***************************************************************************** * 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: St000030 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The sum of the descent differences of a permutations. This statistic is given by $$\pi \mapsto \sum_{i\in\operatorname{Des}(\pi)} (\pi_i-\pi_{i+1}).$$ See [[St000111]] and [[St000154]] for the sum of the descent tops and the descent bottoms, respectively. This statistic was studied in [1] and [2] where is was called the ''drop'' of a permutation. ----------------------------------------------------------------------------- References: [1] Babson, E., Steingr\'ımsson, E. Generalized permutation patterns and a classification of the Mahonian statistics [[MathSciNet:1758852]] [2] Petersen, T. K., Tenner, B. E. The depth of a permutation [[arXiv:1202.4765]] [3] Triangle read by rows: For n >= 1, k >= 0, T(n,k) = the number of permutations pi of n such that the total distance sum_i abs(i-pi(i)) = 2k. Equivalently, k = sum_i max(i-pi(i),0). [[OEIS:A062869]] ----------------------------------------------------------------------------- Code: def statistic(x): return sum(x[i]-x[i+1] for i in range(x.size()-1) if x[i]>x[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] => 4 [3,2,1,4] => 2 [3,2,4,1] => 4 [3,4,1,2] => 3 [3,4,2,1] => 3 [4,1,2,3] => 3 [4,1,3,2] => 4 [4,2,1,3] => 3 [4,2,3,1] => 4 [4,3,1,2] => 3 [4,3,2,1] => 3 [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] => 4 [1,4,3,2,5] => 2 [1,4,3,5,2] => 4 [1,4,5,2,3] => 3 [1,4,5,3,2] => 3 [1,5,2,3,4] => 3 [1,5,2,4,3] => 4 [1,5,3,2,4] => 3 [1,5,3,4,2] => 4 [1,5,4,2,3] => 3 [1,5,4,3,2] => 3 [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] => 5 [2,4,3,1,5] => 3 [2,4,3,5,1] => 5 [2,4,5,1,3] => 4 [2,4,5,3,1] => 4 [2,5,1,3,4] => 4 [2,5,1,4,3] => 5 [2,5,3,1,4] => 4 [2,5,3,4,1] => 5 [2,5,4,1,3] => 4 [2,5,4,3,1] => 4 [3,1,2,4,5] => 2 [3,1,2,5,4] => 3 [3,1,4,2,5] => 4 [3,1,4,5,2] => 5 [3,1,5,2,4] => 5 [3,1,5,4,2] => 5 [3,2,1,4,5] => 2 [3,2,1,5,4] => 3 [3,2,4,1,5] => 4 [3,2,4,5,1] => 5 [3,2,5,1,4] => 5 [3,2,5,4,1] => 5 [3,4,1,2,5] => 3 [3,4,1,5,2] => 6 [3,4,2,1,5] => 3 [3,4,2,5,1] => 6 [3,4,5,1,2] => 4 [3,4,5,2,1] => 4 [3,5,1,2,4] => 