***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew <info@findstat.org> * * * * 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: St001731 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The factorization defect of a permutation. The '''factorization poset''' of a permutation $\sigma$ is the principal order ideal generated by $\sigma$ in the absolute order. In particular, the maximal chains in the factorization poset of $\sigma$ are in bijection with the reduced factorizations of $\sigma$ into transpositions. The '''factorization defect''' of $\sigma$ is the number of rank-2 elements in its factorization poset. This is the statistic "d" defined in [1, Section 6.1], where it was called the '''minimal size of a feedback arc set''' in the cycle graph. The fact that this equals the number of rank-2 elements in the factorization poset follows from [1, Proposition 6.3] together with the shellability of the factorization poset. ----------------------------------------------------------------------------- References: [1] Mühle, H., Ripoll, V. Connectivity Properties of Factorization Posets in Generated Groups [[DOI:10.1007/s11083-019-09496-1]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,2] => 0 [2,1] => 0 [1,2,3] => 0 [1,3,2] => 0 [2,1,3] => 0 [2,3,1] => 1 [3,1,2] => 1 [3,2,1] => 0 [1,2,3,4] => 0 [1,2,4,3] => 0 [1,3,2,4] => 0 [1,3,4,2] => 1 [1,4,2,3] => 1 [1,4,3,2] => 0 [2,1,3,4] => 0 [2,1,4,3] => 1 [2,3,1,4] => 1 [2,3,4,1] => 6 [2,4,1,3] => 6 [2,4,3,1] => 1 [3,1,2,4] => 1 [3,1,4,2] => 6 [3,2,1,4] => 0 [3,2,4,1] => 1 [3,4,1,2] => 1 [3,4,2,1] => 6 [4,1,2,3] => 6 [4,1,3,2] => 1 [4,2,1,3] => 1 [4,2,3,1] => 0 [4,3,1,2] => 6 [4,3,2,1] => 1 [1,2,3,4,5] => 0 [1,2,3,5,4] => 0 [1,2,4,3,5] => 0 [1,2,4,5,3] => 1 [1,2,5,3,4] => 1 [1,2,5,4,3] => 0 [1,3,2,4,5] => 0 [1,3,2,5,4] => 1 [1,3,4,2,5] => 1 [1,3,4,5,2] => 6 [1,3,5,2,4] => 6 [1,3,5,4,2] => 1 [1,4,2,3,5] => 1 [1,4,2,5,3] => 6 [1,4,3,2,5] => 0 [1,4,3,5,2] => 1 [1,4,5,2,3] => 1 [1,4,5,3,2] => 6 [1,5,2,3,4] => 6 [1,5,2,4,3] => 1 [1,5,3,2,4] => 1 [1,5,3,4,2] => 0 [1,5,4,2,3] => 6 [1,5,4,3,2] => 1 [2,1,3,4,5] => 0 [2,1,3,5,4] => 1 [2,1,4,3,5] => 1 [2,1,4,5,3] => 4 [2,1,5,3,4] => 4 [2,1,5,4,3] => 1 [2,3,1,4,5] => 1 [2,3,1,5,4] => 4 [2,3,4,1,5] => 6 [2,3,4,5,1] => 20 [2,3,5,1,4] => 20 [2,3,5,4,1] => 6 [2,4,1,3,5] => 6 [2,4,1,5,3] => 20 [2,4,3,1,5] => 1 [2,4,3,5,1] => 6 [2,4,5,1,3] => 4 [2,4,5,3,1] => 20 [2,5,1,3,4] => 20 [2,5,1,4,3] => 6 [2,5,3,1,4] => 6 [2,5,3,4,1] => 1 [2,5,4,1,3] => 20 [2,5,4,3,1] => 4 [3,1,2,4,5] => 1 [3,1,2,5,4] => 4 [3,1,4,2,5] => 6 [3,1,4,5,2] => 20 [3,1,5,2,4] => 20 [3,1,5,4,2] => 6 [3,2,1,4,5] => 0 [3,2,1,5,4] => 1 [3,2,4,1,5] => 1 [3,2,4,5,1] => 6 [3,2,5,1,4] => 6 [3,2,5,4,1] => 1 [3,4,1,2,5] => 1 [3,4,1,5,2] => 4 [3,4,2,1,5] => 6 [3,4,2,5,1] => 20 [3,4,5,1,2] => 20 [3,4,5,2,1] => 4 [3,5,1,2,4] => 4 [3,5,1,4,2] => 1 [3,5,2,1,4] => 20 [3,5,2,4,1] => 6 [3,5,4,1,2] => 4 [3,5,4,2,1] => 20 [4,1,2,3,5] => 6 [4,1,2,5,3] => 20 [4,1,3,2,5] => 1 [4,1,3,5,2] => 6 [4,1,5,2,3] => 4 [4,1,5,3,2] => 20 [4,2,1,3,5] => 1 [4,2,1,5,3] => 6 [4,2,3,1,5] => 0 [4,2,3,5,1] => 1 [4,2,5,1,3] => 1 [4,2,5,3,1] => 6 [4,3,1,2,5] => 6 [4,3,1,5,2] => 20 [4,3,2,1,5] => 1 [4,3,2,5,1] => 4 [4,3,5,1,2] => 4 [4,3,5,2,1] => 20 [4,5,1,2,3] => 20 [4,5,1,3,2] => 4 [4,5,2,1,3] => 4 [4,5,2,3,1] => 20 [4,5,3,1,2] => 1 [4,5,3,2,1] => 6 [5,1,2,3,4] => 20 [5,1,2,4,3] => 6 [5,1,3,2,4] => 6 [5,1,3,4,2] => 1 [5,1,4,2,3] => 20 [5,1,4,3,2] => 4 [5,2,1,3,4] => 6 [5,2,1,4,3] => 1 [5,2,3,1,4] => 1 [5,2,3,4,1] => 0 [5,2,4,1,3] => 6 [5,2,4,3,1] => 1 [5,3,1,2,4] => 20 [5,3,1,4,2] => 6 [5,3,2,1,4] => 4 [5,3,2,4,1] => 1 [5,3,4,1,2] => 20 [5,3,4,2,1] => 4 [5,4,1,2,3] => 4 [5,4,1,3,2] => 20 [5,4,2,1,3] => 20 [5,4,2,3,1] => 4 [5,4,3,1,2] => 6 [5,4,3,2,1] => 1 [1,2,3,4,5,6] => 0 [1,2,3,4,6,5] => 0 [1,2,3,5,4,6] => 0 [1,2,3,5,6,4] => 1 [1,2,3,6,4,5] => 1 [1,2,3,6,5,4] => 0 [1,2,4,3,5,6] => 0 [1,2,4,3,6,5] => 1 [1,2,4,5,3,6] => 1 [1,2,4,5,6,3] => 6 [1,2,4,6,3,5] => 6 [1,2,4,6,5,3] => 1 [1,2,5,3,4,6] => 1 [1,2,5,3,6,4] => 6 [1,2,5,4,3,6] => 0 [1,2,5,4,6,3] => 1 [1,2,5,6,3,4] => 1 [1,2,5,6,4,3] => 6 [1,2,6,3,4,5] => 6 [1,2,6,3,5,4] => 1 [1,2,6,4,3,5] => 1 [1,2,6,4,5,3] => 0 [1,2,6,5,3,4] => 6 [1,2,6,5,4,3] => 1 [1,3,2,4,5,6] => 0 [1,3,2,4,6,5] => 1 [1,3,2,5,4,6] => 1 [1,3,2,5,6,4] => 4 [1,3,2,6,4,5] => 4 [1,3,2,6,5,4] => 1 [1,3,4,2,5,6] => 1 [1,3,4,2,6,5] => 4 [1,3,4,5,2,6] => 6 [1,3,4,5,6,2] => 20 [1,3,4,6,2,5] => 20 [1,3,4,6,5,2] => 6 [1,3,5,2,4,6] => 6 [1,3,5,2,6,4] => 20 [1,3,5,4,2,6] => 1 [1,3,5,4,6,2] => 6 [1,3,5,6,2,4] => 4 [1,3,5,6,4,2] => 20 [1,3,6,2,4,5] => 20 [1,3,6,2,5,4] => 6 [1,3,6,4,2,5] => 6 [1,3,6,4,5,2] => 1 [1,3,6,5,2,4] => 20 [1,3,6,5,4,2] => 4 [1,4,2,3,5,6] => 1 [1,4,2,3,6,5] => 4 [1,4,2,5,3,6] => 6 [1,4,2,5,6,3] => 20 [1,4,2,6,3,5] => 20 [1,4,2,6,5,3] => 6 [1,4,3,2,5,6] => 0 [1,4,3,2,6,5] => 1 [1,4,3,5,2,6] => 1 [1,4,3,5,6,2] => 6 [1,4,3,6,2,5] => 6 [1,4,3,6,5,2] => 1 [1,4,5,2,3,6] => 1 [1,4,5,2,6,3] => 4 [1,4,5,3,2,6] => 6 [1,4,5,3,6,2] => 20 [1,4,5,6,2,3] => 20 [1,4,5,6,3,2] => 4 [1,4,6,2,3,5] => 4 [1,4,6,2,5,3] => 1 [1,4,6,3,2,5] => 20 [1,4,6,3,5,2] => 6 [1,4,6,5,2,3] => 4 [1,4,6,5,3,2] => 20 [1,5,2,3,4,6] => 6 [1,5,2,3,6,4] => 20 [1,5,2,4,3,6] => 1 [1,5,2,4,6,3] => 6 [1,5,2,6,3,4] => 4 [1,5,2,6,4,3] => 20 [1,5,3,2,4,6] => 1 [1,5,3,2,6,4] => 6 [1,5,3,4,2,6] => 0 [1,5,3,4,6,2] => 1 [1,5,3,6,2,4] => 1 [1,5,3,6,4,2] => 6 [1,5,4,2,3,6] => 6 [1,5,4,2,6,3] => 20 [1,5,4,3,2,6] => 1 [1,5,4,3,6,2] => 4 [1,5,4,6,2,3] => 4 [1,5,4,6,3,2] => 20 [1,5,6,2,3,4] => 20 [1,5,6,2,4,3] => 4 [1,5,6,3,2,4] => 4 [1,5,6,3,4,2] => 20 [1,5,6,4,2,3] => 1 [1,5,6,4,3,2] => 6 [1,6,2,3,4,5] => 20 [1,6,2,3,5,4] => 6 [1,6,2,4,3,5] => 6 [1,6,2,4,5,3] => 1 [1,6,2,5,3,4] => 20 [1,6,2,5,4,3] => 4 [1,6,3,2,4,5] => 6 [1,6,3,2,5,4] => 1 [1,6,3,4,2,5] => 1 [1,6,3,4,5,2] => 0 [1,6,3,5,2,4] => 6 [1,6,3,5,4,2] => 1 [1,6,4,2,3,5] => 20 [1,6,4,2,5,3] => 6 [1,6,4,3,2,5] => 4 [1,6,4,3,5,2] => 1 [1,6,4,5,2,3] => 20 [1,6,4,5,3,2] => 4 [1,6,5,2,3,4] => 4 [1,6,5,2,4,3] => 20 [1,6,5,3,2,4] => 20 [1,6,5,3,4,2] => 4 [1,6,5,4,2,3] => 6 [1,6,5,4,3,2] => 1 [2,1,3,4,5,6] => 0 [2,1,3,4,6,5] => 1 [2,1,3,5,4,6] => 1 [2,1,3,5,6,4] => 4 [2,1,3,6,4,5] => 4 [2,1,3,6,5,4] => 1 [2,1,4,3,5,6] => 1 [2,1,4,3,6,5] => 3 [2,1,4,5,3,6] => 4 [2,1,4,5,6,3] => 12 [2,1,4,6,3,5] => 12 [2,1,4,6,5,3] => 4 [2,1,5,3,4,6] => 4 [2,1,5,3,6,4] => 12 [2,1,5,4,3,6] => 1 [2,1,5,4,6,3] => 4 [2,1,5,6,3,4] => 3 [2,1,5,6,4,3] => 12 [2,1,6,3,4,5] => 12 [2,1,6,3,5,4] => 4 [2,1,6,4,3,5] => 4 [2,1,6,4,5,3] => 1 [2,1,6,5,3,4] => 12 [2,1,6,5,4,3] => 3 [2,3,1,4,5,6] => 1 [2,3,1,4,6,5] => 4 [2,3,1,5,4,6] => 4 [2,3,1,5,6,4] => 11 [2,3,1,6,4,5] => 11 [2,3,1,6,5,4] => 4 [2,3,4,1,5,6] => 6 [2,3,4,1,6,5] => 12 [2,3,4,5,1,6] => 20 [2,3,4,5,6,1] => 50 [2,3,4,6,1,5] => 50 [2,3,4,6,5,1] => 20 [2,3,5,1,4,6] => 20 [2,3,5,1,6,4] => 50 [2,3,5,4,1,6] => 6 [2,3,5,4,6,1] => 20 [2,3,5,6,1,4] => 12 [2,3,5,6,4,1] => 50 [2,3,6,1,4,5] => 50 [2,3,6,1,5,4] => 20 [2,3,6,4,1,5] => 20 [2,3,6,4,5,1] => 6 [2,3,6,5,1,4] => 50 [2,3,6,5,4,1] => 12 [2,4,1,3,5,6] => 6 [2,4,1,3,6,5] => 12 [2,4,1,5,3,6] => 20 [2,4,1,5,6,3] => 50 [2,4,1,6,3,5] => 50 [2,4,1,6,5,3] => 20 [2,4,3,1,5,6] => 1 [2,4,3,1,6,5] => 4 [2,4,3,5,1,6] => 6 [2,4,3,5,6,1] => 20 [2,4,3,6,1,5] => 20 [2,4,3,6,5,1] => 6 [2,4,5,1,3,6] => 4 [2,4,5,1,6,3] => 11 [2,4,5,3,1,6] => 20 [2,4,5,3,6,1] => 50 [2,4,5,6,1,3] => 50 [2,4,5,6,3,1] => 12 [2,4,6,1,3,5] => 11 [2,4,6,1,5,3] => 4 [2,4,6,3,1,5] => 50 [2,4,6,3,5,1] => 20 [2,4,6,5,1,3] => 12 [2,4,6,5,3,1] => 50 [2,5,1,3,4,6] => 20 [2,5,1,3,6,4] => 50 [2,5,1,4,3,6] => 6 [2,5,1,4,6,3] => 20 [2,5,1,6,3,4] => 12 [2,5,1,6,4,3] => 50 [2,5,3,1,4,6] => 6 [2,5,3,1,6,4] => 20 [2,5,3,4,1,6] => 1 [2,5,3,4,6,1] => 6 [2,5,3,6,1,4] => 4 [2,5,3,6,4,1] => 