***************************************************************************** * 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: St000111 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The sum of the descent tops (or Genocchi descents) of a permutation. This statistic is given by $$\pi \mapsto \sum_{i\in\operatorname{Des}(\pi)} \pi_i.$$ ----------------------------------------------------------------------------- References: [1] Babson, E., Steingr\'ımsson, E. Generalized permutation patterns and a classification of the Mahonian statistics [[MathSciNet:1758852]] [2] Nunge, A. An equivalence of multistatistics on permutations [[arXiv:1601.02928]] [3] Clarke, R. J., Steingr\'ımsson, E., Zeng, J. New Euler-Mahonian statistics on permutations and words [[MathSciNet:1436481]] ----------------------------------------------------------------------------- Code: def statistic(pi): return sum( pi[i] for i in range(pi.size()-1) if pi[i] > pi[i+1] ) ----------------------------------------------------------------------------- Statistic values: [1] => 0 [1,2] => 0 [2,1] => 2 [1,2,3] => 0 [1,3,2] => 3 [2,1,3] => 2 [2,3,1] => 3 [3,1,2] => 3 [3,2,1] => 5 [1,2,3,4] => 0 [1,2,4,3] => 4 [1,3,2,4] => 3 [1,3,4,2] => 4 [1,4,2,3] => 4 [1,4,3,2] => 7 [2,1,3,4] => 2 [2,1,4,3] => 6 [2,3,1,4] => 3 [2,3,4,1] => 4 [2,4,1,3] => 4 [2,4,3,1] => 7 [3,1,2,4] => 3 [3,1,4,2] => 7 [3,2,1,4] => 5 [3,2,4,1] => 7 [3,4,1,2] => 4 [3,4,2,1] => 6 [4,1,2,3] => 4 [4,1,3,2] => 7 [4,2,1,3] => 6 [4,2,3,1] => 7 [4,3,1,2] => 7 [4,3,2,1] => 9 [1,2,3,4,5] => 0 [1,2,3,5,4] => 5 [1,2,4,3,5] => 4 [1,2,4,5,3] => 5 [1,2,5,3,4] => 5 [1,2,5,4,3] => 9 [1,3,2,4,5] => 3 [1,3,2,5,4] => 8 [1,3,4,2,5] => 4 [1,3,4,5,2] => 5 [1,3,5,2,4] => 5 [1,3,5,4,2] => 9 [1,4,2,3,5] => 4 [1,4,2,5,3] => 9 [1,4,3,2,5] => 7 [1,4,3,5,2] => 9 [1,4,5,2,3] => 5 [1,4,5,3,2] => 8 [1,5,2,3,4] => 5 [1,5,2,4,3] => 9 [1,5,3,2,4] => 8 [1,5,3,4,2] => 9 [1,5,4,2,3] => 9 [1,5,4,3,2] => 12 [2,1,3,4,5] => 2 [2,1,3,5,4] => 7 [2,1,4,3,5] => 6 [2,1,4,5,3] => 7 [2,1,5,3,4] => 7 [2,1,5,4,3] => 11 [2,3,1,4,5] => 3 [2,3,1,5,4] => 8 [2,3,4,1,5] => 4 [2,3,4,5,1] => 5 [2,3,5,1,4] => 5 [2,3,5,4,1] => 9 [2,4,1,3,5] => 4 [2,4,1,5,3] => 9 [2,4,3,1,5] => 7 [2,4,3,5,1] => 9 [2,4,5,1,3] => 5 [2,4,5,3,1] => 8 [2,5,1,3,4] => 