4 [3,5,1,4,2] => 6 [3,5,2,1,4] => 4 [3,5,2,4,1] => 6 [3,5,4,1,2] => 4 [3,5,4,2,1] => 4 [4,1,2,3,5] => 3 [4,1,2,5,3] => 5 [4,1,3,2,5] => 4 [4,1,3,5,2] => 6 [4,1,5,2,3] => 6 [4,1,5,3,2] => 6 [4,2,1,3,5] => 3 [4,2,1,5,3] => 5 [4,2,3,1,5] => 4 [4,2,3,5,1] => 6 [4,2,5,1,3] => 6 [4,2,5,3,1] => 6 [4,3,1,2,5] => 3 [4,3,1,5,2] => 6 [4,3,2,1,5] => 3 [4,3,2,5,1] => 6 [4,3,5,1,2] => 5 [4,3,5,2,1] => 5 [4,5,1,2,3] => 4 [4,5,1,3,2] => 5 [4,5,2,1,3] => 4 [4,5,2,3,1] => 5 [4,5,3,1,2] => 4 [4,5,3,2,1] => 4 [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] => 6 [5,2,1,3,4] => 4 [5,2,1,4,3] => 5 [5,2,3,1,4] => 5 [5,2,3,4,1] => 6 [5,2,4,1,3] => 6 [5,2,4,3,1] => 6 [5,3,1,2,4] => 4 [5,3,1,4,2] => 6 [5,3,2,1,4] => 4 [5,3,2,4,1] => 6 [5,3,4,1,2] => 5 [5,3,4,2,1] => 5 [5,4,1,2,3] => 4 [5,4,1,3,2] => 5 [5,4,2,1,3] => 4 [5,4,2,3,1] => 5 [5,4,3,1,2] => 4 [5,4,3,2,1] => 4 [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] => 4 [1,2,5,4,3,6] => 2 [1,2,5,4,6,3] => 4 [1,2,5,6,3,4] => 3 [1,2,5,6,4,3] => 3 [1,2,6,3,4,5] => 3 [1,2,6,3,5,4] => 4 [1,2,6,4,3,5] => 3 [1,2,6,4,5,3] => 4 [1,2,6,5,3,4] => 3 [1,2,6,5,4,3] => 3 [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] => 5 [1,3,5,4,2,6] => 3 [1,3,5,4,6,2] => 5 [1,3,5,6,2,4] => 4 [1,3,5,6,4,2] => 4 [1,3,6,2,4,5] => 4 [1,3,6,2,5,4] => 5 [1,3,6,4,2,5] => 4 [1,3,6,4,5,2] => 5 [1,3,6,5,2,4] => 4 [1,3,6,5,4,2] => 4 [1,4,2,3,5,6] => 2 [1,4,2,3,6,5] => 3 [1,4,2,5,3,6] => 4 [1,4,2,5,6,3] => 5 [1,4,2,6,3,5] => 5 [1,4,2,6,5,3] => 5 [1,4,3,2,5,6] => 2 [1,4,3,2,6,5] => 3 [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] => 5 [1,4,5,2,3,6] => 3 [1,4,5,2,6,3] => 6 [1,4,5,3,2,6] => 3 [1,4,5,3,6,2] => 6 [1,4,5,6,2,3] => 4 [1,4,5,6,3,2] => 4 [1,4,6,2,3,5] => 4 [1,4,6,2,5,3] => 6 [1,4,6,3,2,5] => 4 [1,4,6,3,5,2] => 6 [1,4,6,5,2,3] => 4 [1,4,6,5,3,2] => 4 [1,5,2,3,4,6] => 3 [1,5,2,3,6,4] => 5 [1,5,2,4,3,6] => 4 [1,5,2,4,6,3] => 6 [1,5,2,6,3,4] => 6 [1,5,2,6,4,3] => 6 [1,5,3,2,4,6] => 3 [1,5,3,2,6,4] => 5 [1,5,3,4,2,6] => 4 [1,5,3,4,6,2] => 6 [1,5,3,6,2,4] => 6 [1,5,3,6,4,2] => 6 [1,5,4,2,3,6] => 3 [1,5,4,2,6,3] => 6 [1,5,4,3,2,6] => 3 [1,5,4,3,6,2] => 6 [1,5,4,6,2,3] => 5 [1,5,4,6,3,2] => 5 [1,5,6,2,3,4] => 4 [1,5,6,2,4,3] => 5 [1,5,6,3,2,4] => 4 [1,5,6,3,4,2] => 5 [1,5,6,4,2,3] => 4 [1,5,6,4,3,2] => 4 [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] => 6 [1,6,3,2,4,5] => 4 [1,6,3,2,5,4] => 5 [1,6,3,4,2,5] => 5 [1,6,3,4,5,2] => 6 [1,6,3,5,2,4] => 6 [1,6,3,5,4,2] => 6 [1,6,4,2,3,5] => 4 [1,6,4,2,5,3] => 6 [1,6,4,3,2,5] => 4 [1,6,4,3,5,2] => 6 [1,6,4,5,2,3] => 5 [1,6,4,5,3,2] => 5 [1,6,5,2,3,4] => 4 [1,6,5,2,4,3] => 5 [1,6,5,3,2,4] => 4 [1,6,5,3,4,2] => 5 [1,6,5,4,2,3] => 4 [1,6,5,4,3,2] => 4 [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] => 5 [2,1,5,4,3,6] => 3 [2,1,5,4,6,3] => 5 [2,1,5,6,3,4] => 4 [2,1,5,6,4,3] => 4 [2,1,6,3,4,5] => 4 [2,1,6,3,5,4] => 5 [2,1,6,4,3,5] => 4 [2,1,6,4,5,3] => 5 [2,1,6,5,3,4] => 4 [2,1,6,5,4,3] => 4 [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] => 6 [2,3,5,4,1,6] => 4 [2,3,5,4,6,1] => 6 [2,3,5,6,1,4] => 5 [2,3,5,6,4,1] => 5 [2,3,6,1,4,5] => 5 [2,3,6,1,5,4] => 6 [2,3,6,4,1,5] => 5 [2,3,6,4,5,1] => 6 [2,3,6,5,1,4] => 5 [2,3,6,5,4,1] => 5 [2,4,1,3,5,6] => 3 [2,4,1,3,6,5] => 4 [2,4,1,5,3,6] => 5 [2,4,1,5,6,3] => 6 [2,4,1,6,3,5] => 6 [2,4,1,6,5,3] => 6 [2,4,3,1,5,6] => 3 [2,4,3,1,6,5] => 4 [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] => 6 [2,4,5,1,3,6] => 4 [2,4,5,1,6,3] => 7 [2,4,5,3,1,6] => 4 [2,4,5,3,6,1] => 7 [2,4,5,6,1,3] => 5 [2,4,5,6,3,1] => 5 [2,4,6,1,3,5] => 5 [2,4,6,1,5,3] => 7 [2,4,6,3,1,5] => 5 [2,4,6,3,5,1] => 7 [2,4,6,5,1,3] => 5 [2,4,6,5,3,1] => 5 [2,5,1,3,4,6] => 4 [2,5,1,3,6,4] => 6 [2,5,1,4,3,6] => 5 [2,5,1,4,6,3] => 7 [2,5,1,6,3,4] => 7 [2,5,1,6,4,3] => 7 [2,5,3,1,4,6] => 4 [2,5,3,1,6,4] => 6 [2,5,3,4,1,6] => 5 [2,5,3,4,6,1] => 7 [2,5,3,6,1,4] => 7 [2,5,3,6,4,1] => 7 [2,5,4,1,3,6] => 4 [2,5,4,1,6,3] => 7 [2,5,4,3,1,6] => 4 [2,5,4,3,6,1] => 7 [2,5,4,6,1,3] => 6 [2,5,4,6,3,1] => 6 [2,5,6,1,3,4] => 5 [2,5,6,1,4,3] => 6 [2,5,6,3,1,4] => 5 [2,5,6,3,4,1] => 6 [2,5,6,4,1,3] => 5 [2,5,6,4,3,1] => 5 [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] => 7 [2,6,3,1,4,5] => 5 [2,6,3,1,5,4] => 6 [2,6,3,4,1,5] => 6 [2,6,3,4,5,1] => 7 [2,6,3,5,1,4] => 7 [2,6,3,5,4,1] => 7 [2,6,4,1,3,5] => 5 [2,6,4,1,5,3] => 7 [2,6,4,3,1,5] => 5 [2,6,4,3,5,1] => 7 [2,6,4,5,1,3] => 6 [2,6,4,5,3,1] => 6 [2,6,5,1,3,4] => 5 [2,6,5,1,4,3] => 6 [2,6,5,3,1,4] => 5 [2,6,5,3,4,1] => 