20 [2,5,4,1,3,6] => 20 [2,5,4,1,6,3] => 50 [2,5,4,3,1,6] => 4 [2,5,4,3,6,1] => 12 [2,5,4,6,1,3] => 11 [2,5,4,6,3,1] => 50 [2,5,6,1,3,4] => 50 [2,5,6,1,4,3] => 12 [2,5,6,3,1,4] => 11 [2,5,6,3,4,1] => 50 [2,5,6,4,1,3] => 4 [2,5,6,4,3,1] => 20 [2,6,1,3,4,5] => 50 [2,6,1,3,5,4] => 20 [2,6,1,4,3,5] => 20 [2,6,1,4,5,3] => 6 [2,6,1,5,3,4] => 50 [2,6,1,5,4,3] => 12 [2,6,3,1,4,5] => 20 [2,6,3,1,5,4] => 6 [2,6,3,4,1,5] => 6 [2,6,3,4,5,1] => 1 [2,6,3,5,1,4] => 20 [2,6,3,5,4,1] => 4 [2,6,4,1,3,5] => 50 [2,6,4,1,5,3] => 20 [2,6,4,3,1,5] => 12 [2,6,4,3,5,1] => 4 [2,6,4,5,1,3] => 50 [2,6,4,5,3,1] => 11 [2,6,5,1,3,4] => 12 [2,6,5,1,4,3] => 50 [2,6,5,3,1,4] => 50 [2,6,5,3,4,1] => 11 [2,6,5,4,1,3] => 20 [2,6,5,4,3,1] => 4 [3,1,2,4,5,6] => 1 [3,1,2,4,6,5] => 4 [3,1,2,5,4,6] => 4 [3,1,2,5,6,4] => 11 [3,1,2,6,4,5] => 11 [3,1,2,6,5,4] => 4 [3,1,4,2,5,6] => 6 [3,1,4,2,6,5] => 12 [3,1,4,5,2,6] => 20 [3,1,4,5,6,2] => 50 [3,1,4,6,2,5] => 50 [3,1,4,6,5,2] => 20 [3,1,5,2,4,6] => 20 [3,1,5,2,6,4] => 50 [3,1,5,4,2,6] => 6 [3,1,5,4,6,2] => 20 [3,1,5,6,2,4] => 12 [3,1,5,6,4,2] => 50 [3,1,6,2,4,5] => 50 [3,1,6,2,5,4] => 20 [3,1,6,4,2,5] => 20 [3,1,6,4,5,2] => 6 [3,1,6,5,2,4] => 50 [3,1,6,5,4,2] => 12 [3,2,1,4,5,6] => 0 [3,2,1,4,6,5] => 1 [3,2,1,5,4,6] => 1 [3,2,1,5,6,4] => 4 [3,2,1,6,4,5] => 4 [3,2,1,6,5,4] => 1 [3,2,4,1,5,6] => 1 [3,2,4,1,6,5] => 4 [3,2,4,5,1,6] => 6 [3,2,4,5,6,1] => 20 [3,2,4,6,1,5] => 20 [3,2,4,6,5,1] => 6 [3,2,5,1,4,6] => 6 [3,2,5,1,6,4] => 20 [3,2,5,4,1,6] => 1 [3,2,5,4,6,1] => 6 [3,2,5,6,1,4] => 4 [3,2,5,6,4,1] => 20 [3,2,6,1,4,5] => 20 [3,2,6,1,5,4] => 6 [3,2,6,4,1,5] => 6 [3,2,6,4,5,1] => 1 [3,2,6,5,1,4] => 20 [3,2,6,5,4,1] => 4 [3,4,1,2,5,6] => 1 [3,4,1,2,6,5] => 3 [3,4,1,5,2,6] => 4 [3,4,1,5,6,2] => 12 [3,4,1,6,2,5] => 12 [3,4,1,6,5,2] => 4 [3,4,2,1,5,6] => 6 [3,4,2,1,6,5] => 12 [3,4,2,5,1,6] => 20 [3,4,2,5,6,1] => 50 [3,4,2,6,1,5] => 50 [3,4,2,6,5,1] => 20 [3,4,5,1,2,6] => 20 [3,4,5,1,6,2] => 