,1,2,6] => 2 [4,5,3,1,6,2] => 2 [4,5,3,2,1,6] => 2 [4,5,3,2,6,1] => 2 [4,5,3,6,1,2] => 3 [4,5,3,6,2,1] => 2 [4,5,6,1,2,3] => 2 [4,5,6,1,3,2] => 2 [4,5,6,2,1,3] => 2 [4,5,6,2,3,1] => 2 [4,5,6,3,1,2] => 2 [4,5,6,3,2,1] => 1 [4,6,1,2,3,5] => 2 [4,6,1,2,5,3] => 2 [4,6,1,3,2,5] => 3 [4,6,1,3,5,2] => 2 [4,6,1,5,2,3] => 3 [4,6,1,5,3,2] => 2 [4,6,2,1,3,5] => 2 [4,6,2,1,5,3] => 2 [4,6,2,3,1,5] => 3 [4,6,2,3,5,1] => 2 [4,6,2,5,1,3] => 3 [4,6,2,5,3,1] => 2 [4,6,3,1,2,5] => 2 [4,6,3,1,5,2] => 2 [4,6,3,2,1,5] => 2 [4,6,3,2,5,1] => 2 [4,6,3,5,1,2] => 3 [4,6,3,5,2,1] => 2 [4,6,5,1,2,3] => 2 [4,6,5,1,3,2] => 2 [4,6,5,2,1,3] => 2 [4,6,5,2,3,1] => 2 [4,6,5,3,1,2] => 2 [4,6,5,3,2,1] => 1 [5,1,2,3,4,6] => 2 [5,1,2,3,6,4] => 2 [5,1,2,4,3,6] => 3 [5,1,2,4,6,3] => 2 [5,1,2,6,3,4] => 3 [5,1,2,6,4,3] => 2 [5,1,3,2,4,6] => 3 [5,1,3,2,6,4] => 3 [5,1,3,4,2,6] => 3 [5,1,3,4,6,2] => 2 [5,1,3,6,2,4] => 3 [5,1,3,6,4,2] => 2 [5,1,4,2,3,6] => 3 [5,1,4,2,6,3] => 3 [5,1,4,3,2,6] => 3 [5,1,4,3,6,2] => 3 [5,1,4,6,2,3] => 3 [5,1,4,6,3,2] => 2 [5,1,6,2,3,4] => 3 [5,1,6,2,4,3] => 3 [5,1,6,3,2,4] => 3 [5,1,6,3,4,2] => 3 [5,1,6,4,2,3] => 3 [5,1,6,4,3,2] => 2 [5,2,1,3,4,6] => 2 [5,2,1,3,6,4] => 2 [5,2,1,4,3,6] => 3 [5,2,1,4,6,3] => 2 [5,2,1,6,3,4] => 3 [5,2,1,6,4,3] => 2 [5,2,3,1,4,6] => 3 [5,2,3,1,6,4] => 3 [5,2,3,4,1,6] => 3 [5,2,3,4,6,1] => 2 [5,2,3,6,1,4] => 3 [5,2,3,6,4,1] => 2 [5,2,4,1,3,6] => 3 [5,2,4,1,6,3] => 3 [5,2,4,3,1,6] => 3 [5,2,4,3,6,1] => 3 [5,2,4,6,1,3] => 3 [5,2,4,6,3,1] => 2 [5,2,6,1,3,4] => 3 [5,2,6,1,4,3] => 3 [5,2,6,3,1,4] => 3 [5,2,6,3,4,1] => 3 [5,2,6,4,1,3] => 3 [5,2,6,4,3,1] => 2 [5,3,1,2,4,6] => 2 [5,3,1,2,6,4] => 2 [5,3,1,4,2,6] => 3 [5,3,1,4,6,2] => 2 [5,3,1,6,2,4] => 3 [5,3,1,6,4,2] => 2 [5,3,2,1,4,6] => 2 [5,3,2,1,6,4] => 2 [5,3,2,4,1,6] => 3 [5,3,2,4,6,1] => 2 [5,3,2,6,1,4] => 3 [5,3,2,6,4,1] => 2 [5,3,4,1,2,6] => 