***************************************************************************** * 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: St000156 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The Denert index of a permutation. It is defined as \begin{align*} den(\sigma) &= \#\{ 1\leq l < k \leq n : \sigma(k) < \sigma(l) \leq k \} \\ &+ \#\{ 1\leq l < k \leq n : \sigma(l) \leq k < \sigma(k) \} \\ &+ \#\{ 1\leq l < k \leq n : k < \sigma(k) < \sigma(l) \} \end{align*} where $n$ is the size of $\sigma$. It was studied by Denert in [1], and it was shown by Foata and Zeilberger in [2] that the bistatistic $(exc,den)$ is [[Permutations/Descents-Major#Euler-Mahonian_statistics|Euler-Mahonian]]. Here, $exc$ is the number of weak exceedences, see [[St000155]]. ----------------------------------------------------------------------------- References: [1] Denert, M. The genus zeta function of hereditary orders in central simple algebras over global fields [[MathSciNet:0993928]] [2] Foata, D., Zeilberger, D. Denert's permutation statistic is indeed Euler-Mahonian [[MathSciNet:1061147]] [3] Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product_i=0..n-1 (1 + x + ... + x^i), where k ranges from 0 to A000217(n-1). [[OEIS:A008302]] ----------------------------------------------------------------------------- Code: import itertools def statistic(pi): return sum(1 for l, k in itertools.combinations(range(pi.size()), 2) if (pi[k] < pi[l] <= k+1) or (pi[l] <= k+1 < pi[k]) or (k+1 < pi[k] < pi[l])) ----------------------------------------------------------------------------- Statistic values: [1] => 0 [1,2] => 0 [2,1] => 1 [1,2,3] => 0 [1,3,2] => 2 [2,1,3] => 1 [2,3,1] => 3 [3,1,2] => 1 [3,2,1] => 2 [1,2,3,4] => 0 [1,2,4,3] => 3 [1,3,2,4] => 2 [1,3,4,2] => 5 [1,4,2,3] => 2 [1,4,3,2] => 3 [2,1,3,4] => 1 [2,1,4,3] => 4 [2,3,1,4] => 3 [2,3,4,1] => 6 [2,4,1,3] => 3 [2,4,3,1] => 4 [3,1,2,4] => 1 [3,1,4,2] => 4 [3,2,1,4] => 2 [3,2,4,1] => 5 [3,4,1,2] => 3 [3,4,2,1] => 4 [4,1,2,3] => 1 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 3 [4,3,1,2] => 4 [4,3,2,1] => 5 [1,2,3,4,5] => 0 [1,2,3,5,4] => 4 [1,2,4,3,5] => 3 [1,2,4,5,3] => 7 [1,2,5,3,4] => 3 [1,2,5,4,3] => 4 [1,3,2,4,5] => 2 [1,3,2,5,4] => 6 [1,3,4,2,5] => 5 [1,3,4,5,2] => 9 [1,3,5,2,4] => 5 [1,3,5,4,2] => 6 [1,4,2,3,5] => 2 [1,4,2,5,3] => 6 [1,4,3,2,5] => 3 [1,4,3,5,2] => 7 [1,4,5,2,3] => 5 [1,4,5,3,2] => 6 [1,5,2,3,4] => 2 [1,5,2,4,3] => 3 [1,5,3,2,4] => 3 [1,5,3,4,2] => 4 [1,5,4,2,3] => 6 [1,5,4,3,2] => 7 [2,1,3,4,5] => 1 [2,1,3,5,4] => 5 [2,1,4,3,5] => 4 [2,1,4,5,3] => 8 [2,1,5,3,4] => 4 [2,1,5,4,3] => 5 [2,3,1,4,5] => 3 [2,3,1,5,4] => 7 [2,3,4,1,5] => 6 [2,3,4,5,1] => 10 [2,3,5,1,4] => 6 [2,3,5,4,1] => 7 [2,4,1,3,5] => 3 [2,4,1,5,3] => 7 [2,4,3,1,5] => 4 [2,4,3,5,1] => 8 [2,4,5,1,3] => 6 [2,4,5,3,1] => 7 [2,5,1,3,4] => 3 [2,5,1,4,3] => 4 [2,5,3,1,4] => 4 [2,5,3,4,1] => 5 [2,5,4,1,3] => 7 [2,5,4,3,1] => 8 [3,1,2,4,5] => 1 [3,1,2,5,4] => 5 [3,1,4,2,5] => 4 [3,1,4,5,2] => 8 [3,1,5,2,4] => 4 [3,1,5,4,2] => 5 [3,2,1,4,5] => 2 [3,2,1,5,4] => 6 [3,2,4,1,5] => 5 [3,2,4,5,1] => 9 [3,2,5,1,4] => 5 [3,2,5,4,1] => 6 [3,4,1,2,5] => 3 [3,4,1,5,2] => 7 [3,4,2,1,5] => 4 [3,4,2,5,1] => 8 [3,4,5,1,2] => 6 [3,4,5,2,1] => 7 [3,5,1,2,4] => 3 [3,5,1,4,2] => 4 [3,5,2,1,4] => 4 [3,5,2,4,1] => 5 [3,5,4,1,2] => 7 [3,5,4,2,1] => 8 [4,1,2,3,5] => 1 [4,1,2,5,3] => 5 [4,1,3,2,5] => 2 [4,1,3,5,2] => 6 [4,1,5,2,3] => 4 [4,1,5,3,2] => 5 [4,2,1,3,5] => 2 [4,2,1,5,3] => 6 [4,2,3,1,5] => 3 [4,2,3,5,1] => 7 [4,2,5,1,3] => 5 [4,2,5,3,1] => 6 [4,3,1,2,5] => 4 [4,3,1,5,2] => 8 [4,3,2,1,5] => 5 [4,3,2,5,1] => 9 [4,3,5,1,2] => 7 [4,3,5,2,1] => 8 [4,5,1,2,3] => 3 [4,5,1,3,2] => 4 [4,5,2,1,3] => 4 [4,5,2,3,1] => 5 [4,5,3,1,2] => 5 [4,5,3,2,1] => 6 [5,1,2,3,4] => 1 [5,1,2,4,3] => 2 [5,1,3,2,4] => 2 [5,1,3,4,2] => 3 [5,1,4,2,3] => 5 [5,1,4,3,2] => 6 [5,2,1,3,4] => 2 [5,2,1,4,3] => 3 [5,2,3,1,4] => 3 [5,2,3,4,1] => 4 [5,2,4,1,3] => 6 [5,2,4,3,1] => 7 [5,3,1,2,4] => 4 [5,3,1,4,2] => 5 [5,3,2,1,4] => 5 [5,3,2,4,1] => 6 [5,3,4,1,2] => 8 [5,3,4,2,1] => 9 [5,4,1,2,3] => 4 [5,4,1,3,2] => 5 [5,4,2,1,3] => 5 [5,4,2,3,1] => 6 [5,4,3,1,2] => 6 [5,4,3,2,1] => 7 [1,2,3,4,5,6] => 0 [1,2,3,4,6,5] => 5 [1,2,3,5,4,6] => 4 [1,2,3,5,6,4] => 9 [1,2,3,6,4,5] => 4 [1,2,3,6,5,4] => 5 [1,2,4,3,5,6] => 3 [1,2,4,3,6,5] => 8 [1,2,4,5,3,6] => 7 [1,2,4,5,6,3] => 12 [1,2,4,6,3,5] => 7 [1,2,4,6,5,3] => 8 [1,2,5,3,4,6] => 3 [1,2,5,3,6,4] => 8 [1,2,5,4,3,6] => 4 [1,2,5,4,6,3] => 9 [1,2,5,6,3,4] => 7 [1,2,5,6,4,3] => 8 [1,2,6,3,4,5] => 3 [1,2,6,3,5,4] => 4 [1,2,6,4,3,5] => 