***************************************************************************** * 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: St000056 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The decomposition (or block) number of a permutation. For $\pi \in \mathcal{S}_n$, this is given by $$\#\big\{ 1 \leq k \leq n : \{\pi_1,\ldots,\pi_k\} = \{1,\ldots,k\} \big\}.$$ This is also known as the number of connected components [1] or the number of blocks [2] of the permutation, considering it as a direct sum. This is one plus [[St000234]]. ----------------------------------------------------------------------------- References: [1] Callan, D. Counting stabilized-interval-free permutations [[MathSciNet:2049703]] [[arXiv:math/0310157]] [2] Adin, R. M., Bagno, E., Roichman, Y. Block decomposition of permutations and Schur-positivity [[arXiv:1611.06979]] [3] Stanley, R. P. The Descent Set and Connectivity Set of a Permutation [[arXiv:math/0507224]] ----------------------------------------------------------------------------- Code: def statistic(pi): return len([i for i in [1..pi.size()] if sorted(pi[j] for j in range(i)) == [1..i]]) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [1,2] => 2 [2,1] => 1 [1,2,3] => 3 [1,3,2] => 2 [2,1,3] => 2 [2,3,1] => 1 [3,1,2] => 1 [3,2,1] => 1 [1,2,3,4] => 4 [1,2,4,3] => 3 [1,3,2,4] => 3 [1,3,4,2] => 2 [1,4,2,3] => 2 [1,4,3,2] => 2 [2,1,3,4] => 3 [2,1,4,3] => 2 [2,3,1,4] => 2 [2,3,4,1] => 1 [2,4,1,3] => 1 [2,4,3,1] => 1 [3,1,2,4] => 2 [3,1,4,2] => 1 [3,2,1,4] => 2 [3,2,4,1] => 1 [3,4,1,2] => 1 [3,4,2,1] => 1 [4,1,2,3] => 1 [4,1,3,2] => 1 [4,2,1,3] => 1 [4,2,3,1] => 1 [4,3,1,2] => 1 [4,3,2,1] => 1 [1,2,3,4,5] => 5 [1,2,3,5,4] => 4 [1,2,4,3,5] => 4 [1,2,4,5,3] => 3 [1,2,5,3,4] => 3 [1,2,5,4,3] => 3 [1,3,2,4,5] => 4 [1,3,2,5,4] => 3 [1,3,4,2,5] => 3 [1,3,4,5,2] => 2 [1,3,5,2,4] => 2 [1,3,5,4,2] => 2 [1,4,2,3,5] => 3 [1,4,2,5,3] => 2 [1,4,3,2,5] => 3 [1,4,3,5,2] => 2 [1,4,5,2,3] => 2 [1,4,5,3,2] => 2 [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] => 2 [2,1,3,4,5] => 4 [2,1,3,5,4] => 3 [2,1,4,3,5] => 3 [2,1,4,5,3] => 2 [2,1,5,3,4] => 2 [2,1,5,4,3] => 2 [2,3,1,4,5] => 