3 [5,3,4,1,6,2] => 3 [5,3,4,2,1,6] => 3 [5,3,4,2,6,1] => 3 [5,3,4,6,1,2] => 3 [5,3,4,6,2,1] => 2 [5,3,6,1,2,4] => 3 [5,3,6,1,4,2] => 3 [5,3,6,2,1,4] => 3 [5,3,6,2,4,1] => 3 [5,3,6,4,1,2] => 3 [5,3,6,4,2,1] => 2 [5,4,1,2,3,6] => 2 [5,4,1,2,6,3] => 2 [5,4,1,3,2,6] => 3 [5,4,1,3,6,2] => 2 [5,4,1,6,2,3] => 3 [5,4,1,6,3,2] => 2 [5,4,2,1,3,6] => 2 [5,4,2,1,6,3] => 2 [5,4,2,3,1,6] => 3 [5,4,2,3,6,1] => 2 [5,4,2,6,1,3] => 3 [5,4,2,6,3,1] => 2 [5,4,3,1,2,6] => 2 [5,4,3,1,6,2] => 2 [5,4,3,2,1,6] => 2 [5,4,3,2,6,1] => 2 [5,4,3,6,1,2] => 3 [5,4,3,6,2,1] => 2 [5,4,6,1,2,3] => 3 [5,4,6,1,3,2] => 3 [5,4,6,2,1,3] => 3 [5,4,6,2,3,1] => 3 [5,4,6,3,1,2] => 3 [5,4,6,3,2,1] => 2 [5,6,1,2,3,4] => 2 [5,6,1,2,4,3] => 2 [5,6,1,3,2,4] => 3 [5,6,1,3,4,2] => 2 [5,6,1,4,2,3] => 3 [5,6,1,4,3,2] => 2 [5,6,2,1,3,4] => 2 [5,6,2,1,4,3] => 2 [5,6,2,3,1,4] => 3 [5,6,2,3,4,1] => 2 [5,6,2,4,1,3] => 3 [5,6,2,4,3,1] => 2 [5,6,3,1,2,4] => 2 [5,6,3,1,4,2] => 2 [5,6,3,2,1,4] => 2 [5,6,3,2,4,1] => 2 [5,6,3,4,1,2] => 3 [5,6,3,4,2,1] => 2 [5,6,4,1,2,3] => 2 [5,6,4,1,3,2] => 2 [5,6,4,2,1,3] => 2 [5,6,4,2,3,1] => 2 [5,6,4,3,1,2] => 2 [5,6,4,3,2,1] => 1 [6,1,2,3,4,5] => 2 [6,1,2,3,5,4] => 2 [6,1,2,4,3,5] => 3 [6,1,2,4,5,3] => 2 [6,1,2,5,3,4] => 3 [6,1,2,5,4,3] => 2 [6,1,3,2,4,5] => 3 [6,1,3,2,5,4] => 3 [6,1,3,4,2,5] => 3 [6,1,3,4,5,2] => 2 [6,1,3,5,2,4] => 3 [6,1,3,5,4,2] => 2 [6,1,4,2,3,5] => 3 [6,1,4,2,5,3] => 3 [6,1,4,3,2,5] => 3 [6,1,4,3,5,2] => 3 [6,1,4,5,2,3] => 3 [6,1,4,5,3,2] => 2 [6,1,5,2,3,4] => 3 [6,1,5,2,4,3] => 3 [6,1,5,3,2,4] => 3 [6,1,5,3,4,2] => 3 [6,1,5,4,2,3] => 3 [6,1,5,4,3,2] => 2 [6,2,1,3,4,5] => 2 [6,2,1,3,5,4] => 2 [6,2,1,4,3,5] => 3 [6,2,1,4,5,3] => 2 [6,2,1,5,3,4] => 3 [6,2,1,5,4,3] => 2 [6,2,3,1,4,5] => 3 [6,2,3,1,5,4] => 3 [6,2,3,4,1,5] => 3 [6,2,3,4,5,1] => 2 [6,2,3,5,1,4] => 3 [6,2,3,5,4,1] => 2 [6,2,4,1,3,5] => 3 [6,2,4,1,5,3] => 3 [6,2,4,3,1,5] => 3 [6,2,4,3,5,1] => 3 [6,2,4,5,1,3] => 3 [6,2,4,5,3,1] => 2 [6,2,5,1,3,4] => 3 [6,2,5,1,4,3] => 3 [6,2,5,3,1,4] => 3 [6,2,5,3,4,1] => 3 [6,2,5,4,1,3] => 3 [6,2,5,4,3,1] => 2 [6,3,1,2,4,5] => 2 [6,3,1,2,5,4] => 2 [6,3,1,4,2,5] => 3 [6,3,1,4,5,2] => 2 [6,3,1,5,2,4] => 3 [6,3,1,5,4,2] => 2 [6,3,2,1,4,5] => 2 [6,3,2,1,5,4] => 2 [6,3,2,4,1,5] => 3 [6,3,2,4,5,1] => 2 [6,3,2,5,1,4] => 3 [6,3,2,5,4,1] => 2 [6,3,4,1,2,5] => 3 [6,3,4,1,5,2] => 3 [6,3,4,2,1,5] => 3 [6,3,4,2,5,1] => 3 [6,3,4,5,1,2] => 3 [6,3,4,5,2,1] => 2 [6,3,5,1,2,4] => 3 [6,3,5,1,4,2] => 3 [6,3,5,2,1,4] => 3 [6,3,5,2,4,1] => 3 [6,3,5,4,1,2] => 3 [6,3,5,4,2,1] => 2 [6,4,1,2,3,5] => 2 [6,4,1,2,5,3] => 2 [6,4,1,3,2,5] => 3 [6,4,1,3,5,2] => 2 [6,4,1,5,2,3] => 3 [6,4,1,5,3,2] => 2 [6,4,2,1,3,5] => 2 [6,4,2,1,5,3] => 2 [6,4,2,3,1,5] => 3 [6,4,2,3,5,1] => 2 [6,4,2,5,1,3] => 3 [6,4,2,5,3,1] => 2 [6,4,3,1,2,5] => 2 [6,4,3,1,5,2] => 2 [6,4,3,2,1,5] => 2 [6,4,3,2,5,1] => 2 [6,4,3,5,1,2] => 3 [6,4,3,5,2,1] => 2 [6,4,5,1,2,3] => 3 [6,4,5,1,3,2] => 3 [6,4,5,2,1,3] => 3 [6,4,5,2,3,1] => 3 [6,4,5,3,1,2] => 3 [6,4,5,3,2,1] => 2 [6,5,1,2,3,4] => 2 [6,5,1,2,4,3] => 2 [6,5,1,3,2,4] => 3 [6,5,1,3,4,2] => 2 [6,5,1,4,2,3] => 3 [6,5,1,4,3,2] => 2 [6,5,2,1,3,4] => 2 [6,5,2,1,4,3] => 2 [6,5,2,3,1,4] => 3 [6,5,2,3,4,1] => 2 [6,5,2,4,1,3] => 3 [6,5,2,4,3,1] => 2 [6,5,3,1,2,4] => 2 [6,5,3,1,4,2] => 2 [6,5,3,2,1,4] => 2 [6,5,3,2,4,1] => 2 [6,5,3,4,1,2] => 3 [6,5,3,4,2,1] => 2 [6,5,4,1,2,3] => 2 [6,5,4,1,3,2] => 2 [6,5,4,2,1,3] => 2 [6,5,4,2,3,1] => 2 [6,5,4,3,1,2] => 2 [6,5,4,3,2,1] => 1 ----------------------------------------------------------------------------- Created: Jun 13, 2013 at 16:10 by Chris Berg ----------------------------------------------------------------------------- Last Updated: Jun 05, 2017 at 10:07 by Christian Stump