4 [1,2,6,4,5,3] => 5 [1,2,6,5,3,4] => 8 [1,2,6,5,4,3] => 9 [1,3,2,4,5,6] => 2 [1,3,2,4,6,5] => 7 [1,3,2,5,4,6] => 6 [1,3,2,5,6,4] => 11 [1,3,2,6,4,5] => 6 [1,3,2,6,5,4] => 7 [1,3,4,2,5,6] => 5 [1,3,4,2,6,5] => 10 [1,3,4,5,2,6] => 9 [1,3,4,5,6,2] => 14 [1,3,4,6,2,5] => 9 [1,3,4,6,5,2] => 10 [1,3,5,2,4,6] => 5 [1,3,5,2,6,4] => 10 [1,3,5,4,2,6] => 6 [1,3,5,4,6,2] => 11 [1,3,5,6,2,4] => 9 [1,3,5,6,4,2] => 10 [1,3,6,2,4,5] => 5 [1,3,6,2,5,4] => 6 [1,3,6,4,2,5] => 6 [1,3,6,4,5,2] => 7 [1,3,6,5,2,4] => 10 [1,3,6,5,4,2] => 11 [1,4,2,3,5,6] => 2 [1,4,2,3,6,5] => 7 [1,4,2,5,3,6] => 6 [1,4,2,5,6,3] => 11 [1,4,2,6,3,5] => 6 [1,4,2,6,5,3] => 7 [1,4,3,2,5,6] => 3 [1,4,3,2,6,5] => 8 [1,4,3,5,2,6] => 7 [1,4,3,5,6,2] => 12 [1,4,3,6,2,5] => 7 [1,4,3,6,5,2] => 8 [1,4,5,2,3,6] => 5 [1,4,5,2,6,3] => 10 [1,4,5,3,2,6] => 6 [1,4,5,3,6,2] => 11 [1,4,5,6,2,3] => 9 [1,4,5,6,3,2] => 10 [1,4,6,2,3,5] => 5 [1,4,6,2,5,3] => 6 [1,4,6,3,2,5] => 6 [1,4,6,3,5,2] => 7 [1,4,6,5,2,3] => 10 [1,4,6,5,3,2] => 11 [1,5,2,3,4,6] => 2 [1,5,2,3,6,4] => 7 [1,5,2,4,3,6] => 3 [1,5,2,4,6,3] => 8 [1,5,2,6,3,4] => 6 [1,5,2,6,4,3] => 7 [1,5,3,2,4,6] => 3 [1,5,3,2,6,4] => 8 [1,5,3,4,2,6] => 4 [1,5,3,4,6,2] => 9 [1,5,3,6,2,4] => 7 [1,5,3,6,4,2] => 8 [1,5,4,2,3,6] => 6 [1,5,4,2,6,3] => 11 [1,5,4,3,2,6] => 7 [1,5,4,3,6,2] => 12 [1,5,4,6,2,3] => 10 [1,5,4,6,3,2] => 11 [1,5,6,2,3,4] => 5 [1,5,6,2,4,3] => 6 [1,5,6,3,2,4] => 6 [1,5,6,3,4,2] => 7 [1,5,6,4,2,3] => 7 [1,5,6,4,3,2] => 8 [1,6,2,3,4,5] => 2 [1,6,2,3,5,4] => 3 [1,6,2,4,3,5] => 3 [1,6,2,4,5,3] => 4 [1,6,2,5,3,4] => 7 [1,6,2,5,4,3] => 8 [1,6,3,2,4,5] => 3 [1,6,3,2,5,4] => 4 [1,6,3,4,2,5] => 4 [1,6,3,4,5,2] => 5 [1,6,3,5,2,4] => 8 [1,6,3,5,4,2] => 9 [1,6,4,2,3,5] => 6 [1,6,4,2,5,3] => 7 [1,6,4,3,2,5] => 7 [1,6,4,3,5,2] => 8 [1,6,4,5,2,3] => 11 [1,6,4,5,3,2] => 12 [1,6,5,2,3,4] => 6 [1,6,5,2,4,3] => 7 [1,6,5,3,2,4] => 7 [1,6,5,3,4,2] => 8 [1,6,5,4,2,3] => 8 [1,6,5,4,3,2] => 9 [2,1,3,4,5,6] => 1 [2,1,3,4,6,5] => 6 [2,1,3,5,4,6] => 5 [2,1,3,5,6,4] => 10 [2,1,3,6,4,5] => 5 [2,1,3,6,5,4] => 6 [2,1,4,3,5,6] => 4 [2,1,4,3,6,5] => 9 [2,1,4,5,3,6] => 8 [2,1,4,5,6,3] => 13 [2,1,4,6,3,5] => 8 [2,1,4,6,5,3] => 9 [2,1,5,3,4,6] => 4 [2,1,5,3,6,4] => 9 [2,1,5,4,3,6] => 5 [2,1,5,4,6,3] => 10 [2,1,5,6,3,4] => 8 [2,1,5,6,4,3] => 9 [2,1,6,3,4,5] => 