***************************************************************************** * 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: St000018 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The [[/Permutations/Inversions|number of inversions]] of a permutation. This equals the minimal number of simple transpositions $(i,i+1)$ needed to write $\pi$. Thus, it is also the Coxeter length of $\pi$. ----------------------------------------------------------------------------- References: [1] 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]] [2] List of permutations of 1,2,3,...,n for n=1,2,3,..., in lexicographic order. [[OEIS:A030298]] [3] Array of digit sums of factorial representation of numbers 0,1,...,n!-1 for n>=1. [[OEIS:A139365]] ----------------------------------------------------------------------------- Code: def statistic(x): return x.number_of_inversions() ----------------------------------------------------------------------------- Statistic values: [] => 0 [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] => 3 [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] => 3 [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] => 4 [3,1,2,4] => 2 [3,1,4,2] => 3 [3,2,1,4] => 3 [3,2,4,1] => 4 [3,4,1,2] => 4 [3,4,2,1] => 5 [4,1,2,3] => 3 [4,1,3,2] => 4 [4,2,1,3] => 4 [4,2,3,1] => 5 [4,3,1,2] => 5 [4,3,2,1] => 6 [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] => 3 [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] => 4 [1,4,2,3,5] => 2 [1,4,2,5,3] => 3 [1,4,3,2,5] => 3 [1,4,3,5,2] => 4 [1,4,5,2,3] => 4 [1,4,5,3,2] => 5 [1,5,2,3,4] => 3 [1,5,2,4,3] => 4 [1,5,3,2,4] => 4 [1,5,3,4,2] => 5 [1,5,4,2,3] => 5 [1,5,4,3,2] => 6 [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] => 4 [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] => 5 [2,4,1,3,5] => 3 [2,4,1,5,3] => 4 [2,4,3,1,5] => 4 [2,4,3,5,1] => 5 [2,4,5,1,3] => 5 [2,4,5,3,1] => 6 [2,5,1,3,4] => 4 [2,5,1,4,3] => 5 [2,5,3,1,4] => 5 [2,5,3,4,1] => 6 [2,5,4,1,3] => 6 [2,5,4,3,1] => 7 [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] => 5 [3,2,1,4,5] => 3 [3,2,1,5,4] => 4 [3,2,4,1,5] => 4 [3,2,4,5,1] => 5 [3,2,5,1,4] => 5 [3,2,5,4,1] => 6 [3,4,1,2,5] => 4 [3,4,1,5,2] => 5 [3,4,2,1,5] => 5 [3,4,2,5,1] => 6 [3,4,5,1,2] => 6 [3,4,5,2,1] => 7 [3,5,1,2,4] => 5 [3,5,1,4,2] => 6 [3,5,2,1,4] => 6 [3,5,2,4,1] => 7 [3,5,4,1,2] => 7 [3,5,4,2,1] => 8 [4,1,2,3,5] => 3 [4,1,2,5,3] => 4 [4,1,3,2,5] => 4 [4,1,3,5,2] => 5 [4,1,5,2,3] => 5 [4,1,5,3,2] => 6 [4,2,1,3,5] => 4 [4,2,1,5,3] => 5 [4,2,3,1,5] => 5 [4,2,3,5,1] => 6 [4,2,5,1,3] => 6 [4,2,5,3,1] => 7 [4,3,1,2,5] => 5 [4,3,1,5,2] => 6 [4,3,2,1,5] => 6 [4,3,2,5,1] => 7 [4,3,5,1,2] => 7 [4,3,5,2,1] => 8 [4,5,1,2,3] => 6 [4,5,1,3,2] => 7 [4,5,2,1,3] => 7 [4,5,2,3,1] => 8 [4,5,3,1,2] => 8 [4,5,3,2,1] => 9 [5,1,2,3,4] => 4 [5,1,2,4,3] => 5 [5,1,3,2,4] => 5 [5,1,3,4,2] => 6 [5,1,4,2,3] => 6 [5,1,4,3,2] => 7 [5,2,1,3,4] => 5 [5,2,1,4,3] => 6 [5,2,3,1,4] => 6 [5,2,3,4,1] => 7 [5,2,4,1,3] => 7 [5,2,4,3,1] => 8 [5,3,1,2,4] => 6 [5,3,1,4,2] => 7 [5,3,2,1,4] => 7 [5,3,2,4,1] => 8 [5,3,4,1,2] => 8 [5,3,4,2,1] => 9 [5,4,1,2,3] => 7 [5,4,1,3,2] => 8 [5,4,2,1,3] => 8 [5,4,2,3,1] => 9 [5,4,3,1,2] => 9 [5,4,3,2,1] => 10 [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] => 3 [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] => 4 [1,2,5,3,4,6] => 2 [1,2,5,3,6,4] => 3 [1,2,5,4,3,6] => 3 [1,2,5,4,6,3] => 4 [1,2,5,6,3,4] => 4 [1,2,5,6,4,3] => 5 [1,2,6,3,4,5] => 3 [1,2,6,3,5,4] => 4 [1,2,6,4,3,5] => 4 [1,2,6,4,5,3] => 5 [1,2,6,5,3,4] => 5 [1,2,6,5,4,3] => 6 [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] => 4 [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] => 5 [1,3,5,2,4,6] => 3 [1,3,5,2,6,4] => 4 [1,3,5,4,2,6] => 4 [1,3,5,4,6,2] => 5 [1,3,5,6,2,4] => 5 [1,3,5,6,4,2] => 6 [1,3,6,2,4,5] => 4 [1,3,6,2,5,4] => 5 [1,3,6,4,2,5] => 5 [1,3,6,4,5,2] => 6 [1,3,6,5,2,4] => 6 [1,3,6,5,4,2] => 7 [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] => 5 [1,4,3,2,5,6] => 3 [1,4,3,2,6,5] => 4 [1,4,3,5,2,6] => 4 [1,4,3,5,6,2] => 5 [1,4,3,6,2,5] => 5 [1,4,3,6,5,2] => 6 [1,4,5,2,3,6] => 4 [1,4,5,2,6,3] => 5 [1,4,5,3,2,6] => 5 [1,4,5,3,6,2] => 