***************************************************************************** * 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: St001079 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The minimal length of a factorization of a permutation using the permutations (12)(34)..., (23)(45)..., and (12). In symbols, for a permutation $\pi$ this is $$\min\{ k \mid \pi = \tau_{i_1} \cdots \tau_{i_k} \},$$ where, with $m_1$ the largest even number at most $n$ and $m_2$ the largest odd number at most $n$, each factor $\tau_i$ is one of the three permutations $(1,2)(3,4)\cdots(m_1-1,m_1)$ or $(2,3)(4,5)\cdots(m_2-1,m_2)$ or $(1,2)$. ----------------------------------------------------------------------------- References: [1] Pak, I. "Natural" generating sets for symmetric groups. [[MathOverflow:24128]] ----------------------------------------------------------------------------- Code: def statistic(pi): def gens(n): n1 = n if is_even(n) else n-1 n2 = n-2 if is_even(n) else n-1 return [Permutation([i+2 if is_even(i) else i for i in range(n1)]), Permutation([1] + [i+3 if is_even(i) else i+1 for i in range(n2)]), Permutation([2,1])] G = PermutationGroup(gens(len(pi))) pi = G(pi) w = gap.Factorization(G._gap_(), pi._gap_()) return w.Length() ----------------------------------------------------------------------------- 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] => 2 [1,3,2,4] => 1 [1,3,4,2] => 3 [1,4,2,3] => 3 [1,4,3,2] => 4 [2,1,3,4] => 1 [2,1,4,3] => 1 [2,3,1,4] => 2 [2,3,4,1] => 4 [2,4,1,3] => 2 [2,4,3,1] => 4 [3,1,2,4] => 2 [3,1,4,2] => 2 [3,2,1,4] => 3 [3,2,4,1] => 3 [3,4,1,2] => 3 [3,4,2,1] => 4 [4,1,2,3] => 4 [4,1,3,2] => 4 [4,2,1,3] => 3 [4,2,3,1] => 3 [4,3,1,2] => 4 [4,3,2,1] => 4 [1,2,3,4,5] => 0 [1,2,3,5,4] => 6 [1,2,4,3,5] => 2 [1,2,4,5,3] => 6 [1,2,5,3,4] => 6 [1,2,5,4,3] => 7 [1,3,2,4,5] => 5 [1,3,2,5,4] => 1 [1,3,4,2,5] => 5 [1,3,4,5,2] => 6 [1,3,5,2,4] => 3 [1,3,5,4,2] => 7 [1,4,2,3,5] => 5 [1,4,2,5,3] => 3 [1,4,3,2,5] => 5 [1,4,3,5,2] => 6 [1,4,5,2,3] => 5 [1,4,5,3,2] => 8 [1,5,2,3,4] => 6 [1,5,2,4,3] => 7 [1,5,3,2,4] => 6 [1,5,3,4,2] => 4 [1,5,4,2,3] => 8 [1,5,4,3,2] => 6 [2,1,3,4,5] => 1 [2,1,3,5,4] => 5 [2,1,4,3,5] => 1 [2,1,4,5,3] => 7 [2,1,5,3,4] => 7 [2,1,5,4,3] => 7 [2,3,1,4,5] => 4 [2,3,1,5,4] => 2 [2,3,4,1,5] => 4 [2,3,4,5,1] => 7 [2,3,5,1,4] => 4 [2,3,5,4,1] => 8 [2,4,1,3,5] => 6 [2,4,1,5,3] => 2 [2,4,3,1,5] => 6 [2,4,3,5,1] => 5 [2,4,5,1,3] => 4 [2,4,5,3,1] => 7 [2,5,1,3,4] => 7 [2,5,1,4,3] => 7 [2,5,3,1,4] => 7 [2,5,3,4,1] => 5 [2,5,4,1,3] => 7 [2,5,4,3,1] => 5 [3,1,2,4,5] => 4 [3,1,2,5,4] => 2 [3,1,4,2,5] => 6 [3,1,4,5,2] => 7 [3,1,5,2,4] => 2 [3,1,5,4,2] => 7 [3,2,1,4,5] => 3 [3,2,1,5,4] => 3 [3,2,4,1,5] => 5 [3,2,4,5,1] => 8 [3,2,5,1,4] => 3 [3,2,5,4,1] => 8 [3,4,1,2,5] => 8 [3,4,1,5,2] => 7 [3,4,2,1,5] => 8 [3,4,2,5,1] => 6 [3,4,5,1,2] => 7 [3,4,5,2,1] => 6 [3,5,1,2,4] => 7 [3,5,1,4,2] => 3 [3,5,2,1,4] => 7 [3,5,2,4,1] => 4 [3,5,4,1,2] => 5 [3,5,4,2,1] => 6 [4,1,2,3,5] => 4 [4,1,2,5,3] => 4 [4,1,3,2,5] => 6 [4,1,3,5,2] => 7 [4,1,5,2,3] => 4 [4,1,5,3,2] => 7 [4,2,1,3,5] => 5 [4,2,1,5,3] => 3 [4,2,3,1,5] => 7 [4,2,3,5,1] => 6 [4,2,5,1,3] => 3 [4,2,5,3,1] => 6 [4,3,1,2,5] => 8 [4,3,1,5,2] => 7 [4,3,2,1,5] => 7 [4,3,2,5,1] => 7 [4,3,5,1,2] => 7 [4,3,5,2,1] => 7 [4,5,1,2,3] => 7 [4,5,1,3,2] => 5 [4,5,2,1,3] => 7 [4,5,2,3,1] => 4 [4,5,3,1,2] => 7 [4,5,3,2,1] => 6 [5,1,2,3,4] => 7 [5,1,2,4,3] => 8 [5,1,3,2,4] => 5 [5,1,3,4,2] => 5 [5,1,4,2,3] => 7 [5,1,4,3,2] => 5 [5,2,1,3,4] => 8 [5,2,1,4,3] => 8 [5,2,3,1,4] => 6 [5,2,3,4,1] => 6 [5,2,4,1,3] => 6 [5,2,4,3,1] => 6 [5,3,1,2,4] => 6 [5,3,1,4,2] => 4 [5,3,2,1,4] => 7 [5,3,2,4,1] => 5 [5,3,4,1,2] => 4 [5,3,4,2,1] => 5 [5,4,1,2,3] => 6 [5,4,1,3,2] => 6 [5,4,2,1,3] => 7 [5,4,2,3,1] => 5 [5,4,3,1,2] => 6 [5,4,3,2,1] => 5 [1,2,3,4,5,6] => 0 [1,2,3,4,6,5] => 11 [1,2,3,5,4,6] => 6 [1,2,3,5,6,4] => 11 [1,2,3,6,4,5] => 11 [1,2,3,6,5,4] => 9 [1,2,4,3,5,6] => 13 [1,2,4,3,6,5] => 2 [1,2,4,5,3,6] => 11 [1,2,4,5,6,3] => 9 [1,2,4,6,3,5] => 6 [1,2,4,6,5,3] => 13 [1,2,5,3,4,6] => 11 [1,2,5,3,6,4] => 6 [1,2,5,4,3,6] => 7 [1,2,5,4,6,3] => 11 [1,2,5,6,3,4] => 12 [1,2,5,6,4,3] => 16 [1,2,6,3,4,5] => 9 [1,2,6,3,5,4] => 13 [1,2,6,4,3,5] => 11 [1,2,6,4,5,3] => 8 [1,2,6,5,3,4] => 16 [1,2,6,5,4,3] => 12 [1,3,2,4,5,6] => 5 [1,3,2,4,6,5] => 10 [1,3,2,5,4,6] => 1 [1,3,2,5,6,4] => 10 [1,3,2,6,4,5] => 10 [1,3,2,6,5,4] => 12 [1,3,4,2,5,6] => 10 [1,3,4,2,6,5] => 5 [1,3,4,5,2,6] => 6 [1,3,4,5,6,2] => 10 [1,3,4,6,2,5] => 11 [1,3,4,6,5,2] => 15 [1,3,5,2,4,6] => 12 [1,3,5,2,6,4] => 3 [1,3,5,4,2,6] => 