6 [2,6,5,4,1,3] => 5 [2,6,5,4,3,1] => 5 [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] => 4 [3,1,4,2,6,5] => 5 [3,1,4,5,2,6] => 5 [3,1,4,5,6,2] => 6 [3,1,4,6,2,5] => 6 [3,1,4,6,5,2] => 6 [3,1,5,2,4,6] => 5 [3,1,5,2,6,4] => 7 [3,1,5,4,2,6] => 5 [3,1,5,4,6,2] => 7 [3,1,5,6,2,4] => 6 [3,1,5,6,4,2] => 6 [3,1,6,2,4,5] => 6 [3,1,6,2,5,4] => 7 [3,1,6,4,2,5] => 6 [3,1,6,4,5,2] => 7 [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] => 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] => 6 [3,2,5,1,4,6] => 5 [3,2,5,1,6,4] => 7 [3,2,5,4,1,6] => 5 [3,2,5,4,6,1] => 7 [3,2,5,6,1,4] => 6 [3,2,5,6,4,1] => 6 [3,2,6,1,4,5] => 6 [3,2,6,1,5,4] => 7 [3,2,6,4,1,5] => 6 [3,2,6,4,5,1] => 7 [3,2,6,5,1,4] => 6 [3,2,6,5,4,1] => 6 [3,4,1,2,5,6] => 3 [3,4,1,2,6,5] => 4 [3,4,1,5,2,6] => 6 [3,4,1,5,6,2] => 7 [3,4,1,6,2,5] => 7 [3,4,1,6,5,2] => 7 [3,4,2,1,5,6] => 3 [3,4,2,1,6,5] => 4 [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] => 7 [3,4,5,1,2,6] => 4 [3,4,5,1,6,2] => 8 [3,4,5,2,1,6] => 4 [3,4,5,2,6,1] => 8 [3,4,5,6,1,2] => 5 [3,4,5,6,2,1] => 5 [3,4,6,1,2,5] => 5 [3,4,6,1,5,2] => 8 [3,4,6,2,1,5] => 5 [3,4,6,2,5,1] => 8 [3,4,6,5,1,2] => 5 [3,4,6,5,2,1] => 5 [3,5,1,2,4,6] => 4 [3,5,1,2,6,4] => 6 [3,5,1,4,2,6] => 6 [3,5,1,4,6,2] => 8 [3,5,1,6,2,4] => 8 [3,5,1,6,4,2] => 8 [3,5,2,1,4,6] => 4 [3,5,2,1,6,4] => 6 [3,5,2,4,1,6] => 6 [3,5,2,4,6,1] => 8 [3,5,2,6,1,4] => 8 [3,5,2,6,4,1] => 8 [3,5,4,1,2,6] => 4 [3,5,4,1,6,2] => 8 [3,5,4,2,1,6] => 4 [3,5,4,2,6,1] => 8 [3,5,4,6,1,2] => 6 [3,5,4,6,2,1] => 6 [3,5,6,1,2,4] => 5 [3,5,6,1,4,2] => 7 [3,5,6,2,1,4] => 5 [3,5,6,2,4,1] => 7 [3,5,6,4,1,2] => 5 [3,5,6,4,2,1] => 5 [3,6,1,2,4,5] => 5 [3,6,1,2,5,4] => 6 [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] => 8 [3,6,2,1,4,5] => 5 [3,6,2,1,5,4] => 6 [3,6,2,4,1,5] => 7 [3,6,2,4,5,1] => 8 [3,6,2,5,1,4] => 8 [3,6,2,5,4,1] => 8 [3,6,4,1,2,5] => 5 [3,6,4,1,5,2] => 8 [3,6,4,2,1,5] => 5 [3,6,4,2,5,1] => 8 [3,6,4,5,1,2] => 6 [3,6,4,5,2,1] => 6 [3,6,5,1,2,4] => 5 [3,6,5,1,4,2] => 7 [3,6,5,2,1,4] => 5 [3,6,5,2,4,1] => 7 [3,6,5,4,1,2] => 5 [3,6,5,4,2,1] => 5 [4,1,2,3,5,6] => 3 [4,1,2,3,6,5] => 4 [4,1,2,5,3,6] => 5 [4,1,2,5,6,3] => 6 [4,1,2,6,3,5] => 6 [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] => 