6 [1,4,5,6,2,3] => 6 [1,4,5,6,3,2] => 7 [1,4,6,2,3,5] => 5 [1,4,6,2,5,3] => 6 [1,4,6,3,2,5] => 6 [1,4,6,3,5,2] => 7 [1,4,6,5,2,3] => 7 [1,4,6,5,3,2] => 8 [1,5,2,3,4,6] => 3 [1,5,2,3,6,4] => 4 [1,5,2,4,3,6] => 4 [1,5,2,4,6,3] => 5 [1,5,2,6,3,4] => 5 [1,5,2,6,4,3] => 6 [1,5,3,2,4,6] => 4 [1,5,3,2,6,4] => 5 [1,5,3,4,2,6] => 5 [1,5,3,4,6,2] => 6 [1,5,3,6,2,4] => 6 [1,5,3,6,4,2] => 7 [1,5,4,2,3,6] => 5 [1,5,4,2,6,3] => 6 [1,5,4,3,2,6] => 6 [1,5,4,3,6,2] => 7 [1,5,4,6,2,3] => 7 [1,5,4,6,3,2] => 8 [1,5,6,2,3,4] => 6 [1,5,6,2,4,3] => 7 [1,5,6,3,2,4] => 7 [1,5,6,3,4,2] => 8 [1,5,6,4,2,3] => 8 [1,5,6,4,3,2] => 9 [1,6,2,3,4,5] => 4 [1,6,2,3,5,4] => 5 [1,6,2,4,3,5] => 5 [1,6,2,4,5,3] => 6 [1,6,2,5,3,4] => 6 [1,6,2,5,4,3] => 7 [1,6,3,2,4,5] => 5 [1,6,3,2,5,4] => 6 [1,6,3,4,2,5] => 6 [1,6,3,4,5,2] => 7 [1,6,3,5,2,4] => 7 [1,6,3,5,4,2] => 8 [1,6,4,2,3,5] => 6 [1,6,4,2,5,3] => 7 [1,6,4,3,2,5] => 7 [1,6,4,3,5,2] => 8 [1,6,4,5,2,3] => 8 [1,6,4,5,3,2] => 9 [1,6,5,2,3,4] => 7 [1,6,5,2,4,3] => 8 [1,6,5,3,2,4] => 8 [1,6,5,3,4,2] => 9 [1,6,5,4,2,3] => 9 [1,6,5,4,3,2] => 10 [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] => 4 [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] => 5 [2,1,5,3,4,6] => 3 [2,1,5,3,6,4] => 4 [2,1,5,4,3,6] => 4 [2,1,5,4,6,3] => 5 [2,1,5,6,3,4] => 5 [2,1,5,6,4,3] => 6 [2,1,6,3,4,5] => 4 [2,1,6,3,5,4] => 5 [2,1,6,4,3,5] => 5 [2,1,6,4,5,3] => 6 [2,1,6,5,3,4] => 6 [2,1,6,5,4,3] => 7 [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] => 5 [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] => 6 [2,3,5,1,4,6] => 4 [2,3,5,1,6,4] => 5 [2,3,5,4,1,6] => 5 [2,3,5,4,6,1] => 6 [2,3,5,6,1,4] => 6 [2,3,5,6,4,1] => 7 [2,3,6,1,4,5] => 5 [2,3,6,1,5,4] => 6 [2,3,6,4,1,5] => 6 [2,3,6,4,5,1] => 7 [2,3,6,5,1,4] => 7 [2,3,6,5,4,1] => 8 [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] => 6 [2,4,3,1,5,6] => 4 [2,4,3,1,6,5] => 5 [2,4,3,5,1,6] => 5 [2,4,3,5,6,1] => 6 [2,4,3,6,1,5] => 6 [2,4,3,6,5,1] => 7 [2,4,5,1,3,6] => 5 [2,4,5,1,6,3] => 6 [2,4,5,3,1,6] => 6 [2,4,5,3,6,1] => 7 [2,4,5,6,1,3] => 7 [2,4,5,6,3,1] => 8 [2,4,6,1,3,5] => 