10 [1,3,5,4,6,2] => 8 [1,3,5,6,2,4] => 7 [1,3,5,6,4,2] => 12 [1,3,6,2,4,5] => 12 [1,3,6,2,5,4] => 10 [1,3,6,4,2,5] => 15 [1,3,6,4,5,2] => 11 [1,3,6,5,2,4] => 11 [1,3,6,5,4,2] => 9 [1,4,2,3,5,6] => 10 [1,4,2,3,6,5] => 5 [1,4,2,5,3,6] => 12 [1,4,2,5,6,3] => 12 [1,4,2,6,3,5] => 3 [1,4,2,6,5,3] => 10 [1,4,3,2,5,6] => 5 [1,4,3,2,6,5] => 10 [1,4,3,5,2,6] => 11 [1,4,3,5,6,2] => 15 [1,4,3,6,2,5] => 6 [1,4,3,6,5,2] => 10 [1,4,5,2,3,6] => 12 [1,4,5,2,6,3] => 12 [1,4,5,3,2,6] => 15 [1,4,5,3,6,2] => 11 [1,4,5,6,2,3] => 11 [1,4,5,6,3,2] => 11 [1,4,6,2,3,5] => 12 [1,4,6,2,5,3] => 5 [1,4,6,3,2,5] => 10 [1,4,6,3,5,2] => 8 [1,4,6,5,2,3] => 9 [1,4,6,5,3,2] => 12 [1,5,2,3,4,6] => 6 [1,5,2,3,6,4] => 11 [1,5,2,4,3,6] => 10 [1,5,2,4,6,3] => 15 [1,5,2,6,3,4] => 7 [1,5,2,6,4,3] => 11 [1,5,3,2,4,6] => 11 [1,5,3,2,6,4] => 6 [1,5,3,4,2,6] => 11 [1,5,3,4,6,2] => 11 [1,5,3,6,2,4] => 4 [1,5,3,6,4,2] => 9 [1,5,4,2,3,6] => 15 [1,5,4,2,6,3] => 10 [1,5,4,3,2,6] => 11 [1,5,4,3,6,2] => 11 [1,5,4,6,2,3] => 11 [1,5,4,6,3,2] => 12 [1,5,6,2,3,4] => 11 [1,5,6,2,4,3] => 9 [1,5,6,3,2,4] => 11 [1,5,6,3,4,2] => 6 [1,5,6,4,2,3] => 13 [1,5,6,4,3,2] => 10 [1,6,2,3,4,5] => 10 [1,6,2,3,5,4] => 15 [1,6,2,4,3,5] => 8 [1,6,2,4,5,3] => 11 [1,6,2,5,3,4] => 12 [1,6,2,5,4,3] => 9 [1,6,3,2,4,5] => 15 [1,6,3,2,5,4] => 10 [1,6,3,4,2,5] => 11 [1,6,3,4,5,2] => 10 [1,6,3,5,2,4] => 9 [1,6,3,5,4,2] => 12 [1,6,4,2,3,5] => 11 [1,6,4,2,5,3] => 8 [1,6,4,3,2,5] => 11 [1,6,4,3,5,2] => 11 [1,6,4,5,2,3] => 6 [1,6,4,5,3,2] => 9 [1,6,5,2,3,4] => 11 [1,6,5,2,4,3] => 12 [1,6,5,3,2,4] => 12 [1,6,5,3,4,2] => 9 [1,6,5,4,2,3] => 10 [1,6,5,4,3,2] => 7 [2,1,3,4,5,6] => 1 [2,1,3,4,6,5] => 12 [2,1,3,5,4,6] => 5 [2,1,3,5,6,4] => 12 [2,1,3,6,4,5] => 12 [2,1,3,6,5,4] => 10 [2,1,4,3,5,6] => 12 [2,1,4,3,6,5] => 1 [2,1,4,5,3,6] => 10 [2,1,4,5,6,3] => 8 [2,1,4,6,3,5] => 7 [2,1,4,6,5,3] => 12 [2,1,5,3,4,6] => 10 [2,1,5,3,6,4] => 7 [2,1,5,4,3,6] => 8 [2,1,5,4,6,3] => 12 [2,1,5,6,3,4] => 11 [2,1,5,6,4,3] => 15 [2,1,6,3,4,5] => 8 [2,1,6,3,5,4] => 12 [2,1,6,4,3,5] => 12 [2,1,6,4,5,3] => 7 [2,1,6,5,3,4] => 15 [2,1,6,5,4,3] => 13 [2,3,1,4,5,6] => 4 [2,3,1,4,6,5] => 11 [2,3,1,5,4,6] => 2 [2,3,1,5,6,4] => 11 [2,3,1,6,4,5] => 11 [2,3,1,6,5,4] => 13 [2,3,4,1,5,6] => 11 [2,3,4,1,6,5] => 4 [2,3,4,5,1,6] => 7 [2,3,4,5,6,1] => 9 [2,3,4,6,1,5] => 10 [2,3,4,6,5,1] => 14 [2,3,5,1,4,6] => 11 [2,3,5,1,6,4] => 4 [2,3,5,4,1,6] => 9 [2,3,5,4,6,1] => 9 [2,3,5,6,1,4] => 8 [2,3,5,6,4,1] => 13 [2,3,6,1,4,5] => 11 [2,3,6,1,5,4] => 11 [2,3,6,4,1,5] => 14 [2,3,6,4,5,1] => 10 [2,3,6,5,1,4] => 12 [2,3,6,5,4,1] => 10 [2,4,1,3,5,6] => 9 [2,4,1,3,6,5] => 6 [2,4,1,5,3,6] => 11 [2,4,1,5,6,3] => 13 [2,4,1,6,3,5] => 2 [2,4,1,6,5,3] => 9 [2,4,3,1,5,6] => 6 [2,4,3,1,6,5] => 9 [2,4,3,5,1,6] => 12 [2,4,3,5,6,1] => 14 [2,4,3,6,1,5] => 5 [2,4,3,6,5,1] => 10 [2,4,5,1,3,6] => 13 [2,4,5,1,6,3] => 11 [2,4,5,3,1,6] => 14 [2,4,5,3,6,1] => 12 [2,4,5,6,1,3] => 10 [2,4,5,6,3,1] => 10 [2,4,6,1,3,5] => 11 [2,4,6,1,5,3] => 4 [2,4,6,3,1,5] => 11 [2,4,6,3,5,1] => 7 [2,4,6,5,1,3] => 8 [2,4,6,5,3,1] => 11 [2,5,1,3,4,6] => 7 [2,5,1,3,6,4] => 10 [2,5,1,4,3,6] => 9 [2,5,1,4,6,3] => 14 [2,5,1,6,3,4] => 8 [2,5,1,6,4,3] => 12 [2,5,3,1,4,6] => 10 [2,5,3,1,6,4] => 7 [2,5,3,4,1,6] => 10 [2,5,3,4,6,1] => 12 [2,5,3,6,1,4] => 5 [2,5,3,6,4,1] => 10 [2,5,4,1,3,6] => 14 [2,5,4,1,6,3] => 9 [2,5,4,3,1,6] => 12 [2,5,4,3,6,1] => 10 [2,5,4,6,1,3] => 10 [2,5,4,6,3,1] => 13 [2,5,6,1,3,4] => 12 [2,5,6,1,4,3] => 10 [2,5,6,3,1,4] => 11 [2,5,6,3,4,1] => 7 [2,5,6,4,1,3] => 13 [2,5,6,4,3,1] => 10 [2,6,1,3,4,5] => 11 [2,6,1,3,5,4] => 14 [2,6,1,4,3,5] => 7 [2,6,1,4,5,3] => 12 [2,6,1,5,3,4] => 12 [2,6,1,5,4,3] => 8 [2,6,3,1,4,5] => 14 [2,6,3,1,5,4] => 11 [2,6,3,4,1,5] => 10 [2,6,3,4,5,1] => 11 [2,6,3,5,1,4] => 10 [2,6,3,5,4,1] => 11 [2,6,4,1,3,5] => 12 [2,6,4,1,5,3] => 7 [2,6,4,3,1,5] => 12 [2,6,4,3,5,1] => 10 [2,6,4,5,1,3] => 5 [2,6,4,5,3,1] => 8 [2,6,5,1,3,4] => 10 [2,6,5,1,4,3] => 12 [2,6,5,3,1,4] => 13 [2,6,5,3,4,1] => 10 [2,6,5,4,1,3] => 10 [2,6,5,4,3,1] => 7 [3,1,2,4,5,6] => 4 [3,1,2,4,6,5] => 11 [3,1,2,5,4,6] => 2 [3,1,2,5,6,4] => 11 [3,1,2,6,4,5] => 11 [3,1,2,6,5,4] => 13 [3,1,4,2,5,6] => 9 [3,1,4,2,6,5] => 6 [3,1,4,5,2,6] => 7 [3,1,4,5,6,2] => 11 [3,1,4,6,2,5] => 10 [3,1,4,6,5,2] => 14 [3,1,5,2,4,6] => 11 [3,1,5,2,6,4] => 2 [3,1,5,4,2,6] => 9 [3,1,5,4,6,2] => 7 [3,1,5,6,2,4] => 8 [3,1,5,6,4,2] => 12 [3,1,6,2,4,5] => 13 [3,1,6,2,5,4] => 9 [3,1,6,4,2,5] => 14 [3,1,6,4,5,2] => 12 [3,1,6,5,2,4] => 12 [3,1,6,5,4,2] => 8 [3,2,1,4,5,6] => 3 [3,2,1,4,6,5] => 12 [3,2,1,5,4,6] => 3 [3,2,1,5,6,4] => 12 [3,2,1,6,4,5] => 12 [3,2,1,6,5,4] => 12 [3,2,4,1,5,6] => 10 [3,2,4,1,6,5] => 5 [3,2,4,5,1,6] => 8 [3,2,4,5,6,1] => 10 [3,2,4,6,1,5] => 9 [3,2,4,6,5,1] => 14 [3,2,5,1,4,6] => 12 [3,2,5,1,6,4] => 3 [3,2,5,4,1,6] => 8 [3,2,5,4,6,1] => 8 [3,2,5,6,1,4] => 9 [3,2,5,6,4,1] => 13 [3,2,6,1,4,5] => 12 [3,2,6,1,5,4] => 10 [3,2,6,4,1,5] => 13 [3,2,6,4,5,1] => 11 [3,2,6,5,1,4] => 13 [3,2,6,5,4,1] => 9 [3,4,1,2,5,6] => 8 [3,4,1,2,6,5] => 9 [3,4,1,5,2,6] => 8 [3,4,1,5,6,2] => 13 [3,4,1,6,2,5] => 7 [3,4,1,6,5,2] => 12 [3,4,2,1,5,6] => 9 [3,4,2,1,6,5] => 8 [3,4,2,5,1,6] => 9 [3,4,2,5,6,1] => 13 [3,4,2,6,1,5] => 6 [3,4,2,6,5,1] => 11 [3,4,5,1,2,6] => 13 [3,4,5,1,6,2] => 8 [3,4,5,2,1,6] => 13 [3,4,5,2,6,1] => 9 [3,4,5,6,1,2] => 11 [3,4,5,6,2,1] => 12 [3,4,6,1,2,5] => 13 [3,4,6,1,5,2] => 9 [3,4,6,2,1,5] => 12 [3,4,6,2,5,1] => 8 [3,4,6,5,1,2] => 12 [3,4,6,5,2,1] => 11 [3,5,1,2,4,6] => 8 [3,5,1,2,6,4] => 7 [3,5,1,4,2,6] => 10 [3,5,1,4,6,2] => 12 [3,5,1,6,2,4] => 3 [3,5,1,6,4,2] => 8 [3,5,2,1,4,6] => 7 [3,5,2,1,6,4] => 8 [3,5,2,4,1,6] => 11 [3,5,2,4,6,1] => 13 [3,5,2,6,1,4] => 4 [3,5,2,6,4,1] => 9 [3,5,4,1,2,6] => 12 [3,5,4,1,6,2] => 10 [3,5,4,2,1,6] => 13 [3,5,4,2,6,1] => 11 [3,5,4,6,1,2] => 9 [3,5,4,6,2,1] => 10 [3,5,6,1,2,4] => 10 [3,5,6,1,4,2] => 5 [3,5,6,2,1,4] => 11 [3,5,6,2,4,1] => 6 [3,5,6,4,1,2] => 9 [3,5,6,4,2,1] => 10 [3,6,1,2,4,5] => 13 [3,6,1,2,5,4] => 12 [3,6,1,4,2,5] => 12 [3,6,1,4,5,2] => 9 [3,6,1,5,2,4] => 8 [3,6,1,5,4,2] => 11 [3,6,2,1,4,5] => 12 [3,6,2,1,5,4] => 13 [3,6,2,4,1,5] => 11 [3,6,2,4,5,1] => 10 [3,6,2,5,1,4] => 9 [3,6,2,5,4,1] => 12 [3,6,4,1,2,5] => 11 [3,6,4,1,5,2] => 12 [3,6,4,2,1,5] => 12 [3,6,4,2,5,1] => 11 [3,6,4,5,1,2] => 9 [3,6,4,5,2,1] => 8 [3,6,5,1,2,4] => 11 [3,6,5,1,4,2] => 8 [3,6,5,2,1,4] => 11 [3,6,5,2,4,1] => 9 [3,6,5,4,1,2] => 6 [3,6,5,4,2,1] => 7 [4,1,2,3,5,6] => 11 [4,1,2,3,6,5] => 4 [4,1,2,5,3,6] => 11 [4,1,2,5,6,3] => 11 [4,1,2,6,3,5] => 4 [4,1,2,6,5,3] => 11 [4,1,3,2,5,6] => 6 [4,1,3,2,6,5] => 9 [4,1,3,5,2,6] => 10 [4,1,3,5,6,2] => 14 [4,1,3,6,2,5] => 7 [4,1,3,6,5,2] => 11 [4,1,5,2,3,6] => 13 [4,1,5,2,6,3] => 11 [4,1,5,3,2,6] => 14 [4,1,5,3,6,2] => 12 [4,1,5,6,2,3] => 12 [4,1,5,6,3,2] => 10 [4,1,6,2,3,5] => 11 [4,1,6,2,5,3] => 4 [4,1,6,3,2,5] => 9 [4,1,6,3,5,2] => 7 [4,1,6,5,2,3] => 10 [4,1,6,5,3,2] => 