4 [2,1,6,3,5,4] => 5 [2,1,6,4,3,5] => 5 [2,1,6,4,5,3] => 6 [2,1,6,5,3,4] => 9 [2,1,6,5,4,3] => 10 [2,3,1,4,5,6] => 3 [2,3,1,4,6,5] => 8 [2,3,1,5,4,6] => 7 [2,3,1,5,6,4] => 12 [2,3,1,6,4,5] => 7 [2,3,1,6,5,4] => 8 [2,3,4,1,5,6] => 6 [2,3,4,1,6,5] => 11 [2,3,4,5,1,6] => 10 [2,3,4,5,6,1] => 15 [2,3,4,6,1,5] => 10 [2,3,4,6,5,1] => 11 [2,3,5,1,4,6] => 6 [2,3,5,1,6,4] => 11 [2,3,5,4,1,6] => 7 [2,3,5,4,6,1] => 12 [2,3,5,6,1,4] => 10 [2,3,5,6,4,1] => 11 [2,3,6,1,4,5] => 6 [2,3,6,1,5,4] => 7 [2,3,6,4,1,5] => 7 [2,3,6,4,5,1] => 8 [2,3,6,5,1,4] => 11 [2,3,6,5,4,1] => 12 [2,4,1,3,5,6] => 3 [2,4,1,3,6,5] => 8 [2,4,1,5,3,6] => 7 [2,4,1,5,6,3] => 12 [2,4,1,6,3,5] => 7 [2,4,1,6,5,3] => 8 [2,4,3,1,5,6] => 4 [2,4,3,1,6,5] => 9 [2,4,3,5,1,6] => 8 [2,4,3,5,6,1] => 13 [2,4,3,6,1,5] => 8 [2,4,3,6,5,1] => 9 [2,4,5,1,3,6] => 6 [2,4,5,1,6,3] => 11 [2,4,5,3,1,6] => 7 [2,4,5,3,6,1] => 12 [2,4,5,6,1,3] => 10 [2,4,5,6,3,1] => 11 [2,4,6,1,3,5] => 6 [2,4,6,1,5,3] => 7 [2,4,6,3,1,5] => 7 [2,4,6,3,5,1] => 8 [2,4,6,5,1,3] => 11 [2,4,6,5,3,1] => 12 [2,5,1,3,4,6] => 3 [2,5,1,3,6,4] => 8 [2,5,1,4,3,6] => 4 [2,5,1,4,6,3] => 9 [2,5,1,6,3,4] => 7 [2,5,1,6,4,3] => 8 [2,5,3,1,4,6] => 4 [2,5,3,1,6,4] => 9 [2,5,3,4,1,6] => 5 [2,5,3,4,6,1] => 10 [2,5,3,6,1,4] => 8 [2,5,3,6,4,1] => 9 [2,5,4,1,3,6] => 7 [2,5,4,1,6,3] => 12 [2,5,4,3,1,6] => 8 [2,5,4,3,6,1] => 13 [2,5,4,6,1,3] => 11 [2,5,4,6,3,1] => 12 [2,5,6,1,3,4] => 6 [2,5,6,1,4,3] => 7 [2,5,6,3,1,4] => 7 [2,5,6,3,4,1] => 8 [2,5,6,4,1,3] => 8 [2,5,6,4,3,1] => 9 [2,6,1,3,4,5] => 3 [2,6,1,3,5,4] => 4 [2,6,1,4,3,5] => 4 [2,6,1,4,5,3] => 5 [2,6,1,5,3,4] => 8 [2,6,1,5,4,3] => 9 [2,6,3,1,4,5] => 4 [2,6,3,1,5,4] => 5 [2,6,3,4,1,5] => 5 [2,6,3,4,5,1] => 6 [2,6,3,5,1,4] => 9 [2,6,3,5,4,1] => 10 [2,6,4,1,3,5] => 7 [2,6,4,1,5,3] => 8 [2,6,4,3,1,5] => 8 [2,6,4,3,5,1] => 9 [2,6,4,5,1,3] => 12 [2,6,4,5,3,1] => 13 [2,6,5,1,3,4] => 7 [2,6,5,1,4,3] => 8 [2,6,5,3,1,4] => 8 [2,6,5,3,4,1] => 9 [2,6,5,4,1,3] => 9 [2,6,5,4,3,1] => 10 [3,1,2,4,5,6] => 1 [3,1,2,4,6,5] => 6 [3,1,2,5,4,6] => 5 [3,1,2,5,6,4] => 10 [3,1,2,6,4,5] => 5 [3,1,2,6,5,4] => 6 [3,1,4,2,5,6] => 4 [3,1,4,2,6,5] => 9 [3,1,4,5,2,6] => 8 [3,1,4,5,6,2] => 13 [3,1,4,6,2,5] => 8 [3,1,4,6,5,2] => 9 [3,1,5,2,4,6] => 4 [3,1,5,2,6,4] => 9 [3,1,5,4,2,6] => 5 [3,1,5,4,6,2] => 10 [3,1,5,6,2,4] => 8 [3,1,5,6,4,2] => 9 [3,1,6,2,4,5] => 4 [3,1,6,2,5,4] => 5 [3,1,6,4,2,5] => 5 [3,1,6,4,5,2] => 6 [3,1,6,5,2,4] => 9 [3,1,6,5,4,2] => 10 [3,2,1,4,5,6] => 2 [3,2,1,4,6,5] => 7 [3,2,1,5,4,6] => 6 [3,2,1,5,6,4] => 11 [3,2,1,6,4,5] => 6 [3,2,1,6,5,4] => 7 [3,2,4,1,5,6] => 5 [3,2,4,1,6,5] => 10 [3,2,4,5,1,6] => 9 [3,2,4,5,6,1] => 14 [3,2,4,6,1,5] => 9 [3,2,4,6,5,1] => 10 [3,2,5,1,4,6] => 5 [3,2,5,1,6,4] => 10 [3,2,5,4,1,6] => 6 [3,2,5,4,6,1] => 11 [3,2,5,6,1,4] => 9 [3,2,5,6,4,1] => 10 [3,2,6,1,4,5] => 5 [3,2,6,1,5,4] => 6 [3,2,6,4,1,5] => 6 [3,2,6,4,5,1] => 7 [3,2,6,5,1,4] => 10 [3,2,6,5,4,1] => 11 [3,4,1,2,5,6] => 3 [3,4,1,2,6,5] => 8 [3,4,1,5,2,6] => 7 [3,4,1,5,6,2] => 12 [3,4,1,6,2,5] => 7 [3,4,1,6,5,2] => 8 [3,4,2,1,5,6] => 4 [3,4,2,1,6,5] => 9 [3,4,2,5,1,6] => 8 [3,4,2,5,6,1] => 13 [3,4,2,6,1,5] => 8 [3,4,2,6,5,1] => 9 [3,4,5,1,2,6] => 6 [3,4,5,1,6,2] => 11 [3,4,5,2,1,6] => 7 [3,4,5,2,6,1] => 12 [3,4,5,6,1,2] => 10 [3,4,5,6,2,1] => 11 [3,4,6,1,2,5] => 6 [3,4,6,1,5,2] => 7 [3,4,6,2,1,5] => 7 [3,4,6,2,5,1] => 8 [3,4,6,5,1,2] => 11 [3,4,6,5,2,1] => 12 [3,5,1,2,4,6] => 3 [3,5,1,2,6,4] => 8 [3,5,1,4,2,6] => 4 [3,5,1,4,6,2] => 9 [3,5,1,6,2,4] => 7 [3,5,1,6,4,2] => 8 [3,5,2,1,4,6] => 4 [3,5,2,1,6,4] => 9 [3,5,2,4,1,6] => 5 [3,5,2,4,6,1] => 10 [3,5,2,6,1,4] => 8 [3,5,2,6,4,1] => 9 [3,5,4,1,2,6] => 7 [3,5,4,1,6,2] => 12 [3,5,4,2,1,6] => 8 [3,5,4,2,6,1] => 13 [3,5,4,6,1,2] => 11 [3,5,4,6,2,1] => 12 [3,5,6,1,2,4] => 6 [3,5,6,1,4,2] => 7 [3,5,6,2,1,4] => 7 [3,5,6,2,4,1] => 8 [3,5,6,4,1,2] => 8 [3,5,6,4,2,1] => 9 [3,6,1,2,4,5] => 3 [3,6,1,2,5,4] => 4 [3,6,1,4,2,5] => 4 [3,6,1,4,5,2] => 5 [3,6,1,5,2,4] => 8 [3,6,1,5,4,2] => 9 [3,6,2,1,4,5] => 4 [3,6,2,1,5,4] => 5 [3,6,2,4,1,5] => 5 [3,6,2,4,5,1] => 6 [3,6,2,5,1,4] => 9 [3,6,2,5,4,1] => 10 [3,6,4,1,2,5] => 7 [3,6,4,1,5,2] => 8 [3,6,4,2,1,5] => 8 [3,6,4,2,5,1] => 9 [3,6,4,5,1,2] => 12 [3,6,4,5,2,1] => 13 [3,6,5,1,2,4] => 7 [3,6,5,1,4,2] => 8 [3,6,5,2,1,4] => 8 [3,6,5,2,4,1] => 9 [3,6,5,4,1,2] => 9 [3,6,5,4,2,1] => 10 [4,1,2,3,5,6] => 1 [4,1,2,3,6,5] => 6 [4,1,2,5,3,6] => 5 [4,1,2,5,6,3] => 10 [4,1,2,6,3,5] => 5 [4,1,2,6,5,3] => 6 [4,1,3,2,5,6] => 2 [4,1,3,2,6,5] => 7 [4,1,3,5,2,6] => 6 [4,1,3,5,6,2] => 11 [4,1,3,6,2,5] => 6 [4,1,3,6,5,2] => 7 [4,1,5,2,3,6] => 4 [4,1,5,2,6,3] => 