5 [2,5,1,4,3] => 9 [2,5,3,1,4] => 8 [2,5,3,4,1] => 9 [2,5,4,1,3] => 9 [2,5,4,3,1] => 12 [3,1,2,4,5] => 3 [3,1,2,5,4] => 8 [3,1,4,2,5] => 7 [3,1,4,5,2] => 8 [3,1,5,2,4] => 8 [3,1,5,4,2] => 12 [3,2,1,4,5] => 5 [3,2,1,5,4] => 10 [3,2,4,1,5] => 7 [3,2,4,5,1] => 8 [3,2,5,1,4] => 8 [3,2,5,4,1] => 12 [3,4,1,2,5] => 4 [3,4,1,5,2] => 9 [3,4,2,1,5] => 6 [3,4,2,5,1] => 9 [3,4,5,1,2] => 5 [3,4,5,2,1] => 7 [3,5,1,2,4] => 5 [3,5,1,4,2] => 9 [3,5,2,1,4] => 7 [3,5,2,4,1] => 9 [3,5,4,1,2] => 9 [3,5,4,2,1] => 11 [4,1,2,3,5] => 4 [4,1,2,5,3] => 9 [4,1,3,2,5] => 7 [4,1,3,5,2] => 9 [4,1,5,2,3] => 9 [4,1,5,3,2] => 12 [4,2,1,3,5] => 6 [4,2,1,5,3] => 11 [4,2,3,1,5] => 7 [4,2,3,5,1] => 9 [4,2,5,1,3] => 9 [4,2,5,3,1] => 12 [4,3,1,2,5] => 7 [4,3,1,5,2] => 12 [4,3,2,1,5] => 9 [4,3,2,5,1] => 12 [4,3,5,1,2] => 9 [4,3,5,2,1] => 11 [4,5,1,2,3] => 5 [4,5,1,3,2] => 8 [4,5,2,1,3] => 7 [4,5,2,3,1] => 8 [4,5,3,1,2] => 8 [4,5,3,2,1] => 10 [5,1,2,3,4] => 5 [5,1,2,4,3] => 9 [5,1,3,2,4] => 8 [5,1,3,4,2] => 9 [5,1,4,2,3] => 9 [5,1,4,3,2] => 12 [5,2,1,3,4] => 7 [5,2,1,4,3] => 11 [5,2,3,1,4] => 8 [5,2,3,4,1] => 9 [5,2,4,1,3] => 9 [5,2,4,3,1] => 12 [5,3,1,2,4] => 8 [5,3,1,4,2] => 12 [5,3,2,1,4] => 10 [5,3,2,4,1] => 12 [5,3,4,1,2] => 9 [5,3,4,2,1] => 11 [5,4,1,2,3] => 9 [5,4,1,3,2] => 12 [5,4,2,1,3] => 11 [5,4,2,3,1] => 12 [5,4,3,1,2] => 12 [5,4,3,2,1] => 14 [1,2,3,4,5,6] => 0 [1,2,3,4,6,5] => 6 [1,2,3,5,4,6] => 5 [1,2,3,5,6,4] => 6 [1,2,3,6,4,5] => 6 [1,2,3,6,5,4] => 11 [1,2,4,3,5,6] => 4 [1,2,4,3,6,5] => 10 [1,2,4,5,3,6] => 5 [1,2,4,5,6,3] => 6 [1,2,4,6,3,5] => 6 [1,2,4,6,5,3] => 11 [1,2,5,3,4,6] => 5 [1,2,5,3,6,4] => 11 [1,2,5,4,3,6] => 9 [1,2,5,4,6,3] => 11 [1,2,5,6,3,4] => 6 [1,2,5,6,4,3] => 10 [1,2,6,3,4,5] => 6 [1,2,6,3,5,4] => 11 [1,2,6,4,3,5] => 10 [1,2,6,4,5,3] => 11 [1,2,6,5,3,4] => 11 [1,2,6,5,4,3] => 15 [1,3,2,4,5,6] => 3 [1,3,2,4,6,5] => 9 [1,3,2,5,4,6] => 8 [1,3,2,5,6,4] => 9 [1,3,2,6,4,5] => 9 [1,3,2,6,5,4] => 14 [1,3,4,2,5,6] => 4 [1,3,4,2,6,5] => 10 [1,3,4,5,2,6] => 5 [1,3,4,5,6,2] => 6 [1,3,4,6,2,5] => 6 [1,3,4,6,5,2] => 11 [1,3,5,2,4,6] => 5 [1,3,5,2,6,4] => 11 [1,3,5,4,2,6] => 9 [1,3,5,4,6,2] => 11 [1,3,5,6,2,4] => 6 [1,3,5,6,4,2] => 10 [1,3,6,2,4,5] => 6 [1,3,6,2,5,4] => 11 [1,3,6,4,2,5] => 10 [1,3,6,4,5,2] => 11 [1,3,6,5,2,4] => 11 [1,3,6,5,4,2] => 15 [1,4,2,3,5,6] => 4 [1,4,2,3,6,5] => 10 [1,4,2,5,3,6] => 9 [1,4,2,5,6,3] => 10 [1,4,2,6,3,5] => 10 [1,4,2,6,5,3] => 15 [1,4,3,2,5,6] => 7 [1,4,3,2,6,5] => 13 [1,4,3,5,2,6] => 9 [1,4,3,5,6,2] => 10 [1,4,3,6,2,5] => 10 [1,4,3,6,5,2] => 15 [1,4,5,2,3,6] => 5 [1,4,5,2,6,3] => 11 [1,4,5,3,2,6] => 8 [1,4,5,3,6,2] => 11 [1,4,5,6,2,3] => 6 [1,4,5,6,3,2] => 9 [1,4,6,2,3,5] => 6 [1,4,6,2,5,3] => 11 [1,4,6,3,2,5] => 9 [1,4,6,3,5,2] => 11 [1,4,6,5,2,3] => 11 [1,4,6,5,3,2] => 14 [1,5,2,3,4,6] => 5 [1,5,2,3,6,4] => 11 [1,5,2,4,3,6] => 9 [1,5,2,4,6,3] => 11 [1,5,2,6,3,4] => 11 [1,5,2,6,4,3] => 15 [1,5,3,2,4,6] => 8 [1,5,3,2,6,4] => 14 [1,5,3,4,2,6] => 9 [1,5,3,4,6,2] => 11 [1,5,3,6,2,4] => 11 [1,5,3,6,4,2] => 15 [1,5,4,2,3,6] => 9 [1,5,4,2,6,3] => 15 [1,5,4,3,2,6] => 12 [1,5,4,3,6,2] => 15 [1,5,4,6,2,3] => 11 [1,5,4,6,3,2] => 14 [1,5,6,2,3,4] => 6 [1,5,6,2,4,3] => 10 [1,5,6,3,2,4] => 9 [1,5,6,3,4,2] => 10 [1,5,6,4,2,3] => 10 [1,5,6,4,3,2] => 13 [1,6,2,3,4,5] => 6 [1,6,2,3,5,4] => 11 [1,6,2,4,3,5] => 10 [1,6,2,4,5,3] => 11 [1,6,2,5,3,4] => 11 [1,6,2,5,4,3] => 15 [1,6,3,2,4,5] => 9 [1,6,3,2,5,4] => 14 [1,6,3,4,2,5] => 10 [1,6,3,4,5,2] => 11 [1,6,3,5,2,4] => 11 [1,6,3,5,4,2] => 15 [1,6,4,2,3,5] => 10 [1,6,4,2,5,3] => 15 [1,6,4,3,2,5] => 13 [1,6,4,3,5,2] => 15 [1,6,4,5,2,3] => 11 [1,6,4,5,3,2] => 14 [1,6,5,2,3,4] => 11 [1,6,5,2,4,3] => 15 [1,6,5,3,2,4] => 14 [1,6,5,3,4,2] => 15 [1,6,5,4,2,3] => 15 [1,6,5,4,3,2] => 18 [2,1,3,4,5,6] => 2 [2,1,3,4,6,5] => 8 [2,1,3,5,4,6] => 7 [2,1,3,5,6,4] => 8 [2,1,3,6,4,5] => 8 [2,1,3,6,5,4] => 13 [2,1,4,3,5,6] => 6 [2,1,4,3,6,5] => 12 [2,1,4,5,3,6] => 7 [2,1,4,5,6,3] => 8 [2,1,4,6,3,5] => 8 [2,1,4,6,5,3] => 13 [2,1,5,3,4,6] => 7 [2,1,5,3,6,4] => 13 [2,1,5,4,3,6] => 11 [2,1,5,4,6,3] => 13 [2,1,5,6,3,4] => 8 [2,1,5,6,4,3] => 12 [2,1,6,3,4,5] => 8 [2,1,6,3,5,4] => 13 [2,1,6,4,3,5] => 12 [2,1,6,4,5,3] => 13 [2,1,6,5,3,4] => 13 [2,1,6,5,4,3] => 17 [2,3,1,4,5,6] => 3 [2,3,1,4,6,5] => 9 [2,3,1,5,4,6] => 8 [2,3,1,5,6,4] => 9 [2,3,1,6,4,5] => 9 [2,3,1,6,5,4] => 14 [2,3,4,1,5,6] => 4 [2,3,4,1,6,5] => 10 [2,3,4,5,1,6] => 5 [2,3,4,5,6,1] => 6 [2,3,4,6,1,5] => 6 [2,3,4,6,5,1] => 11 [2,3,5,1,4,6] => 5 [2,3,5,1,6,4] => 11 [2,3,5,4,1,6] => 9 [2,3,5,4,6,1] => 11 [2,3,5,6,1,4] => 6 [2,3,5,6,4,1] => 