3 [2,3,1,5,4] => 2 [2,3,4,1,5] => 2 [2,3,4,5,1] => 1 [2,3,5,1,4] => 1 [2,3,5,4,1] => 1 [2,4,1,3,5] => 2 [2,4,1,5,3] => 1 [2,4,3,1,5] => 2 [2,4,3,5,1] => 1 [2,4,5,1,3] => 1 [2,4,5,3,1] => 1 [2,5,1,3,4] => 1 [2,5,1,4,3] => 1 [2,5,3,1,4] => 1 [2,5,3,4,1] => 1 [2,5,4,1,3] => 1 [2,5,4,3,1] => 1 [3,1,2,4,5] => 3 [3,1,2,5,4] => 2 [3,1,4,2,5] => 2 [3,1,4,5,2] => 1 [3,1,5,2,4] => 1 [3,1,5,4,2] => 1 [3,2,1,4,5] => 3 [3,2,1,5,4] => 2 [3,2,4,1,5] => 2 [3,2,4,5,1] => 1 [3,2,5,1,4] => 1 [3,2,5,4,1] => 1 [3,4,1,2,5] => 2 [3,4,1,5,2] => 1 [3,4,2,1,5] => 2 [3,4,2,5,1] => 1 [3,4,5,1,2] => 1 [3,4,5,2,1] => 1 [3,5,1,2,4] => 1 [3,5,1,4,2] => 1 [3,5,2,1,4] => 1 [3,5,2,4,1] => 1 [3,5,4,1,2] => 1 [3,5,4,2,1] => 1 [4,1,2,3,5] => 2 [4,1,2,5,3] => 1 [4,1,3,2,5] => 2 [4,1,3,5,2] => 1 [4,1,5,2,3] => 1 [4,1,5,3,2] => 1 [4,2,1,3,5] => 2 [4,2,1,5,3] => 1 [4,2,3,1,5] => 2 [4,2,3,5,1] => 1 [4,2,5,1,3] => 1 [4,2,5,3,1] => 1 [4,3,1,2,5] => 2 [4,3,1,5,2] => 1 [4,3,2,1,5] => 2 [4,3,2,5,1] => 1 [4,3,5,1,2] => 1 [4,3,5,2,1] => 1 [4,5,1,2,3] => 1 [4,5,1,3,2] => 1 [4,5,2,1,3] => 1 [4,5,2,3,1] => 1 [4,5,3,1,2] => 1 [4,5,3,2,1] => 1 [5,1,2,3,4] => 1 [5,1,2,4,3] => 1 [5,1,3,2,4] => 1 [5,1,3,4,2] => 1 [5,1,4,2,3] => 1 [5,1,4,3,2] => 1 [5,2,1,3,4] => 1 [5,2,1,4,3] => 1 [5,2,3,1,4] => 1 [5,2,3,4,1] => 1 [5,2,4,1,3] => 1 [5,2,4,3,1] => 1 [5,3,1,2,4] => 1 [5,3,1,4,2] => 1 [5,3,2,1,4] => 1 [5,3,2,4,1] => 1 [5,3,4,1,2] => 1 [5,3,4,2,1] => 1 [5,4,1,2,3] => 1 [5,4,1,3,2] => 1 [5,4,2,1,3] => 1 [5,4,2,3,1] => 1 [5,4,3,1,2] => 1 [5,4,3,2,1] => 1 [1,2,3,4,5,6] => 6 [1,2,3,4,6,5] => 5 [1,2,3,5,4,6] => 5 [1,2,3,5,6,4] => 4 [1,2,3,6,4,5] => 4 [1,2,3,6,5,4] => 4 [1,2,4,3,5,6] => 5 [1,2,4,3,6,5] => 4 [1,2,4,5,3,6] => 4 [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] => 4 [1,2,5,3,6,4] => 3 [1,2,5,4,3,6] => 4 [1,2,5,4,6,3] => 3 [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] => 3 [1,2,6,4,3,5] => 3 [1,2,6,4,5,3] => 3 [1,2,6,5,3,4] => 3 [1,2,6,5,4,3] => 3 [1,3,2,4,5,6] => 5 [1,3,2,4,6,5] => 4 [1,3,2,5,4,6] => 4 [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] => 4 [1,3,4,2,6,5] => 3 [1,3,4,5,2,6] => 3 [1,3,4,5,6,2] => 2 [1,3,4,6,2,5] => 