12 [4,2,1,3,5,6] => 10 [4,2,1,3,6,5] => 5 [4,2,1,5,3,6] => 12 [4,2,1,5,6,3] => 12 [4,2,1,6,3,5] => 3 [4,2,1,6,5,3] => 10 [4,2,3,1,5,6] => 7 [4,2,3,1,6,5] => 8 [4,2,3,5,1,6] => 11 [4,2,3,5,6,1] => 13 [4,2,3,6,1,5] => 6 [4,2,3,6,5,1] => 11 [4,2,5,1,3,6] => 13 [4,2,5,1,6,3] => 10 [4,2,5,3,1,6] => 14 [4,2,5,3,6,1] => 11 [4,2,5,6,1,3] => 11 [4,2,5,6,3,1] => 9 [4,2,6,1,3,5] => 10 [4,2,6,1,5,3] => 3 [4,2,6,3,1,5] => 10 [4,2,6,3,5,1] => 6 [4,2,6,5,1,3] => 9 [4,2,6,5,3,1] => 11 [4,3,1,2,5,6] => 9 [4,3,1,2,6,5] => 8 [4,3,1,5,2,6] => 7 [4,3,1,5,6,2] => 12 [4,3,1,6,2,5] => 8 [4,3,1,6,5,2] => 13 [4,3,2,1,5,6] => 10 [4,3,2,1,6,5] => 7 [4,3,2,5,1,6] => 8 [4,3,2,5,6,1] => 12 [4,3,2,6,1,5] => 7 [4,3,2,6,5,1] => 12 [4,3,5,1,2,6] => 13 [4,3,5,1,6,2] => 9 [4,3,5,2,1,6] => 14 [4,3,5,2,6,1] => 10 [4,3,5,6,1,2] => 12 [4,3,5,6,2,1] => 13 [4,3,6,1,2,5] => 12 [4,3,6,1,5,2] => 8 [4,3,6,2,1,5] => 12 [4,3,6,2,5,1] => 7 [4,3,6,5,1,2] => 11 [4,3,6,5,2,1] => 10 [4,5,1,2,3,6] => 13 [4,5,1,2,6,3] => 13 [4,5,1,3,2,6] => 12 [4,5,1,3,6,2] => 11 [4,5,1,6,2,3] => 10 [4,5,1,6,3,2] => 11 [4,5,2,1,3,6] => 13 [4,5,2,1,6,3] => 12 [4,5,2,3,1,6] => 12 [4,5,2,3,6,1] => 10 [4,5,2,6,1,3] => 9 [4,5,2,6,3,1] => 10 [4,5,3,1,2,6] => 13 [4,5,3,1,6,2] => 12 [4,5,3,2,1,6] => 12 [4,5,3,2,6,1] => 12 [4,5,3,6,1,2] => 9 [4,5,3,6,2,1] => 10 [4,5,6,1,2,3] => 10 [4,5,6,1,3,2] => 10 [4,5,6,2,1,3] => 10 [4,5,6,2,3,1] => 9 [4,5,6,3,1,2] => 8 [4,5,6,3,2,1] => 7 [4,6,1,2,3,5] => 8 [4,6,1,2,5,3] => 9 [4,6,1,3,2,5] => 10 [4,6,1,3,5,2] => 12 [4,6,1,5,2,3] => 5 [4,6,1,5,3,2] => 8 [4,6,2,1,3,5] => 9 [4,6,2,1,5,3] => 8 [4,6,2,3,1,5] => 9 [4,6,2,3,5,1] => 11 [4,6,2,5,1,3] => 4 [4,6,2,5,3,1] => 7 [4,6,3,1,2,5] => 12 [4,6,3,1,5,2] => 10 [4,6,3,2,1,5] => 11 [4,6,3,2,5,1] => 9 [4,6,3,5,1,2] => 9 [4,6,3,5,2,1] => 8 [4,6,5,1,2,3] => 10 [4,6,5,1,3,2] => 7 [4,6,5,2,1,3] => 9 [4,6,5,2,3,1] => 6 [4,6,5,3,1,2] => 10 [4,6,5,3,2,1] => 10 [5,1,2,3,4,6] => 7 [5,1,2,3,6,4] => 10 [5,1,2,4,3,6] => 9 [5,1,2,4,6,3] => 14 [5,1,2,6,3,4] => 8 [5,1,2,6,4,3] => 12 [5,1,3,2,4,6] => 12 [5,1,3,2,6,4] => 5 [5,1,3,4,2,6] => 10 [5,1,3,4,6,2] => 10 [5,1,3,6,2,4] => 5 [5,1,3,6,4,2] => 10 [5,1,4,2,3,6] => 14 [5,1,4,2,6,3] => 11 [5,1,4,3,2,6] => 12 [5,1,4,3,6,2] => 12 [5,1,4,6,2,3] => 11 [5,1,4,6,3,2] => 13 [5,1,6,2,3,4] => 10 [5,1,6,2,4,3] => 8 [5,1,6,3,2,4] => 10 [5,1,6,3,4,2] => 5 [5,1,6,4,2,3] => 13 [5,1,6,4,3,2] => 10 [5,2,1,3,4,6] => 8 [5,2,1,3,6,4] => 9 [5,2,1,4,3,6] => 8 [5,2,1,4,6,3] => 13 [5,2,1,6,3,4] => 9 [5,2,1,6,4,3] => 13 [5,2,3,1,4,6] => 11 [5,2,3,1,6,4] => 6 [5,2,3,4,1,6] => 9 [5,2,3,4,6,1] => 11 [5,2,3,6,1,4] => 6 [5,2,3,6,4,1] => 11 [5,2,4,1,3,6] => 14 [5,2,4,1,6,3] => 10 [5,2,4,3,1,6] => 13 [5,2,4,3,6,1] => 11 [5,2,4,6,1,3] => 11 [5,2,4,6,3,1] => 12 [5,2,6,1,3,4] => 11 [5,2,6,1,4,3] => 9 [5,2,6,3,1,4] => 11 [5,2,6,3,4,1] => 6 [5,2,6,4,1,3] => 12 [5,2,6,4,3,1] => 9 [5,3,1,2,4,6] => 9 [5,3,1,2,6,4] => 6 [5,3,1,4,2,6] => 11 [5,3,1,4,6,2] => 11 [5,3,1,6,2,4] => 4 [5,3,1,6,4,2] => 9 [5,3,2,1,4,6] => 8 [5,3,2,1,6,4] => 7 [5,3,2,4,1,6] => 12 [5,3,2,4,6,1] => 12 [5,3,2,6,1,4] => 5 [5,3,2,6,4,1] => 10 [5,3,4,1,2,6] => 12 [5,3,4,1,6,2] => 9 [5,3,4,2,1,6] => 13 [5,3,4,2,6,1] => 10 [5,3,4,6,1,2] => 10 [5,3,4,6,2,1] => 10 [5,3,6,1,2,4] => 9 [5,3,6,1,4,2] => 4 [5,3,6,2,1,4] => 10 [5,3,6,2,4,1] => 5 [5,3,6,4,1,2] => 10 [5,3,6,4,2,1] => 10 [5,4,1,2,3,6] => 13 [5,4,1,2,6,3] => 12 [5,4,1,3,2,6] => 13 [5,4,1,3,6,2] => 12 [5,4,1,6,2,3] => 11 [5,4,1,6,3,2] => 11 [5,4,2,1,3,6] => 14 [5,4,2,1,6,3] => 12 [5,4,2,3,1,6] => 13 [5,4,2,3,6,1] => 11 [5,4,2,6,1,3] => 10 [5,4,2,6,3,1] => 11 [5,4,3,1,2,6] => 12 [5,4,3,1,6,2] => 11 [5,4,3,2,1,6] => 11 [5,4,3,2,6,1] => 11 [5,4,3,6,1,2] => 8 [5,4,3,6,2,1] => 9 [5,4,6,1,2,3] => 10 [5,4,6,1,3,2] => 9 [5,4,6,2,1,3] => 9 [5,4,6,2,3,1] => 8 [5,4,6,3,1,2] => 9 [5,4,6,3,2,1] => 8 [5,6,1,2,3,4] => 11 [5,6,1,2,4,3] => 12 [5,6,1,3,2,4] => 9 [5,6,1,3,4,2] => 9 [5,6,1,4,2,3] => 9 [5,6,1,4,3,2] => 6 [5,6,2,1,3,4] => 12 [5,6,2,1,4,3] => 11 [5,6,2,3,1,4] => 10 [5,6,2,3,4,1] => 8 [5,6,2,4,1,3] => 10 [5,6,2,4,3,1] => 7 [5,6,3,1,2,4] => 9 [5,6,3,1,4,2] => 9 [5,6,3,2,1,4] => 8 [5,6,3,2,4,1] => 10 [5,6,3,4,1,2] => 5 [5,6,3,4,2,1] => 6 [5,6,4,1,2,3] => 8 [5,6,4,1,3,2] => 10 [5,6,4,2,1,3] => 9 [5,6,4,2,3,1] => 9 [5,6,4,3,1,2] => 8 [5,6,4,3,2,1] => 7 [6,1,2,3,4,5] => 9 [6,1,2,3,5,4] => 14 [6,1,2,4,3,5] => 9 [6,1,2,4,5,3] => 10 [6,1,2,5,3,4] => 13 [6,1,2,5,4,3] => 10 [6,1,3,2,4,5] => 14 [6,1,3,2,5,4] => 10 [6,1,3,4,2,5] => 12 [6,1,3,4,5,2] => 11 [6,1,3,5,2,4] => 10 [6,1,3,5,4,2] => 11 [6,1,4,2,3,5] => 12 [6,1,4,2,5,3] => 7 [6,1,4,3,2,5] => 