6 [2,4,6,1,5,3] => 7 [2,4,6,3,1,5] => 7 [2,4,6,3,5,1] => 8 [2,4,6,5,1,3] => 8 [2,4,6,5,3,1] => 9 [2,5,1,3,4,6] => 4 [2,5,1,3,6,4] => 5 [2,5,1,4,3,6] => 5 [2,5,1,4,6,3] => 6 [2,5,1,6,3,4] => 6 [2,5,1,6,4,3] => 7 [2,5,3,1,4,6] => 5 [2,5,3,1,6,4] => 6 [2,5,3,4,1,6] => 6 [2,5,3,4,6,1] => 7 [2,5,3,6,1,4] => 7 [2,5,3,6,4,1] => 8 [2,5,4,1,3,6] => 6 [2,5,4,1,6,3] => 7 [2,5,4,3,1,6] => 7 [2,5,4,3,6,1] => 8 [2,5,4,6,1,3] => 8 [2,5,4,6,3,1] => 9 [2,5,6,1,3,4] => 7 [2,5,6,1,4,3] => 8 [2,5,6,3,1,4] => 8 [2,5,6,3,4,1] => 9 [2,5,6,4,1,3] => 9 [2,5,6,4,3,1] => 10 [2,6,1,3,4,5] => 5 [2,6,1,3,5,4] => 6 [2,6,1,4,3,5] => 6 [2,6,1,4,5,3] => 7 [2,6,1,5,3,4] => 7 [2,6,1,5,4,3] => 8 [2,6,3,1,4,5] => 6 [2,6,3,1,5,4] => 7 [2,6,3,4,1,5] => 7 [2,6,3,4,5,1] => 8 [2,6,3,5,1,4] => 8 [2,6,3,5,4,1] => 9 [2,6,4,1,3,5] => 7 [2,6,4,1,5,3] => 8 [2,6,4,3,1,5] => 8 [2,6,4,3,5,1] => 9 [2,6,4,5,1,3] => 9 [2,6,4,5,3,1] => 10 [2,6,5,1,3,4] => 8 [2,6,5,1,4,3] => 9 [2,6,5,3,1,4] => 9 [2,6,5,3,4,1] => 10 [2,6,5,4,1,3] => 10 [2,6,5,4,3,1] => 11 [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] => 5 [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] => 6 [3,1,5,2,4,6] => 4 [3,1,5,2,6,4] => 5 [3,1,5,4,2,6] => 5 [3,1,5,4,6,2] => 6 [3,1,5,6,2,4] => 6 [3,1,5,6,4,2] => 7 [3,1,6,2,4,5] => 5 [3,1,6,2,5,4] => 6 [3,1,6,4,2,5] => 6 [3,1,6,4,5,2] => 7 [3,1,6,5,2,4] => 7 [3,1,6,5,4,2] => 8 [3,2,1,4,5,6] => 3 [3,2,1,4,6,5] => 4 [3,2,1,5,4,6] => 4 [3,2,1,5,6,4] => 5 [3,2,1,6,4,5] => 5 [3,2,1,6,5,4] => 6 [3,2,4,1,5,6] => 4 [3,2,4,1,6,5] => 5 [3,2,4,5,1,6] => 5 [3,2,4,5,6,1] => 6 [3,2,4,6,1,5] => 6 [3,2,4,6,5,1] => 7 [3,2,5,1,4,6] => 5 [3,2,5,1,6,4] => 6 [3,2,5,4,1,6] => 6 [3,2,5,4,6,1] => 7 [3,2,5,6,1,4] => 7 [3,2,5,6,4,1] => 8 [3,2,6,1,4,5] => 6 [3,2,6,1,5,4] => 7 [3,2,6,4,1,5] => 7 [3,2,6,4,5,1] => 8 [3,2,6,5,1,4] => 8 [3,2,6,5,4,1] => 9 [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] => 7 [3,4,2,1,5,6] => 5 [3,4,2,1,6,5] => 6 [3,4,2,5,1,6] => 6 [3,4,2,5,6,1] => 7 [3,4,2,6,1,5] => 7 [3,4,2,6,5,1] => 8 [3,4,5,1,2,6] => 6 [3,4,5,1,6,2] => 7 [3,4,5,2,1,6] => 7 [3,4,5,2,6,1] => 