10 [2,3,6,1,4,5] => 6 [2,3,6,1,5,4] => 11 [2,3,6,4,1,5] => 10 [2,3,6,4,5,1] => 11 [2,3,6,5,1,4] => 11 [2,3,6,5,4,1] => 15 [2,4,1,3,5,6] => 4 [2,4,1,3,6,5] => 10 [2,4,1,5,3,6] => 9 [2,4,1,5,6,3] => 10 [2,4,1,6,3,5] => 10 [2,4,1,6,5,3] => 15 [2,4,3,1,5,6] => 7 [2,4,3,1,6,5] => 13 [2,4,3,5,1,6] => 9 [2,4,3,5,6,1] => 10 [2,4,3,6,1,5] => 10 [2,4,3,6,5,1] => 15 [2,4,5,1,3,6] => 5 [2,4,5,1,6,3] => 11 [2,4,5,3,1,6] => 8 [2,4,5,3,6,1] => 11 [2,4,5,6,1,3] => 6 [2,4,5,6,3,1] => 9 [2,4,6,1,3,5] => 6 [2,4,6,1,5,3] => 11 [2,4,6,3,1,5] => 9 [2,4,6,3,5,1] => 11 [2,4,6,5,1,3] => 11 [2,4,6,5,3,1] => 14 [2,5,1,3,4,6] => 5 [2,5,1,3,6,4] => 11 [2,5,1,4,3,6] => 9 [2,5,1,4,6,3] => 11 [2,5,1,6,3,4] => 11 [2,5,1,6,4,3] => 15 [2,5,3,1,4,6] => 8 [2,5,3,1,6,4] => 14 [2,5,3,4,1,6] => 9 [2,5,3,4,6,1] => 11 [2,5,3,6,1,4] => 11 [2,5,3,6,4,1] => 15 [2,5,4,1,3,6] => 9 [2,5,4,1,6,3] => 15 [2,5,4,3,1,6] => 12 [2,5,4,3,6,1] => 15 [2,5,4,6,1,3] => 11 [2,5,4,6,3,1] => 14 [2,5,6,1,3,4] => 6 [2,5,6,1,4,3] => 10 [2,5,6,3,1,4] => 9 [2,5,6,3,4,1] => 10 [2,5,6,4,1,3] => 10 [2,5,6,4,3,1] => 13 [2,6,1,3,4,5] => 6 [2,6,1,3,5,4] => 11 [2,6,1,4,3,5] => 10 [2,6,1,4,5,3] => 11 [2,6,1,5,3,4] => 11 [2,6,1,5,4,3] => 15 [2,6,3,1,4,5] => 9 [2,6,3,1,5,4] => 14 [2,6,3,4,1,5] => 10 [2,6,3,4,5,1] => 11 [2,6,3,5,1,4] => 11 [2,6,3,5,4,1] => 15 [2,6,4,1,3,5] => 10 [2,6,4,1,5,3] => 15 [2,6,4,3,1,5] => 13 [2,6,4,3,5,1] => 15 [2,6,4,5,1,3] => 11 [2,6,4,5,3,1] => 14 [2,6,5,1,3,4] => 11 [2,6,5,1,4,3] => 15 [2,6,5,3,1,4] => 14 [2,6,5,3,4,1] => 15 [2,6,5,4,1,3] => 15 [2,6,5,4,3,1] => 18 [3,1,2,4,5,6] => 3 [3,1,2,4,6,5] => 9 [3,1,2,5,4,6] => 8 [3,1,2,5,6,4] => 9 [3,1,2,6,4,5] => 9 [3,1,2,6,5,4] => 14 [3,1,4,2,5,6] => 7 [3,1,4,2,6,5] => 13 [3,1,4,5,2,6] => 8 [3,1,4,5,6,2] => 9 [3,1,4,6,2,5] => 9 [3,1,4,6,5,2] => 14 [3,1,5,2,4,6] => 8 [3,1,5,2,6,4] => 14 [3,1,5,4,2,6] => 12 [3,1,5,4,6,2] => 14 [3,1,5,6,2,4] => 9 [3,1,5,6,4,2] => 13 [3,1,6,2,4,5] => 9 [3,1,6,2,5,4] => 14 [3,1,6,4,2,5] => 13 [3,1,6,4,5,2] => 14 [3,1,6,5,2,4] => 14 [3,1,6,5,4,2] => 18 [3,2,1,4,5,6] => 5 [3,2,1,4,6,5] => 11 [3,2,1,5,4,6] => 10 [3,2,1,5,6,4] => 11 [3,2,1,6,4,5] => 11 [3,2,1,6,5,4] => 16 [3,2,4,1,5,6] => 7 [3,2,4,1,6,5] => 13 [3,2,4,5,1,6] => 8 [3,2,4,5,6,1] => 9 [3,2,4,6,1,5] => 9 [3,2,4,6,5,1] => 14 [3,2,5,1,4,6] => 8 [3,2,5,1,6,4] => 14 [3,2,5,4,1,6] => 12 [3,2,5,4,6,1] => 14 [3,2,5,6,1,4] => 9 [3,2,5,6,4,1] => 13 [3,2,6,1,4,5] => 9 [3,2,6,1,5,4] => 14 [3,2,6,4,1,5] => 13 [3,2,6,4,5,1] => 14 [3,2,6,5,1,4] => 14 [3,2,6,5,4,1] => 18 [3,4,1,2,5,6] => 4 [3,4,1,2,6,5] => 10 [3,4,1,5,2,6] => 9 [3,4,1,5,6,2] => 10 [3,4,1,6,2,5] => 10 [3,4,1,6,5,2] => 15 [3,4,2,1,5,6] => 6 [3,4,2,1,6,5] => 12 [3,4,2,5,1,6] => 9 [3,4,2,5,6,1] => 10 [3,4,2,6,1,5] => 10 [3,4,2,6,5,1] => 15 [3,4,5,1,2,6] => 5 [3,4,5,1,6,2] => 11 [3,4,5,2,1,6] => 7 [3,4,5,2,6,1] => 11 [3,4,5,6,1,2] => 6 [3,4,5,6,2,1] => 8 [3,4,6,1,2,5] => 6 [3,4,6,1,5,2] => 11 [3,4,6,2,1,5] => 8 [3,4,6,2,5,1] => 11 [3,4,6,5,1,2] => 11 [3,4,6,5,2,1] => 13 [3,5,1,2,4,6] => 5 [3,5,1,2,6,4] => 11 [3,5,1,4,2,6] => 9 [3,5,1,4,6,2] => 11 [3,5,1,6,2,4] => 11 [3,5,1,6,4,2] => 15 [3,5,2,1,4,6] => 7 [3,5,2,1,6,4] => 13 [3,5,2,4,1,6] => 9 [3,5,2,4,6,1] => 11 [3,5,2,6,1,4] => 11 [3,5,2,6,4,1] => 15 [3,5,4,1,2,6] => 9 [3,5,4,1,6,2] => 15 [3,5,4,2,1,6] => 11 [3,5,4,2,6,1] => 15 [3,5,4,6,1,2] => 11 [3,5,4,6,2,1] => 13 [3,5,6,1,2,4] => 6 [3,5,6,1,4,2] => 10 [3,5,6,2,1,4] => 8 [3,5,6,2,4,1] => 10 [3,5,6,4,1,2] => 10 [3,5,6,4,2,1] => 12 [3,6,1,2,4,5] => 6 [3,6,1,2,5,4] => 11 [3,6,1,4,2,5] => 10 [3,6,1,4,5,2] => 11 [3,6,1,5,2,4] => 11 [3,6,1,5,4,2] => 15 [3,6,2,1,4,5] => 8 [3,6,2,1,5,4] => 13 [3,6,2,4,1,5] => 10 [3,6,2,4,5,1] => 11 [3,6,2,5,1,4] => 11 [3,6,2,5,4,1] => 15 [3,6,4,1,2,5] => 10 [3,6,4,1,5,2] => 15 [3,6,4,2,1,5] => 12 [3,6,4,2,5,1] => 15 [3,6,4,5,1,2] => 11 [3,6,4,5,2,1] => 13 [3,6,5,1,2,4] => 11 [3,6,5,1,4,2] => 15 [3,6,5,2,1,4] => 13 [3,6,5,2,4,1] => 15 [3,6,5,4,1,2] => 15 [3,6,5,4,2,1] => 17 [4,1,2,3,5,6] => 4 [4,1,2,3,6,5] => 10 [4,1,2,5,3,6] => 9 [4,1,2,5,6,3] => 10 [4,1,2,6,3,5] => 10 [4,1,2,6,5,3] => 15 [4,1,3,2,5,6] => 7 [4,1,3,2,6,5] => 13 [4,1,3,5,2,6] => 9 [4,1,3,5,6,2] => 10 [4,1,3,6,2,5] => 10 [4,1,3,6,5,2] => 15 [4,1,5,2,3,6] => 9 [4,1,5,2,6,3] => 15 [4,1,5,3,2,6] => 12 [4,1,5,3,6,2] => 15 [4,1,5,6,2,3] => 10 [4,1,5,6,3,2] => 13 [4,1,6,2,3,5] => 10 [4,1,6,2,5,3] => 15 [4,1,6,3,2,5] => 13 [4,1,6,3,5,2] => 15 [4,1,6,5,2,3] => 15 [4,1,6,5,3,2] => 18 [4,2,1,3,5,6] => 6 [4,2,1,3,6,5] => 12 [4,2,1,5,3,6] => 11 [4,2,1,5,6,3] => 12 [4,2,1,6,3,5] => 12 [4,2,1,6,5,3] => 17 [4,2,3,1,5,6] => 