2 [1,3,4,6,5,2] => 2 [1,3,5,2,4,6] => 3 [1,3,5,2,6,4] => 2 [1,3,5,4,2,6] => 3 [1,3,5,4,6,2] => 2 [1,3,5,6,2,4] => 2 [1,3,5,6,4,2] => 2 [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] => 2 [1,4,2,3,5,6] => 4 [1,4,2,3,6,5] => 3 [1,4,2,5,3,6] => 3 [1,4,2,5,6,3] => 2 [1,4,2,6,3,5] => 2 [1,4,2,6,5,3] => 2 [1,4,3,2,5,6] => 4 [1,4,3,2,6,5] => 3 [1,4,3,5,2,6] => 3 [1,4,3,5,6,2] => 2 [1,4,3,6,2,5] => 2 [1,4,3,6,5,2] => 2 [1,4,5,2,3,6] => 3 [1,4,5,2,6,3] => 2 [1,4,5,3,2,6] => 3 [1,4,5,3,6,2] => 2 [1,4,5,6,2,3] => 2 [1,4,5,6,3,2] => 2 [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] => 2 [1,5,2,3,4,6] => 3 [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] => 2 [1,5,2,6,4,3] => 2 [1,5,3,2,4,6] => 3 [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] => 2 [1,5,3,6,4,2] => 2 [1,5,4,2,3,6] => 3 [1,5,4,2,6,3] => 2 [1,5,4,3,2,6] => 3 [1,5,4,3,6,2] => 2 [1,5,4,6,2,3] => 2 [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] => 2 [1,6,2,3,4,5] => 2 [1,6,2,3,5,4] => 2 [1,6,2,4,3,5] => 2 [1,6,2,4,5,3] => 2 [1,6,2,5,3,4] => 2 [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] => 2 [1,6,3,4,5,2] => 2 [1,6,3,5,2,4] => 2 [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] => 2 [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] => 2 [2,1,3,4,5,6] => 5 [2,1,3,4,6,5] => 4 [2,1,3,5,4,6] => 4 [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] => 4 [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] => 2 [2,1,4,6,5,3] => 2 [2,1,5,3,4,6] => 3 [2,1,5,3,6,4] => 2 [2,1,5,4,3,6] => 3 [2,1,5,4,6,3] => 2 [2,1,5,6,3,4] => 2 [2,1,5,6,4,3] => 2 [2,1,6,3,4,5] => 2 [2,1,6,3,5,4] => 2 [2,1,6,4,3,5] => 2 [2,1,6,4,5,3] => 2 [2,1,6,5,3,4] => 2 [2,1,6,5,4,3] => 2 [2,3,1,4,5,6] => 4 [2,3,1,4,6,5] => 3 [2,3,1,5,4,6] => 3 [2,3,1,5,6,4] => 2 [2,3,1,6,4,5] => 2 [2,3,1,6,5,4] => 2 [2,3,4,1,5,6] => 3 [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] => 1 [2,3,4,6,5,1] => 1 [2,3,5,1,4,6] => 2 [2,3,5,1,6,4] => 1 [2,3,5,4,1,6] => 2 [2,3,5,4,6,1] => 1 [2,3,5,6,1,4] => 1 [2,3,5,6,4,1] => 1 [2,3,6,1,4,5] => 1 [2,3,6,1,5,4] => 1 [2,3,6,4,1,5] => 1 [2,3,6,4,5,1] => 1 [2,3,6,5,1,4] => 1 [2,3,6,5,4,1] => 1 [2,4,1,3,5,6] => 3 [2,4,1,3,6,5] => 2 [2,4,1,5,3,6] => 2 [2,4,1,5,6,3] => 1 [2,4,1,6,3,5] => 1 [2,4,1,6,5,3] => 1 [2,4,3,1,5,6] => 3 [2,4,3,1,6,5] => 2 [2,4,3,5,1,6] => 2 [2,4,3,5,6,1] => 1 [2,4,3,6,1,5] => 1 [2,4,3,6,5,1] => 1 [2,4,5,1,3,6] => 2 [2,4,5,1,6,3] => 1 [2,4,5,3,1,6] => 2 [2,4,5,3,6,1] => 1 [2,4,5,6,1,3] => 1 [2,4,5,6,3,1] => 1 [2,4,6,1,3,5] => 1 [2,4,6,1,5,3] => 1 [2,4,6,3,1,5] => 1 [2,4,6,3,5,1] => 1 [2,4,6,5,1,3] => 1 [2,4,6,5,3,1] => 1 [2,5,1,3,4,6] => 2 [2,5,1,3,6,4] => 1 [2,5,1,4,3,6] => 2 [2,5,1,4,6,3] => 1 [2,5,1,6,3,4] => 1 [2,5,1,6,4,3] => 1 [2,5,3,1,4,6] => 2 [2,5,3,1,6,4] => 1 [2,5,3,4,1,6] => 2 [2,5,3,4,6,1] => 1 [2,5,3,6,1,4] => 1 [2,5,3,6,4,1] => 1 [2,5,4,1,3,6] => 2 [2,5,4,1,6,3] => 1 [2,5,4,3,1,6] => 2 [2,5,4,3,6,1] => 1 [2,5,4,6,1,3] => 1 [2,5,4,6,3,1] => 1 [2,5,6,1,3,4] => 1 [2,5,6,1,4,3] => 1 [2,5,6,3,1,4] => 1 [2,5,6,3,4,1] => 1 [2,5,6,4,1,3] => 1 [2,5,6,4,3,1] => 1 [2,6,1,3,4,5] => 1 [2,6,1,3,5,4] => 1 [2,6,1,4,3,5] => 1 [2,6,1,4,5,3] => 1 [2,6,1,5,3,4] => 1 [2,6,1,5,4,3] => 1 [2,6,3,1,4,5] => 1 [2,6,3,1,5,4] => 1 [2,6,3,4,1,5] => 1 [2,6,3,4,5,1] => 1 [2,6,3,5,1,4] => 1 [2,6,3,5,4,1] => 1 [2,6,4,1,3,5] => 1 [2,6,4,1,5,3] => 1 [2,6,4,3,1,5] => 1 [2,6,4,3,5,1] => 1 [2,6,4,5,1,3] => 1 [2,6,4,5,3,1] => 1 [2,6,5,1,3,4] => 1 [2,6,5,1,4,3] => 1 [2,6,5,3,1,4] => 1 [2,6,5,3,4,1] => 1 [2,6,5,4,1,3] => 1 [2,6,5,4,3,1] => 1 [3,1,2,4,5,6] => 4 [3,1,2,4,6,5] => 3 [3,1,2,5,4,6] => 3 [3,1,2,5,6,4] => 2 [3,1,2,6,4,5] => 2 [3,1,2,6,5,4] => 2 [3,1,4,2,5,6] => 3 [3,1,4,2,6,5] => 2 [3,1,4,5,2,6] => 2 [3,1,4,5,6,2] => 1 [3,1,4,6,2,5] => 1 [3,1,4,6,5,2] => 1 [3,1,5,2,4,6] => 2 [3,1,5,2,6,4] => 1 [3,1,5,4,2,6] => 2 [3,1,5,4,6,2] => 1 [3,1,5,6,2,4] => 1 [3,1,5,6,4,2] => 1 [3,1,6,2,4,5] => 1 [3,1,6,2,5,4] => 1 [3,1,6,4,2,5] => 1 [3,1,6,4,5,2] => 1 [3,1,6,5,2,4] => 1 [3,1,6,5,4,2] => 1 [3,2,1,4,5,6] => 4 [3,2,1,4,6,5] => 3 [3,2,1,5,4,6] => 3 [3,2,1,5,6,4] => 2 [3,2,1,6,4,5] => 2 [3,2,1,6,5,4] => 2 [3,2,4,1,5,6] => 3 [3,2,4,1,6,5] => 2 [3,2,4,5,1,6] => 2 [3,2,4,5,6,1] => 1 [3,2,4,6,1,5] => 1 [3,2,4,6,5,1] => 1 [3,2,5,1,4,6] => 2 [3,2,5,1,6,4] => 1 [3,2,5,4,1,6] => 2 [3,2,5,4,6,1] => 1 [3,2,5,6,1,4] => 