8 [3,4,5,6,1,2] => 8 [3,4,5,6,2,1] => 9 [3,4,6,1,2,5] => 7 [3,4,6,1,5,2] => 8 [3,4,6,2,1,5] => 8 [3,4,6,2,5,1] => 9 [3,4,6,5,1,2] => 9 [3,4,6,5,2,1] => 10 [3,5,1,2,4,6] => 5 [3,5,1,2,6,4] => 6 [3,5,1,4,2,6] => 6 [3,5,1,4,6,2] => 7 [3,5,1,6,2,4] => 7 [3,5,1,6,4,2] => 8 [3,5,2,1,4,6] => 6 [3,5,2,1,6,4] => 7 [3,5,2,4,1,6] => 7 [3,5,2,4,6,1] => 8 [3,5,2,6,1,4] => 8 [3,5,2,6,4,1] => 9 [3,5,4,1,2,6] => 7 [3,5,4,1,6,2] => 8 [3,5,4,2,1,6] => 8 [3,5,4,2,6,1] => 9 [3,5,4,6,1,2] => 9 [3,5,4,6,2,1] => 10 [3,5,6,1,2,4] => 8 [3,5,6,1,4,2] => 9 [3,5,6,2,1,4] => 9 [3,5,6,2,4,1] => 10 [3,5,6,4,1,2] => 10 [3,5,6,4,2,1] => 11 [3,6,1,2,4,5] => 6 [3,6,1,2,5,4] => 7 [3,6,1,4,2,5] => 7 [3,6,1,4,5,2] => 8 [3,6,1,5,2,4] => 8 [3,6,1,5,4,2] => 9 [3,6,2,1,4,5] => 7 [3,6,2,1,5,4] => 8 [3,6,2,4,1,5] => 8 [3,6,2,4,5,1] => 9 [3,6,2,5,1,4] => 9 [3,6,2,5,4,1] => 10 [3,6,4,1,2,5] => 8 [3,6,4,1,5,2] => 9 [3,6,4,2,1,5] => 9 [3,6,4,2,5,1] => 10 [3,6,4,5,1,2] => 10 [3,6,4,5,2,1] => 11 [3,6,5,1,2,4] => 9 [3,6,5,1,4,2] => 10 [3,6,5,2,1,4] => 10 [3,6,5,2,4,1] => 11 [3,6,5,4,1,2] => 11 [3,6,5,4,2,1] => 12 [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] => 6 [4,1,3,2,5,6] => 4 [4,1,3,2,6,5] => 5 [4,1,3,5,2,6] => 5 [4,1,3,5,6,2] => 6 [4,1,3,6,2,5] => 6 [4,1,3,6,5,2] => 7 [4,1,5,2,3,6] => 5 [4,1,5,2,6,3] => 6 [4,1,5,3,2,6] => 6 [4,1,5,3,6,2] => 7 [4,1,5,6,2,3] => 7 [4,1,5,6,3,2] => 8 [4,1,6,2,3,5] => 6 [4,1,6,2,5,3] => 7 [4,1,6,3,2,5] => 7 [4,1,6,3,5,2] => 8 [4,1,6,5,2,3] => 8 [4,1,6,5,3,2] => 9 [4,2,1,3,5,6] => 4 [4,2,1,3,6,5] => 5 [4,2,1,5,3,6] => 5 [4,2,1,5,6,3] => 6 [4,2,1,6,3,5] => 6 [4,2,1,6,5,3] => 7 [4,2,3,1,5,6] => 5 [4,2,3,1,6,5] => 6 [4,2,3,5,1,6] => 6 [4,2,3,5,6,1] => 7 [4,2,3,6,1,5] => 7 [4,2,3,6,5,1] => 8 [4,2,5,1,3,6] => 6 [4,2,5,1,6,3] => 7 [4,2,5,3,1,6] => 7 [4,2,5,3,6,1] => 8 [4,2,5,6,1,3] => 8 [4,2,5,6,3,1] => 9 [4,2,6,1,3,5] => 7 [4,2,6,1,5,3] => 8 [4,2,6,3,1,5] => 8 [4,2,6,3,5,1] => 9 [4,2,6,5,1,3] => 9 [4,2,6,5,3,1] => 10 [4,3,1,2,5,6] => 5 [4,3,1,2,6,5] => 6 [4,3,1,5,2,6] => 6 [4,3,1,5,6,2] => 7 [4,3,1,6,2,5] => 7 [4,3,1,6,5,2] => 8 [4,3,2,1,5,6] => 