7 [4,2,3,1,6,5] => 13 [4,2,3,5,1,6] => 9 [4,2,3,5,6,1] => 10 [4,2,3,6,1,5] => 10 [4,2,3,6,5,1] => 15 [4,2,5,1,3,6] => 9 [4,2,5,1,6,3] => 15 [4,2,5,3,1,6] => 12 [4,2,5,3,6,1] => 15 [4,2,5,6,1,3] => 10 [4,2,5,6,3,1] => 13 [4,2,6,1,3,5] => 10 [4,2,6,1,5,3] => 15 [4,2,6,3,1,5] => 13 [4,2,6,3,5,1] => 15 [4,2,6,5,1,3] => 15 [4,2,6,5,3,1] => 18 [4,3,1,2,5,6] => 7 [4,3,1,2,6,5] => 13 [4,3,1,5,2,6] => 12 [4,3,1,5,6,2] => 13 [4,3,1,6,2,5] => 13 [4,3,1,6,5,2] => 18 [4,3,2,1,5,6] => 9 [4,3,2,1,6,5] => 15 [4,3,2,5,1,6] => 12 [4,3,2,5,6,1] => 13 [4,3,2,6,1,5] => 13 [4,3,2,6,5,1] => 18 [4,3,5,1,2,6] => 9 [4,3,5,1,6,2] => 15 [4,3,5,2,1,6] => 11 [4,3,5,2,6,1] => 15 [4,3,5,6,1,2] => 10 [4,3,5,6,2,1] => 12 [4,3,6,1,2,5] => 10 [4,3,6,1,5,2] => 15 [4,3,6,2,1,5] => 12 [4,3,6,2,5,1] => 15 [4,3,6,5,1,2] => 15 [4,3,6,5,2,1] => 17 [4,5,1,2,3,6] => 5 [4,5,1,2,6,3] => 11 [4,5,1,3,2,6] => 8 [4,5,1,3,6,2] => 11 [4,5,1,6,2,3] => 11 [4,5,1,6,3,2] => 14 [4,5,2,1,3,6] => 7 [4,5,2,1,6,3] => 13 [4,5,2,3,1,6] => 8 [4,5,2,3,6,1] => 11 [4,5,2,6,1,3] => 11 [4,5,2,6,3,1] => 14 [4,5,3,1,2,6] => 8 [4,5,3,1,6,2] => 14 [4,5,3,2,1,6] => 10 [4,5,3,2,6,1] => 14 [4,5,3,6,1,2] => 11 [4,5,3,6,2,1] => 13 [4,5,6,1,2,3] => 6 [4,5,6,1,3,2] => 9 [4,5,6,2,1,3] => 8 [4,5,6,2,3,1] => 9 [4,5,6,3,1,2] => 9 [4,5,6,3,2,1] => 11 [4,6,1,2,3,5] => 6 [4,6,1,2,5,3] => 11 [4,6,1,3,2,5] => 9 [4,6,1,3,5,2] => 11 [4,6,1,5,2,3] => 11 [4,6,1,5,3,2] => 14 [4,6,2,1,3,5] => 8 [4,6,2,1,5,3] => 13 [4,6,2,3,1,5] => 9 [4,6,2,3,5,1] => 11 [4,6,2,5,1,3] => 11 [4,6,2,5,3,1] => 14 [4,6,3,1,2,5] => 9 [4,6,3,1,5,2] => 14 [4,6,3,2,1,5] => 11 [4,6,3,2,5,1] => 14 [4,6,3,5,1,2] => 11 [4,6,3,5,2,1] => 13 [4,6,5,1,2,3] => 11 [4,6,5,1,3,2] => 14 [4,6,5,2,1,3] => 13 [4,6,5,2,3,1] => 14 [4,6,5,3,1,2] => 14 [4,6,5,3,2,1] => 16 [5,1,2,3,4,6] => 5 [5,1,2,3,6,4] => 11 [5,1,2,4,3,6] => 9 [5,1,2,4,6,3] => 11 [5,1,2,6,3,4] => 11 [5,1,2,6,4,3] => 15 [5,1,3,2,4,6] => 8 [5,1,3,2,6,4] => 14 [5,1,3,4,2,6] => 9 [5,1,3,4,6,2] => 11 [5,1,3,6,2,4] => 11 [5,1,3,6,4,2] => 15 [5,1,4,2,3,6] => 9 [5,1,4,2,6,3] => 15 [5,1,4,3,2,6] => 12 [5,1,4,3,6,2] => 15 [5,1,4,6,2,3] => 11 [5,1,4,6,3,2] => 14 [5,1,6,2,3,4] => 11 [5,1,6,2,4,3] => 15 [5,1,6,3,2,4] => 14 [5,1,6,3,4,2] => 15 [5,1,6,4,2,3] => 15 [5,1,6,4,3,2] => 18 [5,2,1,3,4,6] => 