1 [3,2,5,6,4,1] => 1 [3,2,6,1,4,5] => 1 [3,2,6,1,5,4] => 1 [3,2,6,4,1,5] => 1 [3,2,6,4,5,1] => 1 [3,2,6,5,1,4] => 1 [3,2,6,5,4,1] => 1 [3,4,1,2,5,6] => 3 [3,4,1,2,6,5] => 2 [3,4,1,5,2,6] => 2 [3,4,1,5,6,2] => 1 [3,4,1,6,2,5] => 1 [3,4,1,6,5,2] => 1 [3,4,2,1,5,6] => 3 [3,4,2,1,6,5] => 2 [3,4,2,5,1,6] => 2 [3,4,2,5,6,1] => 1 [3,4,2,6,1,5] => 1 [3,4,2,6,5,1] => 1 [3,4,5,1,2,6] => 2 [3,4,5,1,6,2] => 1 [3,4,5,2,1,6] => 2 [3,4,5,2,6,1] => 1 [3,4,5,6,1,2] => 1 [3,4,5,6,2,1] => 1 [3,4,6,1,2,5] => 1 [3,4,6,1,5,2] => 1 [3,4,6,2,1,5] => 1 [3,4,6,2,5,1] => 1 [3,4,6,5,1,2] => 1 [3,4,6,5,2,1] => 1 [3,5,1,2,4,6] => 2 [3,5,1,2,6,4] => 1 [3,5,1,4,2,6] => 2 [3,5,1,4,6,2] => 1 [3,5,1,6,2,4] => 1 [3,5,1,6,4,2] => 1 [3,5,2,1,4,6] => 2 [3,5,2,1,6,4] => 1 [3,5,2,4,1,6] => 2 [3,5,2,4,6,1] => 1 [3,5,2,6,1,4] => 1 [3,5,2,6,4,1] => 1 [3,5,4,1,2,6] => 2 [3,5,4,1,6,2] => 1 [3,5,4,2,1,6] => 2 [3,5,4,2,6,1] => 1 [3,5,4,6,1,2] => 1 [3,5,4,6,2,1] => 1 [3,5,6,1,2,4] => 1 [3,5,6,1,4,2] => 1 [3,5,6,2,1,4] => 1 [3,5,6,2,4,1] => 1 [3,5,6,4,1,2] => 1 [3,5,6,4,2,1] => 1 [3,6,1,2,4,5] => 1 [3,6,1,2,5,4] => 1 [3,6,1,4,2,5] => 1 [3,6,1,4,5,2] => 1 [3,6,1,5,2,4] => 1 [3,6,1,5,4,2] => 1 [3,6,2,1,4,5] => 1 [3,6,2,1,5,4] => 1 [3,6,2,4,1,5] => 1 [3,6,2,4,5,1] => 1 [3,6,2,5,1,4] => 1 [3,6,2,5,4,1] => 1 [3,6,4,1,2,5] => 1 [3,6,4,1,5,2] => 1 [3,6,4,2,1,5] => 1 [3,6,4,2,5,1] => 1 [3,6,4,5,1,2] => 1 [3,6,4,5,2,1] => 1 [3,6,5,1,2,4] => 1 [3,6,5,1,4,2] => 1 [3,6,5,2,1,4] => 1 [3,6,5,2,4,1] => 1 [3,6,5,4,1,2] => 1 [3,6,5,4,2,1] => 1 [4,1,2,3,5,6] => 3 [4,1,2,3,6,5] => 2 [4,1,2,5,3,6] => 2 [4,1,2,5,6,3] => 1 [4,1,2,6,3,5] => 1 [4,1,2,6,5,3] => 1 [4,1,3,2,5,6] => 3 [4,1,3,2,6,5] => 2 [4,1,3,5,2,6] => 2 [4,1,3,5,6,2] => 1 [4,1,3,6,2,5] => 1 [4,1,3,6,5,2] => 1 [4,1,5,2,3,6] => 2 [4,1,5,2,6,3] => 1 [4,1,5,3,2,6] => 2 [4,1,5,3,6,2] => 1 [4,1,5,6,2,3] => 1 [4,1,5,6,3,2] => 1 [4,1,6,2,3,5] => 1 [4,1,6,2,5,3] => 1 [4,1,6,3,2,5] => 1 [4,1,6,3,5,2] => 1 [4,1,6,5,2,3] => 1 [4,1,6,5,3,2] => 1 [4,2,1,3,5,6] => 3 [4,2,1,3,6,5] => 2 [4,2,1,5,3,6] => 2 [4,2,1,5,6,3] => 1 [4,2,1,6,3,5] => 1 [4,2,1,6,5,3] => 1 [4,2,3,1,5,6] => 3 [4,2,3,1,6,5] => 2 [4,2,3,5,1,6] => 2 [4,2,3,5,6,1] => 1 [4,2,3,6,1,5] => 1 [4,2,3,6,5,1] => 1 [4,2,5,1,3,6] => 2 [4,2,5,1,6,3] => 1 [4,2,5,3,1,6] => 2 [4,2,5,3,6,1] => 1 [4,2,5,6,1,3] => 1 [4,2,5,6,3,1] => 1 [4,2,6,1,3,5] => 1 [4,2,6,1,5,3] => 1 [4,2,6,3,1,5] => 1 [4,2,6,3,5,1] => 1 [4,2,6,5,1,3] => 1 [4,2,6,5,3,1] => 1 [4,3,1,2,5,6] => 3 [4,3,1,2,6,5] => 2 [4,3,1,5,2,6] => 2 [4,3,1,5,6,2] => 1 [4,3,1,6,2,5] => 1 [4,3,1,6,5,2] => 1 [4,3,2,1,5,6] => 3 [4,3,2,1,6,5] => 2 [4,3,2,5,1,6] => 2 [4,3,2,5,6,1] => 1 [4,3,2,6,1,5] => 1 [4,3,2,6,5,1] => 1 [4,3,5,1,2,6] => 2 [4,3,5,1,6,2] => 1 [4,3,5,2,1,6] => 2 [4,3,5,2,6,1] => 1 [4,3,5,6,1,2] => 1 [4,3,5,6,2,1] => 1 [4,3,6,1,2,5] => 1 [4,3,6,1,5,2] => 1 [4,3,6,2,1,5] => 1 [4,3,6,2,5,1] => 1 [4,3,6,5,1,2] => 1 [4,3,6,5,2,1] => 1 [4,5,1,2,3,6] => 2 [4,5,1,2,6,3] => 1 [4,5,1,3,2,6] => 2 [4,5,1,3,6,2] => 1 [4,5,1,6,2,3] => 1 [4,5,1,6,3,2] => 1 [4,5,2,1,3,6] => 2 [4,5,2,1,6,3] => 1 [4,5,2,3,1,6] => 2 [4,5,2,3,6,1] => 1 [4,5,2,6,1,3] => 1 [4,5,2,6,3,1] => 1 [4,5,3,1,2,6] => 2 [4,5,3,1,6,2] => 1 [4,5,3,2,1,6] => 2 [4,5,3,2,6,1] => 1 [4,5,3,6,1,2] => 1 [4,5,3,6,2,1] => 1 [4,5,6,1,2,3] => 1 [4,5,6,1,3,2] => 1 [4,5,6,2,1,3] => 1 [4,5,6,2,3,1] => 1 [4,5,6,3,1,2] => 1 [4,5,6,3,2,1] => 1 [4,6,1,2,3,5] => 1 [4,6,1,2,5,3] => 1 [4,6,1,3,2,5] => 1 [4,6,1,3,5,2] => 1 [4,6,1,5,2,3] => 1 [4,6,1,5,3,2] => 1 [4,6,2,1,3,5] => 1 [4,6,2,1,5,3] => 1 [4,6,2,3,1,5] => 1 [4,6,2,3,5,1] => 1 [4,6,2,5,1,3] => 1 [4,6,2,5,3,1] => 1 [4,6,3,1,2,5] => 1 [4,6,3,1,5,2] => 1 [4,6,3,2,1,5] => 1 [4,6,3,2,5,1] => 1 [4,6,3,5,1,2] => 1 [4,6,3,5,2,1] => 1 [4,6,5,1,2,3] => 1 [4,6,5,1,3,2] => 1 [4,6,5,2,1,3] => 1 [4,6,5,2,3,1] => 1 [4,6,5,3,1,2] => 1 [4,6,5,3,2,1] => 1 [5,1,2,3,4,6] => 2 [5,1,2,3,6,4] => 1 [5,1,2,4,3,6] => 2 [5,1,2,4,6,3] => 1 [5,1,2,6,3,4] => 1 [5,1,2,6,4,3] => 1 [5,1,3,2,4,6] => 2 [5,1,3,2,6,4] => 1 [5,1,3,4,2,6] => 2 [5,1,3,4,6,2] => 1 [5,1,3,6,2,4] => 1 [5,1,3,6,4,2] => 1 [5,1,4,2,3,6] => 2 [5,1,4,2,6,3] => 1 [5,1,4,3,2,6] => 2 [5,1,4,3,6,2] => 1 [5,1,4,6,2,3] => 1 [5,1,4,6,3,2] => 1 [5,1,6,2,3,4] => 1 [5,1,6,2,4,3] => 1 [5,1,6,3,2,4] => 1 [5,1,6,3,4,2] => 1 [5,1,6,4,2,3] => 1 [5,1,6,4,3,2] => 1 [5,2,1,3,4,6] => 2 [5,2,1,3,6,4] => 