9 [4,1,5,3,2,6] => 5 [4,1,5,3,6,2] => 10 [4,1,5,6,2,3] => 8 [4,1,5,6,3,2] => 9 [4,1,6,2,3,5] => 4 [4,1,6,2,5,3] => 5 [4,1,6,3,2,5] => 5 [4,1,6,3,5,2] => 6 [4,1,6,5,2,3] => 9 [4,1,6,5,3,2] => 10 [4,2,1,3,5,6] => 2 [4,2,1,3,6,5] => 7 [4,2,1,5,3,6] => 6 [4,2,1,5,6,3] => 11 [4,2,1,6,3,5] => 6 [4,2,1,6,5,3] => 7 [4,2,3,1,5,6] => 3 [4,2,3,1,6,5] => 8 [4,2,3,5,1,6] => 7 [4,2,3,5,6,1] => 12 [4,2,3,6,1,5] => 7 [4,2,3,6,5,1] => 8 [4,2,5,1,3,6] => 5 [4,2,5,1,6,3] => 10 [4,2,5,3,1,6] => 6 [4,2,5,3,6,1] => 11 [4,2,5,6,1,3] => 9 [4,2,5,6,3,1] => 10 [4,2,6,1,3,5] => 5 [4,2,6,1,5,3] => 6 [4,2,6,3,1,5] => 6 [4,2,6,3,5,1] => 7 [4,2,6,5,1,3] => 10 [4,2,6,5,3,1] => 11 [4,3,1,2,5,6] => 4 [4,3,1,2,6,5] => 9 [4,3,1,5,2,6] => 8 [4,3,1,5,6,2] => 13 [4,3,1,6,2,5] => 8 [4,3,1,6,5,2] => 9 [4,3,2,1,5,6] => 5 [4,3,2,1,6,5] => 10 [4,3,2,5,1,6] => 9 [4,3,2,5,6,1] => 14 [4,3,2,6,1,5] => 9 [4,3,2,6,5,1] => 10 [4,3,5,1,2,6] => 7 [4,3,5,1,6,2] => 12 [4,3,5,2,1,6] => 8 [4,3,5,2,6,1] => 13 [4,3,5,6,1,2] => 11 [4,3,5,6,2,1] => 12 [4,3,6,1,2,5] => 7 [4,3,6,1,5,2] => 8 [4,3,6,2,1,5] => 8 [4,3,6,2,5,1] => 9 [4,3,6,5,1,2] => 12 [4,3,6,5,2,1] => 13 [4,5,1,2,3,6] => 3 [4,5,1,2,6,3] => 8 [4,5,1,3,2,6] => 4 [4,5,1,3,6,2] => 9 [4,5,1,6,2,3] => 7 [4,5,1,6,3,2] => 8 [4,5,2,1,3,6] => 4 [4,5,2,1,6,3] => 9 [4,5,2,3,1,6] => 5 [4,5,2,3,6,1] => 10 [4,5,2,6,1,3] => 8 [4,5,2,6,3,1] => 9 [4,5,3,1,2,6] => 5 [4,5,3,1,6,2] => 10 [4,5,3,2,1,6] => 6 [4,5,3,2,6,1] => 11 [4,5,3,6,1,2] => 9 [4,5,3,6,2,1] => 10 [4,5,6,1,2,3] => 6 [4,5,6,1,3,2] => 7 [4,5,6,2,1,3] => 7 [4,5,6,2,3,1] => 8 [4,5,6,3,1,2] => 8 [4,5,6,3,2,1] => 9 [4,6,1,2,3,5] => 3 [4,6,1,2,5,3] => 4 [4,6,1,3,2,5] => 4 [4,6,1,3,5,2] => 5 [4,6,1,5,2,3] => 8 [4,6,1,5,3,2] => 9 [4,6,2,1,3,5] => 4 [4,6,2,1,5,3] => 5 [4,6,2,3,1,5] => 5 [4,6,2,3,5,1] => 6 [4,6,2,5,1,3] => 9 [4,6,2,5,3,1] => 10 [4,6,3,1,2,5] => 5 [4,6,3,1,5,2] => 6 [4,6,3,2,1,5] => 6 [4,6,3,2,5,1] => 7 [4,6,3,5,1,2] => 10 [4,6,3,5,2,1] => 11 [4,6,5,1,2,3] => 7 [4,6,5,1,3,2] => 8 [4,6,5,2,1,3] => 8 [4,6,5,2,3,1] => 9 [4,6,5,3,1,2] => 9 [4,6,5,3,2,1] => 10 [5,1,2,3,4,6] => 1 [5,1,2,3,6,4] => 6 [5,1,2,4,3,6] => 2 [5,1,2,4,6,3] => 7 [5,1,2,6,3,4] => 5 [5,1,2,6,4,3] => 6 [5,1,3,2,4,6] => 2 [5,1,3,2,6,4] => 7 [5,1,3,4,2,6] => 3 [5,1,3,4,6,2] => 8 [5,1,3,6,2,4] => 6 [5,1,3,6,4,2] => 7 [5,1,4,2,3,6] => 5 [5,1,4,2,6,3] => 10 [5,1,4,3,2,6] => 6 [5,1,4,3,6,2] => 11 [5,1,4,6,2,3] => 9 [5,1,4,6,3,2] => 10 [5,1,6,2,3,4] => 4 [5,1,6,2,4,3] => 5 [5,1,6,3,2,4] => 5 [5,1,6,3,4,2] => 6 [5,1,6,4,2,3] => 6 [5,1,6,4,3,2] => 7 [5,2,1,3,4,6] => 2 [5,2,1,3,6,4] => 7 [5,2,1,4,3,6] => 3 [5,2,1,4,6,3] => 8 [5,2,1,6,3,4] => 6 [5,2,1,6,4,3] => 7 [5,2,3,1,4,6] => 3 [5,2,3,1,6,4] => 8 [5,2,3,4,1,6] => 4 [5,2,3,4,6,1] => 9 [5,2,3,6,1,4] => 7 [5,2,3,6,4,1] => 8 [5,2,4,1,3,6] => 6 [5,2,4,1,6,3] => 11 [5,2,4,3,1,6] => 7 [5,2,4,3,6,1] => 12 [5,2,4,6,1,3] => 10 [5,2,4,6,3,1] => 11 [5,2,6,1,3,4] => 5 [5,2,6,1,4,3] => 6 [5,2,6,3,1,4] => 6 [5,2,6,3,4,1] => 7 [5,2,6,4,1,3] => 7 [5,2,6,4,3,1] => 8 [5,3,1,2,4,6] => 4 [5,3,1,2,6,4] => 9 [5,3,1,4,2,6] => 5 [5,3,1,4,6,2] => 10 [5,3,1,6,2,4] => 8 [5,3,1,6,4,2] => 9 [5,3,2,1,4,6] => 5 [5,3,2,1,6,4] => 10 [5,3,2,4,1,6] => 6 [5,3,2,4,6,1] => 11 [5,3,2,6,1,4] => 9 [5,3,2,6,4,1] => 10 [5,3,4,1,2,6] => 8 [5,3,4,1,6,2] => 13 [5,3,4,2,1,6] => 9 [5,3,4,2,6,1] => 14 [5,3,4,6,1,2] => 12 [5,3,4,6,2,1] => 13 [5,3,6,1,2,4] => 7 [5,3,6,1,4,2] => 8 [5,3,6,2,1,4] => 8 [5,3,6,2,4,1] => 9 [5,3,6,4,1,2] => 9 [5,3,6,4,2,1] => 10 [5,4,1,2,3,6] => 4 [5,4,1,2,6,3] => 9 [5,4,1,3,2,6] => 5 [5,4,1,3,6,2] => 10 [5,4,1,6,2,3] => 8 [5,4,1,6,3,2] => 9 [5,4,2,1,3,6] => 5 [5,4,2,1,6,3] => 10 [5,4,2,3,1,6] => 6 [5,4,2,3,6,1] => 11 [5,4,2,6,1,3] => 9 [5,4,2,6,3,1] => 10 [5,4,3,1,2,6] => 6 [5,4,3,1,6,2] => 11 [5,4,3,2,1,6] => 7 [5,4,3,2,6,1] => 12 [5,4,3,6,1,2] => 10 [5,4,3,6,2,1] => 11 [5,4,6,1,2,3] => 7 [5,4,6,1,3,2] => 8 [5,4,6,2,1,3] => 8 [5,4,6,2,3,1] => 9 [5,4,6,3,1,2] => 9 [5,4,6,3,2,1] => 10 [5,6,1,2,3,4] => 3 [5,6,1,2,4,3] => 4 [5,6,1,3,2,4] => 4 [5,6,1,3,4,2] => 5 [5,6,1,4,2,3] => 5 [5,6,1,4,3,2] => 6 [5,6,2,1,3,4] => 4 [5,6,2,1,4,3] => 5 [5,6,2,3,1,4] => 5 [5,6,2,3,4,1] => 6 [5,6,2,4,1,3] => 6 [5,6,2,4,3,1] => 7 [5,6,3,1,2,4] => 5 [5,6,3,1,4,2] => 6 [5,6,3,2,1,4] => 6 [5,6,3,2,4,1] => 7 [5,6,3,4,1,2] => 7 [5,6,3,4,2,1] => 8 [5,6,4,1,2,3] => 8 [5,6,4,1,3,2] => 9 [5,6,4,2,1,3] => 9 [5,6,4,2,3,1] => 10 [5,6,4,3,1,2] => 10 [5,6,4,3,2,1] => 11 [6,1,2,3,4,5] => 1 [6,1,2,3,5,4] => 2 [6,1,2,4,3,5] => 2 [6,1,2,4,5,3] => 3 [6,1,2,5,3,4] => 6 [6,1,2,5,4,3] => 7 [6,1,3,2,4,5] => 2 [6,1,3,2,5,4] => 3 [6,1,3,4,2,5] => 