6 [4,3,2,1,6,5] => 7 [4,3,2,5,1,6] => 7 [4,3,2,5,6,1] => 8 [4,3,2,6,1,5] => 8 [4,3,2,6,5,1] => 9 [4,3,5,1,2,6] => 7 [4,3,5,1,6,2] => 8 [4,3,5,2,1,6] => 8 [4,3,5,2,6,1] => 9 [4,3,5,6,1,2] => 9 [4,3,5,6,2,1] => 10 [4,3,6,1,2,5] => 8 [4,3,6,1,5,2] => 9 [4,3,6,2,1,5] => 9 [4,3,6,2,5,1] => 10 [4,3,6,5,1,2] => 10 [4,3,6,5,2,1] => 11 [4,5,1,2,3,6] => 6 [4,5,1,2,6,3] => 7 [4,5,1,3,2,6] => 7 [4,5,1,3,6,2] => 8 [4,5,1,6,2,3] => 8 [4,5,1,6,3,2] => 9 [4,5,2,1,3,6] => 7 [4,5,2,1,6,3] => 8 [4,5,2,3,1,6] => 8 [4,5,2,3,6,1] => 9 [4,5,2,6,1,3] => 9 [4,5,2,6,3,1] => 10 [4,5,3,1,2,6] => 8 [4,5,3,1,6,2] => 9 [4,5,3,2,1,6] => 9 [4,5,3,2,6,1] => 10 [4,5,3,6,1,2] => 10 [4,5,3,6,2,1] => 11 [4,5,6,1,2,3] => 9 [4,5,6,1,3,2] => 10 [4,5,6,2,1,3] => 10 [4,5,6,2,3,1] => 11 [4,5,6,3,1,2] => 11 [4,5,6,3,2,1] => 12 [4,6,1,2,3,5] => 7 [4,6,1,2,5,3] => 8 [4,6,1,3,2,5] => 8 [4,6,1,3,5,2] => 9 [4,6,1,5,2,3] => 9 [4,6,1,5,3,2] => 10 [4,6,2,1,3,5] => 8 [4,6,2,1,5,3] => 9 [4,6,2,3,1,5] => 9 [4,6,2,3,5,1] => 10 [4,6,2,5,1,3] => 10 [4,6,2,5,3,1] => 11 [4,6,3,1,2,5] => 9 [4,6,3,1,5,2] => 10 [4,6,3,2,1,5] => 10 [4,6,3,2,5,1] => 11 [4,6,3,5,1,2] => 11 [4,6,3,5,2,1] => 12 [4,6,5,1,2,3] => 10 [4,6,5,1,3,2] => 11 [4,6,5,2,1,3] => 11 [4,6,5,2,3,1] => 12 [4,6,5,3,1,2] => 12 [4,6,5,3,2,1] => 13 [5,1,2,3,4,6] => 4 [5,1,2,3,6,4] => 5 [5,1,2,4,3,6] => 5 [5,1,2,4,6,3] => 6 [5,1,2,6,3,4] => 6 [5,1,2,6,4,3] => 7 [5,1,3,2,4,6] => 5 [5,1,3,2,6,4] => 6 [5,1,3,4,2,6] => 6 [5,1,3,4,6,2] => 7 [5,1,3,6,2,4] => 7 [5,1,3,6,4,2] => 8 [5,1,4,2,3,6] => 6 [5,1,4,2,6,3] => 7 [5,1,4,3,2,6] => 7 [5,1,4,3,6,2] => 8 [5,1,4,6,2,3] => 8 [5,1,4,6,3,2] => 9 [5,1,6,2,3,4] => 7 [5,1,6,2,4,3] => 8 [5,1,6,3,2,4] => 8 [5,1,6,3,4,2] => 9 [5,1,6,4,2,3] => 9 [5,1,6,4,3,2] => 10 [5,2,1,3,4,6] => 5 [5,2,1,3,6,4] => 6 [5,2,1,4,3,6] => 6 [5,2,1,4,6,3] => 7 [5,2,1,6,3,4] => 7 [5,2,1,6,4,3] => 8 [5,2,3,1,4,6] => 6 [5,2,3,1,6,4] => 7 [5,2,3,4,1,6] => 7 [5,2,3,4,6,1] => 8 [5,2,3,6,1,4] => 8 [5,2,3,6,4,1] => 9 [5,2,4,1,3,6] => 7 [5,2,4,1,6,3] => 8 [5,2,4,3,1,6] => 8 [5,2,4,3,6,1] => 9 [5,2,4,6,1,3] => 9 [5,2,4,6,3,1] => 10 [5,2,6,1,3,4] => 8 [5,2,6,1,4,3] => 9 [5,2,6,3,1,4] => 9 [5,2,6,3,4,1] => 10 [5,2,6,4,1,3] => 10 [5,2,6,4,3,1] => 11 [5,3,1,2,4,6] => 6 [5,3,1,2,6,4] => 7 [5,3,1,4,2,6] => 7 [5,3,1,4,6,2] => 8 [5,3,1,6,2,4] => 8 [5,3,1,6,4,2] => 9 [5,3,2,1,4,6] => 7 [5,3,2,1,6,4] => 8 [5,3,2,4,1,6] => 8 [5,3,2,4,6,1] => 9 [5,3,2,6,1,4] => 9 [5,3,2,6,4,1] => 10 [5,3,4,1,2,6] => 8 [5,3,4,1,6,2] => 9 [5,3,4,2,1,6] => 9 [5,3,4,2,6,1] => 10 [5,3,4,6,1,2] => 10 [5,3,4,6,2,1] => 11 [5,3,6,1,2,4] => 9 [5,3,6,1,4,2] => 10 [5,3,6,2,1,4] => 10 [5,3,6,2,4,1] => 11 [5,3,6,4,1,2] => 11 [5,3,6,4,2,1] => 12 [5,4,1,2,3,6] => 7 [5,4,1,2,6,3] => 8 [5,4,1,3,2,6] => 8 [5,4,1,3,6,2] => 9 [5,4,1,6,2,3] => 9 [5,4,1,6,3,2] => 10 [5,4,2,1,3,6] => 8 [5,4,2,1,6,3] => 9 [5,4,2,3,1,6] => 9 [5,4,2,3,6,1] => 10 [5,4,2,6,1,3] => 10 [5,4,2,6,3,1] => 11 [5,4,3,1,2,6] => 9 [5,4,3,1,6,2] => 10 [5,4,3,2,1,6] => 10 [5,4,3,2,6,1] => 11 [5,4,3,6,1,2] => 11 [5,4,3,6,2,1] => 12 [5,4,6,1,2,3] => 10 [5,4,6,1,3,2] => 11 [5,4,6,2,1,3] => 11 [5,4,6,2,3,1] => 12 [5,4,6,3,1,2] => 12 [5,4,6,3,2,1] => 13 [5,6,1,2,3,4] => 8 [5,6,1,2,4,3] => 9 [5,6,1,3,2,4] => 9 [5,6,1,3,4,2] => 10 [5,6,1,4,2,3] => 10 [5,6,1,4,3,2] => 11 [5,6,2,1,3,4] => 9 [5,6,2,1,4,3] => 10 [5,6,2,3,1,4] => 10 [5,6,2,3,4,1] => 11 [5,6,2,4,1,3] => 11 [5,6,2,4,3,1] => 12 [5,6,3,1,2,4] => 10 [5,6,3,1,4,2] => 11 [5,6,3,2,1,4] => 11 [5,6,3,2,4,1] => 12 [5,6,3,4,1,2] => 12 [5,6,3,4,2,1] => 13 [5,6,4,1,2,3] => 11 [5,6,4,1,3,2] => 12 [5,6,4,2,1,3] => 12 [5,6,4,2,3,1] => 13 [5,6,4,3,1,2] => 13 [5,6,4,3,2,1] => 14 [6,1,2,3,4,5] => 5 [6,1,2,3,5,4] => 6 [6,1,2,4,3,5] => 6 [6,1,2,4,5,3] => 7 [6,1,2,5,3,4] => 7 [6,1,2,5,4,3] => 8 [6,1,3,2,4,5] => 6 [6,1,3,2,5,4] => 7 [6,1,3,4,2,5] => 7 [6,1,3,4,5,2] => 8 [6,1,3,5,2,4] => 8 [6,1,3,5,4,2] => 9 [6,1,4,2,3,5] => 7 [6,1,4,2,5,3] => 8 [6,1,4,3,2,5] => 8 [6,1,4,3,5,2] => 9 [6,1,4,5,2,3] => 9 [6,1,4,5,3,2] => 10 [6,1,5,2,3,4] => 8 [6,1,5,2,4,3] => 9 [6,1,5,3,2,4] => 9 [6,1,5,3,4,2] => 10 [6,1,5,4,2,3] => 10 [6,1,5,4,3,2] => 11 [6,2,1,3,4,5] => 6 [6,2,1,3,5,4] => 7 [6,2,1,4,3,5] => 7 [6,2,1,4,5,3] => 8 [6,2,1,5,3,4] => 8 [6,2,1,5,4,3] => 9 [6,2,3,1,4,5] => 7 [6,2,3,1,5,4] => 8 [6,2,3,4,1,5] => 8 [6,2,3,4,5,1] => 9 [6,2,3,5,1,4] => 9 [6,2,3,5,4,1] => 10 [6,2,4,1,3,5] => 8 [6,2,4,1,5,3] => 9 [6,2,4,3,1,5] => 9 [6,2,4,3,5,1] => 10 [6,2,4,5,1,3] => 10 [6,2,4,5,3,1] => 11 [6,2,5,1,3,4] => 9 [6,2,5,1,4,3] => 10 [6,2,5,3,1,4] => 10 [6,2,5,3,4,1] => 11 [6,2,5,4,1,3] => 11 [6,2,5,4,3,1] => 12 [6,3,1,2,4,5] => 7 [6,3,1,2,5,4] => 8 [6,3,1,4,2,5] => 8 [6,3,1,4,5,2] => 9 [6,3,1,5,2,4] => 9 [6,3,1,5,4,2] => 10 [6,3,2,1,4,5] => 8 [6,3,2,1,5,4] => 9 [6,3,2,4,1,5] => 9 [6,3,2,4,5,1] => 10 [6,3,2,5,1,4] => 10 [6,3,2,5,4,1] => 11 [6,3,4,1,2,5] => 9 [6,3,4,1,5,2] => 10 [6,3,4,2,1,5] => 10 [6,3,4,2,5,1] => 11 [6,3,4,5,1,2] => 11 [6,3,4,5,2,1] => 12 [6,3,5,1,2,4] => 10 [6,3,5,1,4,2] => 11 [6,3,5,2,1,4] => 11 [6,3,5,2,4,1] => 12 [6,3,5,4,1,2] => 12 [6,3,5,4,2,1] => 13 [6,4,1,2,3,5] => 8 [6,4,1,2,5,3] => 9 [6,4,1,3,2,5] => 9 [6,4,1,3,5,2] => 10 [6,4,1,5,2,3] => 10 [6,4,1,5,3,2] => 11 [6,4,2,1,3,5] => 9 [6,4,2,1,5,3] => 10 [6,4,2,3,1,5] => 10 [6,4,2,3,5,1] => 11 [6,4,2,5,1,3] => 11 [6,4,2,5,3,1] => 12 [6,4,3,1,2,5] => 10 [6,4,3,1,5,2] => 11 [6,4,3,2,1,5] => 11 [6,4,3,2,5,1] => 12 [6,4,3,5,1,2] => 12 [6,4,3,5,2,1] => 13 [6,4,5,1,2,3] => 11 [6,4,5,1,3,2] => 12 [6,4,5,2,1,3] => 12 [6,4,5,2,3,1] => 13 [6,4,5,3,1,2] => 13 [6,4,5,3,2,1] => 14 [6,5,1,2,3,4] => 9 [6,5,1,2,4,3] => 10 [6,5,1,3,2,4] => 10 [6,5,1,3,4,2] => 11 [6,5,1,4,2,3] => 11 [6,5,1,4,3,2] => 12 [6,5,2,1,3,4] => 10 [6,5,2,1,4,3] => 11 [6,5,2,3,1,4] => 11 [6,5,2,3,4,1] => 12 [6,5,2,4,1,3] => 12 [6,5,2,4,3,1] => 13 [6,5,3,1,2,4] => 11 [6,5,3,1,4,2] => 12 [6,5,3,2,1,4] => 12 [6,5,3,2,4,1] => 13 [6,5,3,4,1,2] => 13 [6,5,3,4,2,1] => 14 [6,5,4,1,2,3] => 12 [6,5,4,1,3,2] => 13 [6,5,4,2,1,3] => 13 [6,5,4,2,3,1] => 14 [6,5,4,3,1,2] => 14 [6,5,4,3,2,1] => 15 ----------------------------------------------------------------------------- Created: Sep 27, 2011 at 23:29 by Christian Stump ----------------------------------------------------------------------------- Last Updated: May 10, 2019 at 17:10 by Henning Ulfarsson