***************************************************************************** * 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: St000616 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The inversion index of a permutation. The ''inversion index'' of a permutation $\sigma=\sigma_1\sigma_2\ldots\sigma_n$ is defined as $$\sum_{\mbox{inversion pairs } (\sigma_i,\sigma_j)} \sigma_i$$ where $(\sigma_i,\sigma_j)$ is an inversion pair if i < j and $\sigma_i > \sigma_j$. This equals the sum of the entries in the corresponding descending plane partition; see [1]. ----------------------------------------------------------------------------- References: [1] Striker, J. A direct bijection between descending plane partitions with no special parts and permutation matrices [[arXiv:1002.3391]] [2] Irregular triangle read by rows: row n gives expansion of g.f. for descending plane partitions of order n with weight equal to sum of the parts. [[OEIS:A198890]] ----------------------------------------------------------------------------- Code: def statistic(p): return sum( p[i-1] for i,j in p.inversions() ) ----------------------------------------------------------------------------- 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] => 5 [3,1,2] => 6 [3,2,1] => 8 [1,2,3,4] => 0 [1,2,4,3] => 4 [1,3,2,4] => 3 [1,3,4,2] => 7 [1,4,2,3] => 8 [1,4,3,2] => 11 [2,1,3,4] => 2 [2,1,4,3] => 6 [2,3,1,4] => 5 [2,3,4,1] => 9 [2,4,1,3] => 10 [2,4,3,1] => 13 [3,1,2,4] => 6 [3,1,4,2] => 10 [3,2,1,4] => 8 [3,2,4,1] => 12 [3,4,1,2] => 14 [3,4,2,1] => 16 [4,1,2,3] => 12 [4,1,3,2] => 15 [4,2,1,3] => 14 [4,2,3,1] => 17 [4,3,1,2] => 18 [4,3,2,1] => 20 [1,2,3,4,5] => 0 [1,2,3,5,4] => 5 [1,2,4,3,5] => 4 [1,2,4,5,3] => 9 [1,2,5,3,4] => 10 [1,2,5,4,3] => 14 [1,3,2,4,5] => 3 [1,3,2,5,4] => 8 [1,3,4,2,5] => 7 [1,3,4,5,2] => 12 [1,3,5,2,4] => 13 [1,3,5,4,2] => 17 [1,4,2,3,5] => 8 [1,4,2,5,3] => 13 [1,4,3,2,5] => 11 [1,4,3,5,2] => 16 [1,4,5,2,3] => 18 [1,4,5,3,2] => 21 [1,5,2,3,4] => 15 [1,5,2,4,3] => 19 [1,5,3,2,4] => 18 [1,5,3,4,2] => 22 [1,5,4,2,3] => 23 [1,5,4,3,2] => 26 [2,1,3,4,5] => 2 [2,1,3,5,4] => 7 [2,1,4,3,5] => 6 [2,1,4,5,3] => 11 [2,1,5,3,4] => 12 [2,1,5,4,3] => 16 [2,3,1,4,5] => 5 [2,3,1,5,4] => 10 [2,3,4,1,5] => 9 [2,3,4,5,1] => 14 [2,3,5,1,4] => 15 [2,3,5,4,1] => 19 [2,4,1,3,5] => 