6 [4,1,3,5,6,2] => 7 [4,1,3,6,2,5] => 7 [4,1,3,6,5,2] => 7 [4,1,5,2,3,6] => 6 [4,1,5,2,6,3] => 9 [4,1,5,3,2,6] => 6 [4,1,5,3,6,2] => 9 [4,1,5,6,2,3] => 7 [4,1,5,6,3,2] => 7 [4,1,6,2,3,5] => 7 [4,1,6,2,5,3] => 9 [4,1,6,3,2,5] => 7 [4,1,6,3,5,2] => 9 [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] => 5 [4,2,1,5,6,3] => 6 [4,2,1,6,3,5] => 6 [4,2,1,6,5,3] => 6 [4,2,3,1,5,6] => 4 [4,2,3,1,6,5] => 5 [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] => 7 [4,2,5,1,3,6] => 6 [4,2,5,1,6,3] => 9 [4,2,5,3,1,6] => 6 [4,2,5,3,6,1] => 9 [4,2,5,6,1,3] => 7 [4,2,5,6,3,1] => 7 [4,2,6,1,3,5] => 7 [4,2,6,1,5,3] => 9 [4,2,6,3,1,5] => 7 [4,2,6,3,5,1] => 9 [4,2,6,5,1,3] => 7 [4,2,6,5,3,1] => 7 [4,3,1,2,5,6] => 3 [4,3,1,2,6,5] => 4 [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] => 7 [4,3,2,1,5,6] => 3 [4,3,2,1,6,5] => 4 [4,3,2,5,1,6] => 6 [4,3,2,5,6,1] => 7 [4,3,2,6,1,5] => 7 [4,3,2,6,5,1] => 7 [4,3,5,1,2,6] => 5 [4,3,5,1,6,2] => 9 [4,3,5,2,1,6] => 5 [4,3,5,2,6,1] => 9 [4,3,5,6,1,2] => 6 [4,3,5,6,2,1] => 6 [4,3,6,1,2,5] => 6 [4,3,6,1,5,2] => 9 [4,3,6,2,1,5] => 6 [4,3,6,2,5,1] => 9 [4,3,6,5,1,2] => 6 [4,3,6,5,2,1] => 6 [4,5,1,2,3,6] => 4 [4,5,1,2,6,3] => 7 [4,5,1,3,2,6] => 5 [4,5,1,3,6,2] => 8 [4,5,1,6,2,3] => 8 [4,5,1,6,3,2] => 8 [4,5,2,1,3,6] => 4 [4,5,2,1,6,3] => 7 [4,5,2,3,1,6] => 5 [4,5,2,3,6,1] => 8 [4,5,2,6,1,3] => 8 [4,5,2,6,3,1] => 8 [4,5,3,1,2,6] => 4 [4,5,3,1,6,2] => 8 [4,5,3,2,1,6] => 4 [4,5,3,2,6,1] => 8 [4,5,3,6,1,2] => 7 [4,5,3,6,2,1] => 7 [4,5,6,1,2,3] => 5 [4,5,6,1,3,2] => 6 [4,5,6,2,1,3] => 5 [4,5,6,2,3,1] => 6 [4,5,6,3,1,2] => 5 [4,5,6,3,2,1] => 5 [4,6,1,2,3,5] => 5 [4,6,1,2,5,3] => 7 [4,6,1,3,2,5] => 6 [4,6,1,3,5,2] => 8 [4,6,1,5,2,3] => 8 [4,6,1,5,3,2] => 8 [4,6,2,1,3,5] => 5 [4,6,2,1,5,3] => 7 [4,6,2,3,1,5] => 6 [4,6,2,3,5,1] => 8 [4,6,2,5,1,3] => 8 [4,6,2,5,3,1] => 8 [4,6,3,1,2,5] => 5 [4,6,3,1,5,2] => 8 [4,6,3,2,1,5] => 5 [4,6,3,2,5,1] => 8 [4,6,3,5,1,2] => 7 [4,6,3,5,2,1] => 7 [4,6,5,1,2,3] => 5 [4,6,5,1,3,2] => 6 [4,6,5,2,1,3] => 5 [4,6,5,2,3,1] => 6 [4,6,5,3,1,2] => 5 [4,6,5,3,2,1] => 5 [5,1,2,3,4,6] => 4 [5,1,2,3,6,4] => 6 [5,1,2,4,3,6] => 5 [5,1,2,4,6,3] => 7 [5,1,2,6,3,4] => 7 [5,1,2,6,4,3] => 7 [5,1,3,2,4,6] => 5 [5,1,3,2,6,4] => 