1 [5,2,1,4,3,6] => 2 [5,2,1,4,6,3] => 1 [5,2,1,6,3,4] => 1 [5,2,1,6,4,3] => 1 [5,2,3,1,4,6] => 2 [5,2,3,1,6,4] => 1 [5,2,3,4,1,6] => 2 [5,2,3,4,6,1] => 1 [5,2,3,6,1,4] => 1 [5,2,3,6,4,1] => 1 [5,2,4,1,3,6] => 2 [5,2,4,1,6,3] => 1 [5,2,4,3,1,6] => 2 [5,2,4,3,6,1] => 1 [5,2,4,6,1,3] => 1 [5,2,4,6,3,1] => 1 [5,2,6,1,3,4] => 1 [5,2,6,1,4,3] => 1 [5,2,6,3,1,4] => 1 [5,2,6,3,4,1] => 1 [5,2,6,4,1,3] => 1 [5,2,6,4,3,1] => 1 [5,3,1,2,4,6] => 2 [5,3,1,2,6,4] => 1 [5,3,1,4,2,6] => 2 [5,3,1,4,6,2] => 1 [5,3,1,6,2,4] => 1 [5,3,1,6,4,2] => 1 [5,3,2,1,4,6] => 2 [5,3,2,1,6,4] => 1 [5,3,2,4,1,6] => 2 [5,3,2,4,6,1] => 1 [5,3,2,6,1,4] => 1 [5,3,2,6,4,1] => 1 [5,3,4,1,2,6] => 2 [5,3,4,1,6,2] => 1 [5,3,4,2,1,6] => 2 [5,3,4,2,6,1] => 1 [5,3,4,6,1,2] => 1 [5,3,4,6,2,1] => 1 [5,3,6,1,2,4] => 1 [5,3,6,1,4,2] => 1 [5,3,6,2,1,4] => 1 [5,3,6,2,4,1] => 1 [5,3,6,4,1,2] => 1 [5,3,6,4,2,1] => 1 [5,4,1,2,3,6] => 2 [5,4,1,2,6,3] => 1 [5,4,1,3,2,6] => 2 [5,4,1,3,6,2] => 1 [5,4,1,6,2,3] => 1 [5,4,1,6,3,2] => 1 [5,4,2,1,3,6] => 2 [5,4,2,1,6,3] => 1 [5,4,2,3,1,6] => 2 [5,4,2,3,6,1] => 1 [5,4,2,6,1,3] => 1 [5,4,2,6,3,1] => 1 [5,4,3,1,2,6] => 2 [5,4,3,1,6,2] => 1 [5,4,3,2,1,6] => 2 [5,4,3,2,6,1] => 1 [5,4,3,6,1,2] => 1 [5,4,3,6,2,1] => 1 [5,4,6,1,2,3] => 1 [5,4,6,1,3,2] => 1 [5,4,6,2,1,3] => 1 [5,4,6,2,3,1] => 1 [5,4,6,3,1,2] => 1 [5,4,6,3,2,1] => 1 [5,6,1,2,3,4] => 1 [5,6,1,2,4,3] => 1 [5,6,1,3,2,4] => 1 [5,6,1,3,4,2] => 1 [5,6,1,4,2,3] => 1 [5,6,1,4,3,2] => 1 [5,6,2,1,3,4] => 1 [5,6,2,1,4,3] => 1 [5,6,2,3,1,4] => 1 [5,6,2,3,4,1] => 1 [5,6,2,4,1,3] => 1 [5,6,2,4,3,1] => 1 [5,6,3,1,2,4] => 1 [5,6,3,1,4,2] => 1 [5,6,3,2,1,4] => 1 [5,6,3,2,4,1] => 1 [5,6,3,4,1,2] => 1 [5,6,3,4,2,1] => 1 [5,6,4,1,2,3] => 1 [5,6,4,1,3,2] => 1 [5,6,4,2,1,3] => 1 [5,6,4,2,3,1] => 1 [5,6,4,3,1,2] => 1 [5,6,4,3,2,1] => 1 [6,1,2,3,4,5] => 1 [6,1,2,3,5,4] => 1 [6,1,2,4,3,5] => 1 [6,1,2,4,5,3] => 1 [6,1,2,5,3,4] => 1 [6,1,2,5,4,3] => 1 [6,1,3,2,4,5] => 1 [6,1,3,2,5,4] => 1 [6,1,3,4,2,5] => 1 [6,1,3,4,5,2] => 1 [6,1,3,5,2,4] => 1 [6,1,3,5,4,2] => 1 [6,1,4,2,3,5] => 1 [6,1,4,2,5,3] => 1 [6,1,4,3,2,5] => 1 [6,1,4,3,5,2] => 1 [6,1,4,5,2,3] => 1 [6,1,4,5,3,2] => 1 [6,1,5,2,3,4] => 1 [6,1,5,2,4,3] => 1 [6,1,5,3,2,4] => 1 [6,1,5,3,4,2] => 1 [6,1,5,4,2,3] => 1 [6,1,5,4,3,2] => 1 [6,2,1,3,4,5] => 1 [6,2,1,3,5,4] => 1 [6,2,1,4,3,5] => 1 [6,2,1,4,5,3] => 1 [6,2,1,5,3,4] => 1 [6,2,1,5,4,3] => 1 [6,2,3,1,4,5] => 1 [6,2,3,1,5,4] => 1 [6,2,3,4,1,5] => 1 [6,2,3,4,5,1] => 1 [6,2,3,5,1,4] => 1 [6,2,3,5,4,1] => 1 [6,2,4,1,3,5] => 1 [6,2,4,1,5,3] => 1 [6,2,4,3,1,5] => 1 [6,2,4,3,5,1] => 1 [6,2,4,5,1,3] => 1 [6,2,4,5,3,1] => 1 [6,2,5,1,3,4] => 1 [6,2,5,1,4,3] => 1 [6,2,5,3,1,4] => 1 [6,2,5,3,4,1] => 1 [6,2,5,4,1,3] => 1 [6,2,5,4,3,1] => 1 [6,3,1,2,4,5] => 1 [6,3,1,2,5,4] => 1 [6,3,1,4,2,5] => 1 [6,3,1,4,5,2] => 1 [6,3,1,5,2,4] => 1 [6,3,1,5,4,2] => 1 [6,3,2,1,4,5] => 1 [6,3,2,1,5,4] => 1 [6,3,2,4,1,5] => 1 [6,3,2,4,5,1] => 1 [6,3,2,5,1,4] => 1 [6,3,2,5,4,1] => 1 [6,3,4,1,2,5] => 1 [6,3,4,1,5,2] => 1 [6,3,4,2,1,5] => 1 [6,3,4,2,5,1] => 1 [6,3,4,5,1,2] => 1 [6,3,4,5,2,1] => 1 [6,3,5,1,2,4] => 1 [6,3,5,1,4,2] => 1 [6,3,5,2,1,4] => 1 [6,3,5,2,4,1] => 1 [6,3,5,4,1,2] => 1 [6,3,5,4,2,1] => 1 [6,4,1,2,3,5] => 1 [6,4,1,2,5,3] => 1 [6,4,1,3,2,5] => 1 [6,4,1,3,5,2] => 1 [6,4,1,5,2,3] => 1 [6,4,1,5,3,2] => 1 [6,4,2,1,3,5] => 1 [6,4,2,1,5,3] => 1 [6,4,2,3,1,5] => 1 [6,4,2,3,5,1] => 1 [6,4,2,5,1,3] => 1 [6,4,2,5,3,1] => 1 [6,4,3,1,2,5] => 1 [6,4,3,1,5,2] => 1 [6,4,3,2,1,5] => 1 [6,4,3,2,5,1] => 1 [6,4,3,5,1,2] => 1 [6,4,3,5,2,1] => 1 [6,4,5,1,2,3] => 1 [6,4,5,1,3,2] => 1 [6,4,5,2,1,3] => 1 [6,4,5,2,3,1] => 1 [6,4,5,3,1,2] => 1 [6,4,5,3,2,1] => 1 [6,5,1,2,3,4] => 1 [6,5,1,2,4,3] => 1 [6,5,1,3,2,4] => 1 [6,5,1,3,4,2] => 1 [6,5,1,4,2,3] => 1 [6,5,1,4,3,2] => 1 [6,5,2,1,3,4] => 1 [6,5,2,1,4,3] => 1 [6,5,2,3,1,4] => 1 [6,5,2,3,4,1] => 1 [6,5,2,4,1,3] => 1 [6,5,2,4,3,1] => 1 [6,5,3,1,2,4] => 1 [6,5,3,1,4,2] => 1 [6,5,3,2,1,4] => 1 [6,5,3,2,4,1] => 1 [6,5,3,4,1,2] => 1 [6,5,3,4,2,1] => 1 [6,5,4,1,2,3] => 1 [6,5,4,1,3,2] => 1 [6,5,4,2,1,3] => 1 [6,5,4,2,3,1] => 1 [6,5,4,3,1,2] => 1 [6,5,4,3,2,1] => 1 ----------------------------------------------------------------------------- Created: Mar 26, 2013 at 06:07 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Jul 12, 2017 at 16:47 by Christian Stump