10 [6,1,4,3,5,2] => 10 [6,1,4,5,2,3] => 7 [6,1,4,5,3,2] => 10 [6,1,5,2,3,4] => 10 [6,1,5,2,4,3] => 11 [6,1,5,3,2,4] => 13 [6,1,5,3,4,2] => 8 [6,1,5,4,2,3] => 10 [6,1,5,4,3,2] => 7 [6,2,1,3,4,5] => 10 [6,2,1,3,5,4] => 14 [6,2,1,4,3,5] => 8 [6,2,1,4,5,3] => 11 [6,2,1,5,3,4] => 13 [6,2,1,5,4,3] => 9 [6,2,3,1,4,5] => 13 [6,2,3,1,5,4] => 11 [6,2,3,4,1,5] => 11 [6,2,3,4,5,1] => 12 [6,2,3,5,1,4] => 11 [6,2,3,5,4,1] => 12 [6,2,4,1,3,5] => 11 [6,2,4,1,5,3] => 6 [6,2,4,3,1,5] => 11 [6,2,4,3,5,1] => 9 [6,2,4,5,1,3] => 6 [6,2,4,5,3,1] => 9 [6,2,5,1,3,4] => 9 [6,2,5,1,4,3] => 11 [6,2,5,3,1,4] => 12 [6,2,5,3,4,1] => 9 [6,2,5,4,1,3] => 9 [6,2,5,4,3,1] => 6 [6,3,1,2,4,5] => 13 [6,3,1,2,5,4] => 11 [6,3,1,4,2,5] => 13 [6,3,1,4,5,2] => 10 [6,3,1,5,2,4] => 9 [6,3,1,5,4,2] => 12 [6,3,2,1,4,5] => 12 [6,3,2,1,5,4] => 12 [6,3,2,4,1,5] => 12 [6,3,2,4,5,1] => 11 [6,3,2,5,1,4] => 10 [6,3,2,5,4,1] => 12 [6,3,4,1,2,5] => 10 [6,3,4,1,5,2] => 11 [6,3,4,2,1,5] => 11 [6,3,4,2,5,1] => 10 [6,3,4,5,1,2] => 8 [6,3,4,5,2,1] => 7 [6,3,5,1,2,4] => 10 [6,3,5,1,4,2] => 7 [6,3,5,2,1,4] => 11 [6,3,5,2,4,1] => 8 [6,3,5,4,1,2] => 7 [6,3,5,4,2,1] => 8 [6,4,1,2,3,5] => 9 [6,4,1,2,5,3] => 8 [6,4,1,3,2,5] => 11 [6,4,1,3,5,2] => 11 [6,4,1,5,2,3] => 6 [6,4,1,5,3,2] => 9 [6,4,2,1,3,5] => 10 [6,4,2,1,5,3] => 7 [6,4,2,3,1,5] => 10 [6,4,2,3,5,1] => 10 [6,4,2,5,1,3] => 5 [6,4,2,5,3,1] => 8 [6,4,3,1,2,5] => 12 [6,4,3,1,5,2] => 9 [6,4,3,2,1,5] => 11 [6,4,3,2,5,1] => 8 [6,4,3,5,1,2] => 10 [6,4,3,5,2,1] => 9 [6,4,5,1,2,3] => 9 [6,4,5,1,3,2] => 6 [6,4,5,2,1,3] => 8 [6,4,5,2,3,1] => 5 [6,4,5,3,1,2] => 9 [6,4,5,3,2,1] => 10 [6,5,1,2,3,4] => 12 [6,5,1,2,4,3] => 11 [6,5,1,3,2,4] => 10 [6,5,1,3,4,2] => 8 [6,5,1,4,2,3] => 10 [6,5,1,4,3,2] => 7 [6,5,2,1,3,4] => 13 [6,5,2,1,4,3] => 10 [6,5,2,3,1,4] => 10 [6,5,2,3,4,1] => 7 [6,5,2,4,1,3] => 10 [6,5,2,4,3,1] => 8 [6,5,3,1,2,4] => 10 [6,5,3,1,4,2] => 8 [6,5,3,2,1,4] => 9 [6,5,3,2,4,1] => 9 [6,5,3,4,1,2] => 6 [6,5,3,4,2,1] => 7 [6,5,4,1,2,3] => 7 [6,5,4,1,3,2] => 10 [6,5,4,2,1,3] => 8 [6,5,4,2,3,1] => 10 [6,5,4,3,1,2] => 7 [6,5,4,3,2,1] => 6 ----------------------------------------------------------------------------- Created: Jan 08, 2018 at 23:38 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jan 09, 2018 at 19:40 by Martin Rubey