7 [5,1,3,4,2,6] => 6 [5,1,3,4,6,2] => 8 [5,1,3,6,2,4] => 8 [5,1,3,6,4,2] => 8 [5,1,4,2,3,6] => 6 [5,1,4,2,6,3] => 9 [5,1,4,3,2,6] => 6 [5,1,4,3,6,2] => 9 [5,1,4,6,2,3] => 8 [5,1,4,6,3,2] => 8 [5,1,6,2,3,4] => 8 [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] => 8 [5,2,1,3,4,6] => 4 [5,2,1,3,6,4] => 6 [5,2,1,4,3,6] => 5 [5,2,1,4,6,3] => 7 [5,2,1,6,3,4] => 7 [5,2,1,6,4,3] => 7 [5,2,3,1,4,6] => 5 [5,2,3,1,6,4] => 7 [5,2,3,4,1,6] => 6 [5,2,3,4,6,1] => 8 [5,2,3,6,1,4] => 8 [5,2,3,6,4,1] => 8 [5,2,4,1,3,6] => 6 [5,2,4,1,6,3] => 9 [5,2,4,3,1,6] => 6 [5,2,4,3,6,1] => 9 [5,2,4,6,1,3] => 8 [5,2,4,6,3,1] => 8 [5,2,6,1,3,4] => 8 [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] => 8 [5,3,1,2,4,6] => 4 [5,3,1,2,6,4] => 6 [5,3,1,4,2,6] => 6 [5,3,1,4,6,2] => 8 [5,3,1,6,2,4] => 8 [5,3,1,6,4,2] => 8 [5,3,2,1,4,6] => 4 [5,3,2,1,6,4] => 6 [5,3,2,4,1,6] => 6 [5,3,2,4,6,1] => 8 [5,3,2,6,1,4] => 8 [5,3,2,6,4,1] => 8 [5,3,4,1,2,6] => 5 [5,3,4,1,6,2] => 9 [5,3,4,2,1,6] => 5 [5,3,4,2,6,1] => 9 [5,3,4,6,1,2] => 7 [5,3,4,6,2,1] => 7 [5,3,6,1,2,4] => 7 [5,3,6,1,4,2] => 9 [5,3,6,2,1,4] => 7 [5,3,6,2,4,1] => 9 [5,3,6,4,1,2] => 7 [5,3,6,4,2,1] => 7 [5,4,1,2,3,6] => 4 [5,4,1,2,6,3] => 7 [5,4,1,3,2,6] => 5 [5,4,1,3,6,2] => 8 [5,4,1,6,2,3] => 8 [5,4,1,6,3,2] => 8 [5,4,2,1,3,6] => 4 [5,4,2,1,6,3] => 7 [5,4,2,3,1,6] => 5 [5,4,2,3,6,1] => 8 [5,4,2,6,1,3] => 8 [5,4,2,6,3,1] => 8 [5,4,3,1,2,6] => 4 [5,4,3,1,6,2] => 8 [5,4,3,2,1,6] => 4 [5,4,3,2,6,1] => 8 [5,4,3,6,1,2] => 7 [5,4,3,6,2,1] => 7 [5,4,6,1,2,3] => 6 [5,4,6,1,3,2] => 7 [5,4,6,2,1,3] => 6 [5,4,6,2,3,1] => 7 [5,4,6,3,1,2] => 6 [5,4,6,3,2,1] => 6 [5,6,1,2,3,4] => 5 [5,6,1,2,4,3] => 6 [5,6,1,3,2,4] => 6 [5,6,1,3,4,2] => 7 [5,6,1,4,2,3] => 7 [5,6,1,4,3,2] => 7 [5,6,2,1,3,4] => 5 [5,6,2,1,4,3] => 6 [5,6,2,3,1,4] => 6 [5,6,2,3,4,1] => 7 [5,6,2,4,1,3] => 7 [5,6,2,4,3,1] => 7 [5,6,3,1,2,4] => 5 [5,6,3,1,4,2] => 7 [5,6,3,2,1,4] => 5 [5,6,3,2,4,1] => 7 [5,6,3,4,1,2] => 6 [5,6,3,4,2,1] => 6 [5,6,4,1,2,3] => 5 [5,6,4,1,3,2] => 6 [5,6,4,2,1,3] => 5 [5,6,4,2,3,1] => 6 [5,6,4,3,1,2] => 5 [5,6,4,3,2,1] => 5 [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] => 7 [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] => 8 [6,1,4,2,3,5] => 7 [6,1,4,2,5,3] => 9 [6,1,4,3,2,5] => 7 [6,1,4,3,5,2] => 9 [6,1,4,5,2,3] => 8 [6,1,4,5,3,2] => 8 [6,1,5,2,3,4] => 8 [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] => 8 [6,2,1,3,4,5] => 5 [6,2,1,3,5,4] => 6 [6,2,1,4,3,5] => 6 [6,2,1,4,5,3] => 7 [6,2,1,5,3,4] => 7 [6,2,1,5,4,3] => 7 [6,2,3,1,4,5] => 6 [6,2,3,1,5,4] => 7 [6,2,3,4,1,5] => 7 [6,2,3,4,5,1] => 8 [6,2,3,5,1,4] => 8 [6,2,3,5,4,1] => 8 [6,2,4,1,3,5] => 7 [6,2,4,1,5,3] => 9 [6,2,4,3,1,5] => 7 [6,2,4,3,5,1] => 9 [6,2,4,5,1,3] => 8 [6,2,4,5,3,1] => 8 [6,2,5,1,3,4] => 8 [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] => 8 [6,3,1,2,4,5] => 5 [6,3,1,2,5,4] => 6 [6,3,1,4,2,5] => 7 [6,3,1,4,5,2] => 8 [6,3,1,5,2,4] => 8 [6,3,1,5,4,2] => 8 [6,3,2,1,4,5] => 5 [6,3,2,1,5,4] => 6 [6,3,2,4,1,5] => 7 [6,3,2,4,5,1] => 8 [6,3,2,5,1,4] => 8 [6,3,2,5,4,1] => 8 [6,3,4,1,2,5] => 6 [6,3,4,1,5,2] => 9 [6,3,4,2,1,5] => 6 [6,3,4,2,5,1] => 9 [6,3,4,5,1,2] => 7 [6,3,4,5,2,1] => 7 [6,3,5,1,2,4] => 7 [6,3,5,1,4,2] => 9 [6,3,5,2,1,4] => 7 [6,3,5,2,4,1] => 9 [6,3,5,4,1,2] => 7 [6,3,5,4,2,1] => 7 [6,4,1,2,3,5] => 5 [6,4,1,2,5,3] => 7 [6,4,1,3,2,5] => 6 [6,4,1,3,5,2] => 8 [6,4,1,5,2,3] => 8 [6,4,1,5,3,2] => 8 [6,4,2,1,3,5] => 5 [6,4,2,1,5,3] => 7 [6,4,2,3,1,5] => 6 [6,4,2,3,5,1] => 8 [6,4,2,5,1,3] => 8 [6,4,2,5,3,1] => 8 [6,4,3,1,2,5] => 5 [6,4,3,1,5,2] => 8 [6,4,3,2,1,5] => 5 [6,4,3,2,5,1] => 8 [6,4,3,5,1,2] => 7 [6,4,3,5,2,1] => 7 [6,4,5,1,2,3] => 6 [6,4,5,1,3,2] => 7 [6,4,5,2,1,3] => 6 [6,4,5,2,3,1] => 7 [6,4,5,3,1,2] => 6 [6,4,5,3,2,1] => 6 [6,5,1,2,3,4] => 5 [6,5,1,2,4,3] => 6 [6,5,1,3,2,4] => 6 [6,5,1,3,4,2] => 7 [6,5,1,4,2,3] => 7 [6,5,1,4,3,2] => 7 [6,5,2,1,3,4] => 5 [6,5,2,1,4,3] => 6 [6,5,2,3,1,4] => 6 [6,5,2,3,4,1] => 7 [6,5,2,4,1,3] => 7 [6,5,2,4,3,1] => 7 [6,5,3,1,2,4] => 5 [6,5,3,1,4,2] => 7 [6,5,3,2,1,4] => 5 [6,5,3,2,4,1] => 7 [6,5,3,4,1,2] => 6 [6,5,3,4,2,1] => 6 [6,5,4,1,2,3] => 5 [6,5,4,1,3,2] => 6 [6,5,4,2,1,3] => 5 [6,5,4,2,3,1] => 6 [6,5,4,3,1,2] => 5 [6,5,4,3,2,1] => 5 ----------------------------------------------------------------------------- Created: Nov 30, 2012 at 21:30 by Chris Berg ----------------------------------------------------------------------------- Last Updated: May 29, 2015 at 16:16 by Martin Rubey