50 [3,4,5,2,1,6] => 4 [3,4,5,2,6,1] => 12 [3,4,5,6,1,2] => 11 [3,4,5,6,2,1] => 50 [3,4,6,1,2,5] => 50 [3,4,6,1,5,2] => 20 [3,4,6,2,1,5] => 12 [3,4,6,2,5,1] => 4 [3,4,6,5,1,2] => 50 [3,4,6,5,2,1] => 11 [3,5,1,2,4,6] => 4 [3,5,1,2,6,4] => 12 [3,5,1,4,2,6] => 1 [3,5,1,4,6,2] => 4 [3,5,1,6,2,4] => 3 [3,5,1,6,4,2] => 12 [3,5,2,1,4,6] => 20 [3,5,2,1,6,4] => 50 [3,5,2,4,1,6] => 6 [3,5,2,4,6,1] => 20 [3,5,2,6,1,4] => 12 [3,5,2,6,4,1] => 50 [3,5,4,1,2,6] => 4 [3,5,4,1,6,2] => 11 [3,5,4,2,1,6] => 20 [3,5,4,2,6,1] => 50 [3,5,4,6,1,2] => 50 [3,5,4,6,2,1] => 12 [3,5,6,1,2,4] => 12 [3,5,6,1,4,2] => 50 [3,5,6,2,1,4] => 50 [3,5,6,2,4,1] => 11 [3,5,6,4,1,2] => 20 [3,5,6,4,2,1] => 4 [3,6,1,2,4,5] => 12 [3,6,1,2,5,4] => 4 [3,6,1,4,2,5] => 4 [3,6,1,4,5,2] => 1 [3,6,1,5,2,4] => 12 [3,6,1,5,4,2] => 3 [3,6,2,1,4,5] => 50 [3,6,2,1,5,4] => 20 [3,6,2,4,1,5] => 20 [3,6,2,4,5,1] => 6 [3,6,2,5,1,4] => 50 [3,6,2,5,4,1] => 12 [3,6,4,1,2,5] => 11 [3,6,4,1,5,2] => 4 [3,6,4,2,1,5] => 50 [3,6,4,2,5,1] => 20 [3,6,4,5,1,2] => 12 [3,6,4,5,2,1] => 50 [3,6,5,1,2,4] => 50 [3,6,5,1,4,2] => 12 [3,6,5,2,1,4] => 11 [3,6,5,2,4,1] => 50 [3,6,5,4,1,2] => 4 [3,6,5,4,2,1] => 20 [4,1,2,3,5,6] => 6 [4,1,2,3,6,5] => 12 [4,1,2,5,3,6] => 20 [4,1,2,5,6,3] => 50 [4,1,2,6,3,5] => 50 [4,1,2,6,5,3] => 20 [4,1,3,2,5,6] => 1 [4,1,3,2,6,5] => 4 [4,1,3,5,2,6] => 6 [4,1,3,5,6,2] => 20 [4,1,3,6,2,5] => 20 [4,1,3,6,5,2] => 6 [4,1,5,2,3,6] => 4 [4,1,5,2,6,3] => 11 [4,1,5,3,2,6] => 20 [4,1,5,3,6,2] => 50 [4,1,5,6,2,3] => 50 [4,1,5,6,3,2] => 12 [4,1,6,2,3,5] => 11 [4,1,6,2,5,3] => 4 [4,1,6,3,2,5] => 50 [4,1,6,3,5,2] => 20 [4,1,6,5,2,3] => 12 [4,1,6,5,3,2] => 50 [4,2,1,3,5,6] => 1 [4,2,1,3,6,5] => 4 [4,2,1,5,3,6] => 6 [4,2,1,5,6,3] => 20 [4,2,1,6,3,5] => 20 [4,2,1,6,5,3] => 6 [4,2,3,1,5,6] => 0 [4,2,3,1,6,5] => 1 [4,2,3,5,1,6] => 1 [4,2,3,5,6,1] => 6 [4,2,3,6,1,5] => 6 [4,2,3,6,5,1] => 1 [4,2,5,1,3,6] => 1 [4,2,5,1,6,3] => 4 [4,2,5,3,1,6] => 6 [4,2,5,3,6,1] => 