7 [5,2,1,3,6,4] => 13 [5,2,1,4,3,6] => 11 [5,2,1,4,6,3] => 13 [5,2,1,6,3,4] => 13 [5,2,1,6,4,3] => 17 [5,2,3,1,4,6] => 8 [5,2,3,1,6,4] => 14 [5,2,3,4,1,6] => 9 [5,2,3,4,6,1] => 11 [5,2,3,6,1,4] => 11 [5,2,3,6,4,1] => 15 [5,2,4,1,3,6] => 9 [5,2,4,1,6,3] => 15 [5,2,4,3,1,6] => 12 [5,2,4,3,6,1] => 15 [5,2,4,6,1,3] => 11 [5,2,4,6,3,1] => 14 [5,2,6,1,3,4] => 11 [5,2,6,1,4,3] => 15 [5,2,6,3,1,4] => 14 [5,2,6,3,4,1] => 15 [5,2,6,4,1,3] => 15 [5,2,6,4,3,1] => 18 [5,3,1,2,4,6] => 8 [5,3,1,2,6,4] => 14 [5,3,1,4,2,6] => 12 [5,3,1,4,6,2] => 14 [5,3,1,6,2,4] => 14 [5,3,1,6,4,2] => 18 [5,3,2,1,4,6] => 10 [5,3,2,1,6,4] => 16 [5,3,2,4,1,6] => 12 [5,3,2,4,6,1] => 14 [5,3,2,6,1,4] => 14 [5,3,2,6,4,1] => 18 [5,3,4,1,2,6] => 9 [5,3,4,1,6,2] => 15 [5,3,4,2,1,6] => 11 [5,3,4,2,6,1] => 15 [5,3,4,6,1,2] => 11 [5,3,4,6,2,1] => 13 [5,3,6,1,2,4] => 11 [5,3,6,1,4,2] => 15 [5,3,6,2,1,4] => 13 [5,3,6,2,4,1] => 15 [5,3,6,4,1,2] => 15 [5,3,6,4,2,1] => 17 [5,4,1,2,3,6] => 9 [5,4,1,2,6,3] => 15 [5,4,1,3,2,6] => 12 [5,4,1,3,6,2] => 15 [5,4,1,6,2,3] => 15 [5,4,1,6,3,2] => 18 [5,4,2,1,3,6] => 11 [5,4,2,1,6,3] => 17 [5,4,2,3,1,6] => 12 [5,4,2,3,6,1] => 15 [5,4,2,6,1,3] => 15 [5,4,2,6,3,1] => 18 [5,4,3,1,2,6] => 12 [5,4,3,1,6,2] => 18 [5,4,3,2,1,6] => 14 [5,4,3,2,6,1] => 18 [5,4,3,6,1,2] => 15 [5,4,3,6,2,1] => 17 [5,4,6,1,2,3] => 11 [5,4,6,1,3,2] => 14 [5,4,6,2,1,3] => 13 [5,4,6,2,3,1] => 14 [5,4,6,3,1,2] => 14 [5,4,6,3,2,1] => 16 [5,6,1,2,3,4] => 6 [5,6,1,2,4,3] => 10 [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] => 13 [5,6,2,1,3,4] => 8 [5,6,2,1,4,3] => 12 [5,6,2,3,1,4] => 9 [5,6,2,3,4,1] => 10 [5,6,2,4,1,3] => 10 [5,6,2,4,3,1] => 13 [5,6,3,1,2,4] => 9 [5,6,3,1,4,2] => 13 [5,6,3,2,1,4] => 11 [5,6,3,2,4,1] => 13 [5,6,3,4,1,2] => 10 [5,6,3,4,2,1] => 12 [5,6,4,1,2,3] => 10 [5,6,4,1,3,2] => 13 [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] => 15 [6,1,2,3,4,5] => 6 [6,1,2,3,5,4] => 11 [6,1,2,4,3,5] => 10 [6,1,2,4,5,3] => 11 [6,1,2,5,3,4] => 11 [6,1,2,5,4,3] => 15 [6,1,3,2,4,5] => 9 [6,1,3,2,5,4] => 14 [6,1,3,4,2,5] => 10 [6,1,3,4,5,2] => 11 [6,1,3,5,2,4] => 11 [6,1,3,5,4,2] => 15 [6,1,4,2,3,5] => 10 [6,1,4,2,5,3] => 15 [6,1,4,3,2,5] => 13 [6,1,4,3,5,2] => 15 [6,1,4,5,2,3] => 11 [6,1,4,5,3,2] => 14 [6,1,5,2,3,4] => 11 [6,1,5,2,4,3] => 