3 [6,1,3,4,5,2] => 4 [6,1,3,5,2,4] => 7 [6,1,3,5,4,2] => 8 [6,1,4,2,3,5] => 5 [6,1,4,2,5,3] => 6 [6,1,4,3,2,5] => 6 [6,1,4,3,5,2] => 7 [6,1,4,5,2,3] => 10 [6,1,4,5,3,2] => 11 [6,1,5,2,3,4] => 5 [6,1,5,2,4,3] => 6 [6,1,5,3,2,4] => 6 [6,1,5,3,4,2] => 7 [6,1,5,4,2,3] => 7 [6,1,5,4,3,2] => 8 [6,2,1,3,4,5] => 2 [6,2,1,3,5,4] => 3 [6,2,1,4,3,5] => 3 [6,2,1,4,5,3] => 4 [6,2,1,5,3,4] => 7 [6,2,1,5,4,3] => 8 [6,2,3,1,4,5] => 3 [6,2,3,1,5,4] => 4 [6,2,3,4,1,5] => 4 [6,2,3,4,5,1] => 5 [6,2,3,5,1,4] => 8 [6,2,3,5,4,1] => 9 [6,2,4,1,3,5] => 6 [6,2,4,1,5,3] => 7 [6,2,4,3,1,5] => 7 [6,2,4,3,5,1] => 8 [6,2,4,5,1,3] => 11 [6,2,4,5,3,1] => 12 [6,2,5,1,3,4] => 6 [6,2,5,1,4,3] => 7 [6,2,5,3,1,4] => 7 [6,2,5,3,4,1] => 8 [6,2,5,4,1,3] => 8 [6,2,5,4,3,1] => 9 [6,3,1,2,4,5] => 4 [6,3,1,2,5,4] => 5 [6,3,1,4,2,5] => 5 [6,3,1,4,5,2] => 6 [6,3,1,5,2,4] => 9 [6,3,1,5,4,2] => 10 [6,3,2,1,4,5] => 5 [6,3,2,1,5,4] => 6 [6,3,2,4,1,5] => 6 [6,3,2,4,5,1] => 7 [6,3,2,5,1,4] => 10 [6,3,2,5,4,1] => 11 [6,3,4,1,2,5] => 8 [6,3,4,1,5,2] => 9 [6,3,4,2,1,5] => 9 [6,3,4,2,5,1] => 10 [6,3,4,5,1,2] => 13 [6,3,4,5,2,1] => 14 [6,3,5,1,2,4] => 8 [6,3,5,1,4,2] => 9 [6,3,5,2,1,4] => 9 [6,3,5,2,4,1] => 10 [6,3,5,4,1,2] => 10 [6,3,5,4,2,1] => 11 [6,4,1,2,3,5] => 4 [6,4,1,2,5,3] => 5 [6,4,1,3,2,5] => 5 [6,4,1,3,5,2] => 6 [6,4,1,5,2,3] => 9 [6,4,1,5,3,2] => 10 [6,4,2,1,3,5] => 5 [6,4,2,1,5,3] => 6 [6,4,2,3,1,5] => 6 [6,4,2,3,5,1] => 7 [6,4,2,5,1,3] => 10 [6,4,2,5,3,1] => 11 [6,4,3,1,2,5] => 6 [6,4,3,1,5,2] => 7 [6,4,3,2,1,5] => 7 [6,4,3,2,5,1] => 8 [6,4,3,5,1,2] => 11 [6,4,3,5,2,1] => 12 [6,4,5,1,2,3] => 8 [6,4,5,1,3,2] => 9 [6,4,5,2,1,3] => 9 [6,4,5,2,3,1] => 10 [6,4,5,3,1,2] => 10 [6,4,5,3,2,1] => 11 [6,5,1,2,3,4] => 4 [6,5,1,2,4,3] => 5 [6,5,1,3,2,4] => 5 [6,5,1,3,4,2] => 6 [6,5,1,4,2,3] => 6 [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] => 8 [6,5,3,1,2,4] => 6 [6,5,3,1,4,2] => 7 [6,5,3,2,1,4] => 7 [6,5,3,2,4,1] => 8 [6,5,3,4,1,2] => 8 [6,5,3,4,2,1] => 9 [6,5,4,1,2,3] => 9 [6,5,4,1,3,2] => 10 [6,5,4,2,1,3] => 10 [6,5,4,2,3,1] => 11 [6,5,4,3,1,2] => 11 [6,5,4,3,2,1] => 12 ----------------------------------------------------------------------------- Created: Jul 24, 2013 at 12:25 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Feb 27, 2023 at 12:37 by Martin Rubey