10 [2,4,1,5,3] => 15 [2,4,3,1,5] => 13 [2,4,3,5,1] => 18 [2,4,5,1,3] => 20 [2,4,5,3,1] => 23 [2,5,1,3,4] => 17 [2,5,1,4,3] => 21 [2,5,3,1,4] => 20 [2,5,3,4,1] => 24 [2,5,4,1,3] => 25 [2,5,4,3,1] => 28 [3,1,2,4,5] => 6 [3,1,2,5,4] => 11 [3,1,4,2,5] => 10 [3,1,4,5,2] => 15 [3,1,5,2,4] => 16 [3,1,5,4,2] => 20 [3,2,1,4,5] => 8 [3,2,1,5,4] => 13 [3,2,4,1,5] => 12 [3,2,4,5,1] => 17 [3,2,5,1,4] => 18 [3,2,5,4,1] => 22 [3,4,1,2,5] => 14 [3,4,1,5,2] => 19 [3,4,2,1,5] => 16 [3,4,2,5,1] => 21 [3,4,5,1,2] => 24 [3,4,5,2,1] => 26 [3,5,1,2,4] => 21 [3,5,1,4,2] => 25 [3,5,2,1,4] => 23 [3,5,2,4,1] => 27 [3,5,4,1,2] => 29 [3,5,4,2,1] => 31 [4,1,2,3,5] => 12 [4,1,2,5,3] => 17 [4,1,3,2,5] => 15 [4,1,3,5,2] => 20 [4,1,5,2,3] => 22 [4,1,5,3,2] => 25 [4,2,1,3,5] => 14 [4,2,1,5,3] => 19 [4,2,3,1,5] => 17 [4,2,3,5,1] => 22 [4,2,5,1,3] => 24 [4,2,5,3,1] => 27 [4,3,1,2,5] => 18 [4,3,1,5,2] => 23 [4,3,2,1,5] => 20 [4,3,2,5,1] => 25 [4,3,5,1,2] => 28 [4,3,5,2,1] => 30 [4,5,1,2,3] => 27 [4,5,1,3,2] => 30 [4,5,2,1,3] => 29 [4,5,2,3,1] => 32 [4,5,3,1,2] => 33 [4,5,3,2,1] => 35 [5,1,2,3,4] => 20 [5,1,2,4,3] => 24 [5,1,3,2,4] => 23 [5,1,3,4,2] => 27 [5,1,4,2,3] => 28 [5,1,4,3,2] => 31 [5,2,1,3,4] => 22 [5,2,1,4,3] => 26 [5,2,3,1,4] => 25 [5,2,3,4,1] => 29 [5,2,4,1,3] => 30 [5,2,4,3,1] => 33 [5,3,1,2,4] => 26 [5,3,1,4,2] => 30 [5,3,2,1,4] => 28 [5,3,2,4,1] => 32 [5,3,4,1,2] => 34 [5,3,4,2,1] => 36 [5,4,1,2,3] => 32 [5,4,1,3,2] => 35 [5,4,2,1,3] => 34 [5,4,2,3,1] => 37 [5,4,3,1,2] => 38 [5,4,3,2,1] => 40 [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] => 11 [1,2,3,6,4,5] => 12 [1,2,3,6,5,4] => 17 [1,2,4,3,5,6] => 4 [1,2,4,3,6,5] => 10 [1,2,4,5,3,6] => 9 [1,2,4,5,6,3] => 15 [1,2,4,6,3,5] => 16 [1,2,4,6,5,3] => 21 [1,2,5,3,4,6] => 10 [1,2,5,3,6,4] => 16 [1,2,5,4,3,6] => 14 [1,2,5,4,6,3] => 20 [1,2,5,6,3,4] => 22 [1,2,5,6,4,3] => 26 [1,2,6,3,4,5] => 18 [1,2,6,3,5,4] => 23 [1,2,6,4,3,5] => 22 [1,2,6,4,5,3] => 27 [1,2,6,5,3,4] => 28 [1,2,6,5,4,3] => 32 [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] => 14 [1,3,2,6,4,5] => 15 [1,3,2,6,5,4] => 20 [1,3,4,2,5,6] => 7 [1,3,4,2,6,5] => 13 [1,3,4,5,2,6] => 12 [1,3,4,5,6,2] => 18 [1,3,4,6,2,5] => 19 [1,3,4,6,5,2] => 24 [1,3,5,2,4,6] => 13 [1,3,5,2,6,4] => 19 [1,3,5,4,2,6] => 17 [1,3,5,4,6,2] => 23 [1,3,5,6,2,4] => 25 [1,3,5,6,4,2] => 29 [1,3,6,2,4,5] => 21 [1,3,6,2,5,4] => 26 [1,3,6,4,2,5] => 25 [1,3,6,4,5,2] => 30 [1,3,6,5,2,4] => 31 [1,3,6,5,4,2] => 35 [1,4,2,3,5,6] => 8 [1,4,2,3,6,5] => 14 [1,4,2,5,3,6] => 13 [1,4,2,5,6,3] => 19 [1,4,2,6,3,5] => 20 [1,4,2,6,5,3] => 25 [1,4,3,2,5,6] => 11 [1,4,3,2,6,5] => 17 [1,4,3,5,2,6] => 16 [1,4,3,5,6,2] => 22 [1,4,3,6,2,5] => 23 [1,4,3,6,5,2] => 28 [1,4,5,2,3,6] => 18 [1,4,5,2,6,3] => 24 [1,4,5,3,2,6] => 21 [1,4,5,3,6,2] => 27 [1,4,5,6,2,3] => 30 [1,4,5,6,3,2] => 33 [1,4,6,2,3,5] => 26 [1,4,6,2,5,3] => 31 [1,4,6,3,2,5] => 29 [1,4,6,3,5,2] => 34 [1,4,6,5,2,3] => 36 [1,4,6,5,3,2] => 39 [1,5,2,3,4,6] => 15 [1,5,2,3,6,4] => 21 [1,5,2,4,3,6] => 19 [1,5,2,4,6,3] => 25 [1,5,2,6,3,4] => 27 [1,5,2,6,4,3] => 31 [1,5,3,2,4,6] => 18 [1,5,3,2,6,4] => 24 [1,5,3,4,2,6] => 22 [1,5,3,4,6,2] => 28 [1,5,3,6,2,4] => 30 [1,5,3,6,4,2] => 34 [1,5,4,2,3,6] => 23 [1,5,4,2,6,3] => 29 [1,5,4,3,2,6] => 26 [1,5,4,3,6,2] => 32 [1,5,4,6,2,3] => 35 [1,5,4,6,3,2] => 38 [1,5,6,2,3,4] => 33 [1,5,6,2,4,3] => 37 [1,5,6,3,2,4] => 36 [1,5,6,3,4,2] => 40 [1,5,6,4,2,3] => 41 [1,5,6,4,3,2] => 44 [1,6,2,3,4,5] => 24 [1,6,2,3,5,4] => 29 [1,6,2,4,3,5] => 28 [1,6,2,4,5,3] => 33 [1,6,2,5,3,4] => 34 [1,6,2,5,4,3] => 38 [1,6,3,2,4,5] => 27 [1,6,3,2,5,4] => 32 [1,6,3,4,2,5] => 31 [1,6,3,4,5,2] => 36 [1,6,3,5,2,4] => 37 [1,6,3,5,4,2] => 41 [1,6,4,2,3,5] => 32 [1,6,4,2,5,3] => 37 [1,6,4,3,2,5] => 35 [1,6,4,3,5,2] => 40 [1,6,4,5,2,3] => 42 [1,6,4,5,3,2] => 45 [1,6,5,2,3,4] => 39 [1,6,5,2,4,3] => 43 [1,6,5,3,2,4] => 42 [1,6,5,3,4,2] => 46 [1,6,5,4,2,3] => 47 [1,6,5,4,3,2] => 50 [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] => 13 [2,1,3,6,4,5] => 14 [2,1,3,6,5,4] => 19 [2,1,4,3,5,6] => 6 [2,1,4,3,6,5] => 12 [2,1,4,5,3,6] => 11 [2,1,4,5,6,3] => 17 [2,1,4,6,3,5] => 18 [2,1,4,6,5,3] => 23 [2,1,5,3,4,6] => 12 [2,1,5,3,6,4] => 18 [2,1,5,4,3,6] => 16 [2,1,5,4,6,3] => 22 [2,1,5,6,3,4] => 24 [2,1,5,6,4,3] => 28 [2,1,6,3,4,5] => 20 [2,1,6,3,5,4] => 25 [2,1,6,4,3,5] => 24 [2,1,6,4,5,3] => 29 [2,1,6,5,3,4] => 30 [2,1,6,5,4,3] => 34 [2,3,1,4,5,6] => 5 [2,3,1,4,6,5] => 11 [2,3,1,5,4,6] => 10 [2,3,1,5,6,4] => 16 [2,3,1,6,4,5] => 17 [2,3,1,6,5,4] => 22 [2,3,4,1,5,6] => 9 [2,3,4,1,6,5] => 15 [2,3,4,5,1,6] => 14 [2,3,4,5,6,1] => 20 [2,3,4,6,1,5] => 21 [2,3,4,6,5,1] => 26 [2,3,5,1,4,6] => 15 [2,3,5,1,6,4] => 21 [2,3,5,4,1,6] => 19 [2,3,5,4,6,1] => 25 [2,3,5,6,1,4] => 27 [2,3,5,6,4,1] => 31 [2,3,6,1,4,5] => 23 [2,3,6,1,5,4] => 28 [2,3,6,4,1,5] => 27 [2,3,6,4,5,1] => 32 [2,3,6,5,1,4] => 33 [2,3,6,5,4,1] => 37 [2,4,1,3,5,6] => 10 [2,4,1,3,6,5] => 16 [2,4,1,5,3,6] => 15 [2,4,1,5,6,3] => 21 [2,4,1,6,3,5] => 22 [2,4,1,6,5,3] => 27 [2,4,3,1,5,6] => 13 [2,4,3,1,6,5] => 19 [2,4,3,5,1,6] => 18 [2,4,3,5,6,1] => 24 [2,4,3,6,1,5] => 25 [2,4,3,6,5,1] => 30 [2,4,5,1,3,6] => 20 [2,4,5,1,6,3] => 26 [2,4,5,3,1,6] => 23 [2,4,5,3,6,1] => 29 [2,4,5,6,1,3] => 32 [2,4,5,6,3,1] => 35 [2,4,6,1,3,5] => 28 [2,4,6,1,5,3] => 33 [2,4,6,3,1,5] => 31 [2,4,6,3,5,1] => 36 [2,4,6,5,1,3] => 38 [2,4,6,5,3,1] => 41 [2,5,1,3,4,6] => 17 [2,5,1,3,6,4] => 23 [2,5,1,4,3,6] => 21 [2,5,1,4,6,3] => 27 [2,5,1,6,3,4] => 29 [2,5,1,6,4,3] => 33 [2,5,3,1,4,6] => 20 [2,5,3,1,6,4] => 26 [2,5,3,4,1,6] => 24 [2,5,3,4,6,1] => 30 [2,5,3,6,1,4] => 32 [2,5,3,6,4,1] => 36 [2,5,4,1,3,6] => 25 [2,5,4,1,6,3] => 31 [2,5,4,3,1,6] => 28 [2,5,4,3,6,1] => 34 [2,5,4,6,1,3] => 37 [2,5,4,6,3,1] => 40 [2,5,6,1,3,4] => 35 [2,5,6,1,4,3] => 39 [2,5,6,3,1,4] => 38 [2,5,6,3,4,1] => 42 [2,5,6,4,1,3] => 43 [2,5,6,4,3,1] => 46 [2,6,1,3,4,5] => 26 [2,6,1,3,5,4] => 31 [2,6,1,4,3,5] => 30 [2,6,1,4,5,3] => 35 [2,6,1,5,3,4] => 36 [2,6,1,5,4,3] => 40 [2,6,3,1,4,5] => 29 [2,6,3,1,5,4] => 34 [2,6,3,4,1,5] => 33 [2,6,3,4,5,1] => 38 [2,6,3,5,1,4] => 39 [2,6,3,5,4,1] => 43 [2,6,4,1,3,5] => 34 [2,6,4,1,5,3] => 39 [2,6,4,3,1,5] => 37 [2,6,4,3,5,1] => 42 [2,6,4,5,1,3] => 44 [2,6,4,5,3,1] => 47 [2,6,5,1,3,4] => 41 [2,6,5,1,4,3] => 45 [2,6,5,3,1,4] => 44 [2,6,5,3,4,1] => 48 [2,6,5,4,1,3] => 49 [2,6,5,4,3,1] => 52 [3,1,2,4,5,6] => 6 [3,1,2,4,6,5] => 12 [3,1,2,5,4,6] => 11 [3,1,2,5,6,4] => 17 [3,1,2,6,4,5] => 18 [3,1,2,6,5,4] => 23 [3,1,4,2,5,6] => 10 [3,1,4,2,6,5] => 16 [3,1,4,5,2,6] => 15 [3,1,4,5,6,2] => 21 [3,1,4,6,2,5] => 22 [3,1,4,6,5,2] => 27 [3,1,5,2,4,6] => 16 [3,1,5,2,6,4] => 22 [3,1,5,4,2,6] => 20 [3,1,5,4,6,2] => 26 [3,1,5,6,2,4] => 28 [3,1,5,6,4,2] => 32 [3,1,6,2,4,5] => 24 [3,1,6,2,5,4] => 29 [3,1,6,4,2,5] => 28 [3,1,6,4,5,2] => 33 [3,1,6,5,2,4] => 34 [3,1,6,5,4,2] => 38 [3,2,1,4,5,6] => 8 [3,2,1,4,6,5] => 14 [3,2,1,5,4,6] => 13 [3,2,1,5,6,4] => 19 [3,2,1,6,4,5] => 20 [3,2,1,6,5,4] => 25 [3,2,4,1,5,6] => 12 [3,2,4,1,6,5] => 18 [3,2,4,5,1,6] => 17 [3,2,4,5,6,1] => 23 [3,2,4,6,1,5] => 24 [3,2,4,6,5,1] => 29 [3,2,5,1,4,6] => 18 [3,2,5,1,6,4] => 24 [3,2,5,4,1,6] => 22 [3,2,5,4,6,1] => 28 [3,2,5,6,1,4] => 30 [3,2,5,6,4,1] => 34 [3,2,6,1,4,5] => 26 [3,2,6,1,5,4] => 31 [3,2,6,4,1,5] => 30 [3,2,6,4,5,1] => 35 [3,2,6,5,1,4] => 36 [3,2,6,5,4,1] => 40 [3,4,1,2,5,6] => 14 [3,4,1,2,6,5] => 20 [3,4,1,5,2,6] => 19 [3,4,1,5,6,2] => 25 [3,4,1,6,2,5] => 26 [3,4,1,6,5,2] => 31 [3,4,2,1,5,6] => 16 [3,4,2,1,6,5] => 22 [3,4,2,5,1,6] => 21 [3,4,2,5,6,1] => 27 [3,4,2,6,1,5] => 28 [3,4,2,6,5,1] => 33 [3,4,5,1,2,6] => 24 [3,4,5,1,6,2] => 30 [3,4,5,2,1,6] => 26 [3,4,5,2,6,1] => 32 [3,4,5,6,1,2] => 36 [3,4,5,6,2,1] => 38 [3,4,6,1,2,5] => 32 [3,4,6,1,5,2] => 37 [3,4,6,2,1,5] => 34 [3,4,6,2,5,1] => 39 [3,4,6,5,1,2] => 42 [3,4,6,5,2,1] => 44 [3,5,1,2,4,6] => 21 [3,5,1,2,6,4] => 27 [3,5,1,4,2,6] => 25 [3,5,1,4,6,2] => 31 [3,5,1,6,2,4] => 33 [3,5,1,6,4,2] => 37 [3,5,2,1,4,6] => 23 [3,5,2,1,6,4] => 29 [3,5,2,4,1,6] => 27 [3,5,2,4,6,1] => 33 [3,5,2,6,1,4] => 35 [3,5,2,6,4,1] => 39 [3,5,4,1,2,6] => 29 [3,5,4,1,6,2] => 35 [3,5,4,2,1,6] => 31 [3,5,4,2,6,1] => 37 [3,5,4,6,1,2] => 41 [3,5,4,6,2,1] => 43 [3,5,6,1,2,4] => 39 [3,5,6,1,4,2] => 43 [3,5,6,2,1,4] => 41 [3,5,6,2,4,1] => 45 [3,5,6,4,1,2] => 47 [3,5,6,4,2,1] => 49 [3,6,1,2,4,5] => 30 [3,6,1,2,5,4] => 35 [3,6,1,4,2,5] => 34 [3,6,1,4,5,2] => 39 [3,6,1,5,2,4] => 40 [3,6,1,5,4,2] => 44 [3,6,2,1,4,5] => 32 [3,6,2,1,5,4] => 37 [3,6,2,4,1,5] => 36 [3,6,2,4,5,1] => 41 [3,6,2,5,1,4] => 42 [3,6,2,5,4,1] => 46 [3,6,4,1,2,5] => 38 [3,6,4,1,5,2] => 43 [3,6,4,2,1,5] => 40 [3,6,4,2,5,1] => 45 [3,6,4,5,1,2] => 48 [3,6,4,5,2,1] => 50 [3,6,5,1,2,4] => 45 [3,6,5,1,4,2] => 49 [3,6,5,2,1,4] => 47 [3,6,5,2,4,1] => 51 [3,6,5,4,1,2] => 53 [3,6,5,4,2,1] => 55 [4,1,2,3,5,6] => 12 [4,1,2,3,6,5] => 18 [4,1,2,5,3,6] => 17 [4,1,2,5,6,3] => 23 [4,1,2,6,3,5] => 24 [4,1,2,6,5,3] => 29 [4,1,3,2,5,6] => 15 [4,1,3,2,6,5] => 21 [4,1,3,5,2,6] => 20 [4,1,3,5,6,2] => 26 [4,1,3,6,2,5] => 27 [4,1,3,6,5,2] => 32 [4,1,5,2,3,6] => 22 [4,1,5,2,6,3] => 28 [4,1,5,3,2,6] => 25 [4,1,5,3,6,2] => 31 [4,1,5,6,2,3] => 34 [4,1,5,6,3,2] => 37 [4,1,6,2,3,5] => 30 [4,1,6,2,5,3] => 35 [4,1,6,3,2,5] => 33 [4,1,6,3,5,2] => 38 [4,1,6,5,2,3] => 40 [4,1,6,5,3,2] => 43 [4,2,1,3,5,6] => 14 [4,2,1,3,6,5] => 20 [4,2,1,5,3,6] => 19 [4,2,1,5,6,3] => 25 [4,2,1,6,3,5] => 26 [4,2,1,6,5,3] => 31 [4,2,3,1,5,6] => 17 [4,2,3,1,6,5] => 23 [4,2,3,5,1,6] => 22 [4,2,3,5,6,1] => 28 [4,2,3,6,1,5] => 29 [4,2,3,6,5,1] => 34 [4,2,5,1,3,6] => 24 [4,2,5,1,6,3] => 30 [4,2,5,3,1,6] => 27 [4,2,5,3,6,1] => 33 [4,2,5,6,1,3] => 36 [4,2,5,6,3,1] => 39 [4,2,6,1,3,5] => 32 [4,2,6,1,5,3] => 37 [4,2,6,3,1,5] => 35 [4,2,6,3,5,1] => 40 [4,2,6,5,1,3] => 42 [4,2,6,5,3,1] => 45 [4,3,1,2,5,6] => 18 [4,3,1,2,6,5] => 24 [4,3,1,5,2,6] => 23 [4,3,1,5,6,2] => 29 [4,3,1,6,2,5] => 30 [4,3,1,6,5,2] => 35 [4,3,2,1,5,6] => 20 [4,3,2,1,6,5] => 26 [4,3,2,5,1,6] => 25 [4,3,2,5,6,1] => 31 [4,3,2,6,1,5] => 32 [4,3,2,6,5,1] => 37 [4,3,5,1,2,6] => 28 [4,3,5,1,6,2] => 34 [4,3,5,2,1,6] => 30 [4,3,5,2,6,1] => 36 [4,3,5,6,1,2] => 40 [4,3,5,6,2,1] => 42 [4,3,6,1,2,5] => 36 [4,3,6,1,5,2] => 41 [4,3,6,2,1,5] => 38 [4,3,6,2,5,1] => 43 [4,3,6,5,1,2] => 46 [4,3,6,5,2,1] => 48 [4,5,1,2,3,6] => 27 [4,5,1,2,6,3] => 33 [4,5,1,3,2,6] => 30 [4,5,1,3,6,2] => 36 [4,5,1,6,2,3] => 39 [4,5,1,6,3,2] => 42 [4,5,2,1,3,6] => 29 [4,5,2,1,6,3] => 35 [4,5,2,3,1,6] => 32 [4,5,2,3,6,1] => 38 [4,5,2,6,1,3] => 41 [4,5,2,6,3,1] => 44 [4,5,3,1,2,6] => 33 [4,5,3,1,6,2] => 39 [4,5,3,2,1,6] => 35 [4,5,3,2,6,1] => 41 [4,5,3,6,1,2] => 45 [4,5,3,6,2,1] => 47 [4,5,6,1,2,3] => 45 [4,5,6,1,3,2] => 48 [4,5,6,2,1,3] => 47 [4,5,6,2,3,1] => 50 [4,5,6,3,1,2] => 51 [4,5,6,3,2,1] => 53 [4,6,1,2,3,5] => 36 [4,6,1,2,5,3] => 41 [4,6,1,3,2,5] => 39 [4,6,1,3,5,2] => 44 [4,6,1,5,2,3] => 46 [4,6,1,5,3,2] => 49 [4,6,2,1,3,5] => 38 [4,6,2,1,5,3] => 43 [4,6,2,3,1,5] => 41 [4,6,2,3,5,1] => 46 [4,6,2,5,1,3] => 48 [4,6,2,5,3,1] => 51 [4,6,3,1,2,5] => 42 [4,6,3,1,5,2] => 47 [4,6,3,2,1,5] => 44 [4,6,3,2,5,1] => 49 [4,6,3,5,1,2] => 52 [4,6,3,5,2,1] => 54 [4,6,5,1,2,3] => 51 [4,6,5,1,3,2] => 54 [4,6,5,2,1,3] => 53 [4,6,5,2,3,1] => 56 [4,6,5,3,1,2] => 57 [4,6,5,3,2,1] => 59 [5,1,2,3,4,6] => 20 [5,1,2,3,6,4] => 26 [5,1,2,4,3,6] => 24 [5,1,2,4,6,3] => 30 [5,1,2,6,3,4] => 32 [5,1,2,6,4,3] => 36 [5,1,3,2,4,6] => 23 [5,1,3,2,6,4] => 29 [5,1,3,4,2,6] => 27 [5,1,3,4,6,2] => 33 [5,1,3,6,2,4] => 35 [5,1,3,6,4,2] => 39 [5,1,4,2,3,6] => 28 [5,1,4,2,6,3] => 34 [5,1,4,3,2,6] => 31 [5,1,4,3,6,2] => 37 [5,1,4,6,2,3] => 40 [5,1,4,6,3,2] => 43 [5,1,6,2,3,4] => 38 [5,1,6,2,4,3] => 42 [5,1,6,3,2,4] => 41 [5,1,6,3,4,2] => 45 [5,1,6,4,2,3] => 46 [5,1,6,4,3,2] => 49 [5,2,1,3,4,6] => 22 [5,2,1,3,6,4] => 28 [5,2,1,4,3,6] => 26 [5,2,1,4,6,3] => 32 [5,2,1,6,3,4] => 34 [5,2,1,6,4,3] => 38 [5,2,3,1,4,6] => 25 [5,2,3,1,6,4] => 31 [5,2,3,4,1,6] => 29 [5,2,3,4,6,1] => 35 [5,2,3,6,1,4] => 37 [5,2,3,6,4,1] => 41 [5,2,4,1,3,6] => 30 [5,2,4,1,6,3] => 36 [5,2,4,3,1,6] => 33 [5,2,4,3,6,1] => 39 [5,2,4,6,1,3] => 42 [5,2,4,6,3,1] => 45 [5,2,6,1,3,4] => 40 [5,2,6,1,4,3] => 44 [5,2,6,3,1,4] => 43 [5,2,6,3,4,1] => 47 [5,2,6,4,1,3] => 48 [5,2,6,4,3,1] => 51 [5,3,1,2,4,6] => 26 [5,3,1,2,6,4] => 32 [5,3,1,4,2,6] => 30 [5,3,1,4,6,2] => 36 [5,3,1,6,2,4] => 38 [5,3,1,6,4,2] => 42 [5,3,2,1,4,6] => 28 [5,3,2,1,6,4] => 34 [5,3,2,4,1,6] => 32 [5,3,2,4,6,1] => 38 [5,3,2,6,1,4] => 40 [5,3,2,6,4,1] => 44 [5,3,4,1,2,6] => 34 [5,3,4,1,6,2] => 40 [5,3,4,2,1,6] => 36 [5,3,4,2,6,1] => 42 [5,3,4,6,1,2] => 46 [5,3,4,6,2,1] => 48 [5,3,6,1,2,4] => 44 [5,3,6,1,4,2] => 48 [5,3,6,2,1,4] => 46 [5,3,6,2,4,1] => 50 [5,3,6,4,1,2] => 52 [5,3,6,4,2,1] => 54 [5,4,1,2,3,6] => 32 [5,4,1,2,6,3] => 38 [5,4,1,3,2,6] => 35 [5,4,1,3,6,2] => 41 [5,4,1,6,2,3] => 44 [5,4,1,6,3,2] => 47 [5,4,2,1,3,6] => 34 [5,4,2,1,6,3] => 40 [5,4,2,3,1,6] => 37 [5,4,2,3,6,1] => 43 [5,4,2,6,1,3] => 46 [5,4,2,6,3,1] => 49 [5,4,3,1,2,6] => 38 [5,4,3,1,6,2] => 44 [5,4,3,2,1,6] => 40 [5,4,3,2,6,1] => 46 [5,4,3,6,1,2] => 50 [5,4,3,6,2,1] => 52 [5,4,6,1,2,3] => 50 [5,4,6,1,3,2] => 53 [5,4,6,2,1,3] => 52 [5,4,6,2,3,1] => 55 [5,4,6,3,1,2] => 56 [5,4,6,3,2,1] => 58 [5,6,1,2,3,4] => 44 [5,6,1,2,4,3] => 48 [5,6,1,3,2,4] => 47 [5,6,1,3,4,2] => 51 [5,6,1,4,2,3] => 52 [5,6,1,4,3,2] => 55 [5,6,2,1,3,4] => 46 [5,6,2,1,4,3] => 50 [5,6,2,3,1,4] => 49 [5,6,2,3,4,1] => 53 [5,6,2,4,1,3] => 54 [5,6,2,4,3,1] => 57 [5,6,3,1,2,4] => 50 [5,6,3,1,4,2] => 54 [5,6,3,2,1,4] => 52 [5,6,3,2,4,1] => 56 [5,6,3,4,1,2] => 58 [5,6,3,4,2,1] => 60 [5,6,4,1,2,3] => 56 [5,6,4,1,3,2] => 59 [5,6,4,2,1,3] => 58 [5,6,4,2,3,1] => 61 [5,6,4,3,1,2] => 62 [5,6,4,3,2,1] => 64 [6,1,2,3,4,5] => 30 [6,1,2,3,5,4] => 35 [6,1,2,4,3,5] => 34 [6,1,2,4,5,3] => 39 [6,1,2,5,3,4] => 40 [6,1,2,5,4,3] => 44 [6,1,3,2,4,5] => 33 [6,1,3,2,5,4] => 38 [6,1,3,4,2,5] => 37 [6,1,3,4,5,2] => 42 [6,1,3,5,2,4] => 43 [6,1,3,5,4,2] => 47 [6,1,4,2,3,5] => 38 [6,1,4,2,5,3] => 43 [6,1,4,3,2,5] => 41 [6,1,4,3,5,2] => 46 [6,1,4,5,2,3] => 48 [6,1,4,5,3,2] => 51 [6,1,5,2,3,4] => 45 [6,1,5,2,4,3] => 49 [6,1,5,3,2,4] => 48 [6,1,5,3,4,2] => 52 [6,1,5,4,2,3] => 53 [6,1,5,4,3,2] => 56 [6,2,1,3,4,5] => 32 [6,2,1,3,5,4] => 37 [6,2,1,4,3,5] => 36 [6,2,1,4,5,3] => 41 [6,2,1,5,3,4] => 42 [6,2,1,5,4,3] => 46 [6,2,3,1,4,5] => 35 [6,2,3,1,5,4] => 40 [6,2,3,4,1,5] => 39 [6,2,3,4,5,1] => 44 [6,2,3,5,1,4] => 45 [6,2,3,5,4,1] => 49 [6,2,4,1,3,5] => 40 [6,2,4,1,5,3] => 45 [6,2,4,3,1,5] => 43 [6,2,4,3,5,1] => 48 [6,2,4,5,1,3] => 50 [6,2,4,5,3,1] => 53 [6,2,5,1,3,4] => 47 [6,2,5,1,4,3] => 51 [6,2,5,3,1,4] => 50 [6,2,5,3,4,1] => 54 [6,2,5,4,1,3] => 55 [6,2,5,4,3,1] => 58 [6,3,1,2,4,5] => 36 [6,3,1,2,5,4] => 41 [6,3,1,4,2,5] => 40 [6,3,1,4,5,2] => 45 [6,3,1,5,2,4] => 46 [6,3,1,5,4,2] => 50 [6,3,2,1,4,5] => 38 [6,3,2,1,5,4] => 43 [6,3,2,4,1,5] => 42 [6,3,2,4,5,1] => 47 [6,3,2,5,1,4] => 48 [6,3,2,5,4,1] => 52 [6,3,4,1,2,5] => 44 [6,3,4,1,5,2] => 49 [6,3,4,2,1,5] => 46 [6,3,4,2,5,1] => 51 [6,3,4,5,1,2] => 54 [6,3,4,5,2,1] => 56 [6,3,5,1,2,4] => 51 [6,3,5,1,4,2] => 55 [6,3,5,2,1,4] => 53 [6,3,5,2,4,1] => 57 [6,3,5,4,1,2] => 59 [6,3,5,4,2,1] => 61 [6,4,1,2,3,5] => 42 [6,4,1,2,5,3] => 47 [6,4,1,3,2,5] => 45 [6,4,1,3,5,2] => 50 [6,4,1,5,2,3] => 52 [6,4,1,5,3,2] => 55 [6,4,2,1,3,5] => 44 [6,4,2,1,5,3] => 49 [6,4,2,3,1,5] => 47 [6,4,2,3,5,1] => 52 [6,4,2,5,1,3] => 54 [6,4,2,5,3,1] => 57 [6,4,3,1,2,5] => 48 [6,4,3,1,5,2] => 53 [6,4,3,2,1,5] => 50 [6,4,3,2,5,1] => 55 [6,4,3,5,1,2] => 58 [6,4,3,5,2,1] => 60 [6,4,5,1,2,3] => 57 [6,4,5,1,3,2] => 60 [6,4,5,2,1,3] => 59 [6,4,5,2,3,1] => 62 [6,4,5,3,1,2] => 63 [6,4,5,3,2,1] => 65 [6,5,1,2,3,4] => 50 [6,5,1,2,4,3] => 54 [6,5,1,3,2,4] => 53 [6,5,1,3,4,2] => 57 [6,5,1,4,2,3] => 58 [6,5,1,4,3,2] => 61 [6,5,2,1,3,4] => 52 [6,5,2,1,4,3] => 56 [6,5,2,3,1,4] => 55 [6,5,2,3,4,1] => 59 [6,5,2,4,1,3] => 60 [6,5,2,4,3,1] => 63 [6,5,3,1,2,4] => 56 [6,5,3,1,4,2] => 60 [6,5,3,2,1,4] => 58 [6,5,3,2,4,1] => 62 [6,5,3,4,1,2] => 64 [6,5,3,4,2,1] => 66 [6,5,4,1,2,3] => 62 [6,5,4,1,3,2] => 65 [6,5,4,2,1,3] => 64 [6,5,4,2,3,1] => 67 [6,5,4,3,1,2] => 68 [6,5,4,3,2,1] => 70 ----------------------------------------------------------------------------- Created: Aug 22, 2016 at 17:56 by Jessica Striker ----------------------------------------------------------------------------- Last Updated: Dec 30, 2016 at 10:30 by Christian Stump