15 [6,1,5,3,2,4] => 14 [6,1,5,3,4,2] => 15 [6,1,5,4,2,3] => 15 [6,1,5,4,3,2] => 18 [6,2,1,3,4,5] => 8 [6,2,1,3,5,4] => 13 [6,2,1,4,3,5] => 12 [6,2,1,4,5,3] => 13 [6,2,1,5,3,4] => 13 [6,2,1,5,4,3] => 17 [6,2,3,1,4,5] => 9 [6,2,3,1,5,4] => 14 [6,2,3,4,1,5] => 10 [6,2,3,4,5,1] => 11 [6,2,3,5,1,4] => 11 [6,2,3,5,4,1] => 15 [6,2,4,1,3,5] => 10 [6,2,4,1,5,3] => 15 [6,2,4,3,1,5] => 13 [6,2,4,3,5,1] => 15 [6,2,4,5,1,3] => 11 [6,2,4,5,3,1] => 14 [6,2,5,1,3,4] => 11 [6,2,5,1,4,3] => 15 [6,2,5,3,1,4] => 14 [6,2,5,3,4,1] => 15 [6,2,5,4,1,3] => 15 [6,2,5,4,3,1] => 18 [6,3,1,2,4,5] => 9 [6,3,1,2,5,4] => 14 [6,3,1,4,2,5] => 13 [6,3,1,4,5,2] => 14 [6,3,1,5,2,4] => 14 [6,3,1,5,4,2] => 18 [6,3,2,1,4,5] => 11 [6,3,2,1,5,4] => 16 [6,3,2,4,1,5] => 13 [6,3,2,4,5,1] => 14 [6,3,2,5,1,4] => 14 [6,3,2,5,4,1] => 18 [6,3,4,1,2,5] => 10 [6,3,4,1,5,2] => 15 [6,3,4,2,1,5] => 12 [6,3,4,2,5,1] => 15 [6,3,4,5,1,2] => 11 [6,3,4,5,2,1] => 13 [6,3,5,1,2,4] => 11 [6,3,5,1,4,2] => 15 [6,3,5,2,1,4] => 13 [6,3,5,2,4,1] => 15 [6,3,5,4,1,2] => 15 [6,3,5,4,2,1] => 17 [6,4,1,2,3,5] => 10 [6,4,1,2,5,3] => 15 [6,4,1,3,2,5] => 13 [6,4,1,3,5,2] => 15 [6,4,1,5,2,3] => 15 [6,4,1,5,3,2] => 18 [6,4,2,1,3,5] => 12 [6,4,2,1,5,3] => 17 [6,4,2,3,1,5] => 13 [6,4,2,3,5,1] => 15 [6,4,2,5,1,3] => 15 [6,4,2,5,3,1] => 18 [6,4,3,1,2,5] => 13 [6,4,3,1,5,2] => 18 [6,4,3,2,1,5] => 15 [6,4,3,2,5,1] => 18 [6,4,3,5,1,2] => 15 [6,4,3,5,2,1] => 17 [6,4,5,1,2,3] => 11 [6,4,5,1,3,2] => 14 [6,4,5,2,1,3] => 13 [6,4,5,2,3,1] => 14 [6,4,5,3,1,2] => 14 [6,4,5,3,2,1] => 16 [6,5,1,2,3,4] => 11 [6,5,1,2,4,3] => 15 [6,5,1,3,2,4] => 14 [6,5,1,3,4,2] => 15 [6,5,1,4,2,3] => 15 [6,5,1,4,3,2] => 18 [6,5,2,1,3,4] => 13 [6,5,2,1,4,3] => 17 [6,5,2,3,1,4] => 14 [6,5,2,3,4,1] => 15 [6,5,2,4,1,3] => 15 [6,5,2,4,3,1] => 18 [6,5,3,1,2,4] => 14 [6,5,3,1,4,2] => 18 [6,5,3,2,1,4] => 16 [6,5,3,2,4,1] => 18 [6,5,3,4,1,2] => 15 [6,5,3,4,2,1] => 17 [6,5,4,1,2,3] => 15 [6,5,4,1,3,2] => 18 [6,5,4,2,1,3] => 17 [6,5,4,2,3,1] => 18 [6,5,4,3,1,2] => 18 [6,5,4,3,2,1] => 20 ----------------------------------------------------------------------------- Created: Jun 15, 2013 at 13:31 by Chris Berg ----------------------------------------------------------------------------- Last Updated: Apr 06, 2016 at 06:56 by Martin Rubey