20 [4,2,5,6,1,3] => 20 [4,2,5,6,3,1] => 4 [4,2,6,1,3,5] => 4 [4,2,6,1,5,3] => 1 [4,2,6,3,1,5] => 20 [4,2,6,3,5,1] => 6 [4,2,6,5,1,3] => 4 [4,2,6,5,3,1] => 20 [4,3,1,2,5,6] => 6 [4,3,1,2,6,5] => 12 [4,3,1,5,2,6] => 20 [4,3,1,5,6,2] => 50 [4,3,1,6,2,5] => 50 [4,3,1,6,5,2] => 20 [4,3,2,1,5,6] => 1 [4,3,2,1,6,5] => 3 [4,3,2,5,1,6] => 4 [4,3,2,5,6,1] => 12 [4,3,2,6,1,5] => 12 [4,3,2,6,5,1] => 4 [4,3,5,1,2,6] => 4 [4,3,5,1,6,2] => 12 [4,3,5,2,1,6] => 20 [4,3,5,2,6,1] => 50 [4,3,5,6,1,2] => 50 [4,3,5,6,2,1] => 11 [4,3,6,1,2,5] => 12 [4,3,6,1,5,2] => 4 [4,3,6,2,1,5] => 50 [4,3,6,2,5,1] => 20 [4,3,6,5,1,2] => 11 [4,3,6,5,2,1] => 50 [4,5,1,2,3,6] => 20 [4,5,1,2,6,3] => 50 [4,5,1,3,2,6] => 4 [4,5,1,3,6,2] => 11 [4,5,1,6,2,3] => 12 [4,5,1,6,3,2] => 50 [4,5,2,1,3,6] => 4 [4,5,2,1,6,3] => 12 [4,5,2,3,1,6] => 20 [4,5,2,3,6,1] => 50 [4,5,2,6,1,3] => 50 [4,5,2,6,3,1] => 11 [4,5,3,1,2,6] => 1 [4,5,3,1,6,2] => 4 [4,5,3,2,1,6] => 6 [4,5,3,2,6,1] => 20 [4,5,3,6,1,2] => 20 [4,5,3,6,2,1] => 4 [4,5,6,1,2,3] => 3 [4,5,6,1,3,2] => 12 [4,5,6,2,1,3] => 12 [4,5,6,2,3,1] => 50 [4,5,6,3,1,2] => 50 [4,5,6,3,2,1] => 12 [4,6,1,2,3,5] => 50 [4,6,1,2,5,3] => 20 [4,6,1,3,2,5] => 11 [4,6,1,3,5,2] => 4 [4,6,1,5,2,3] => 50 [4,6,1,5,3,2] => 12 [4,6,2,1,3,5] => 12 [4,6,2,1,5,3] => 4 [4,6,2,3,1,5] => 50 [4,6,2,3,5,1] => 20 [4,6,2,5,1,3] => 11 [4,6,2,5,3,1] => 50 [4,6,3,1,2,5] => 4 [4,6,3,1,5,2] => 1 [4,6,3,2,1,5] => 20 [4,6,3,2,5,1] => 6 [4,6,3,5,1,2] => 4 [4,6,3,5,2,1] => 20 [4,6,5,1,2,3] => 12 [4,6,5,1,3,2] => 3 [4,6,5,2,1,3] => 50 [4,6,5,2,3,1] => 12 [4,6,5,3,1,2] => 12 [4,6,5,3,2,1] => 50 [5,1,2,3,4,6] => 20 [5,1,2,3,6,4] => 50 [5,1,2,4,3,6] => 6 [5,1,2,4,6,3] => 20 [5,1,2,6,3,4] => 12 [5,1,2,6,4,3] => 50 [5,1,3,2,4,6] => 6 [5,1,3,2,6,4] => 20 [5,1,3,4,2,6] => 1 [5,1,3,4,6,2] => 6 [5,1,3,6,2,4] => 4 [5,1,3,6,4,2] => 20 [5,1,4,2,3,6] => 20 [5,1,4,2,6,3] => 50 [5,1,4,3,2,6] => 4 [5,1,4,3,6,2] => 12 [5,1,4,6,2,3] => 11 [5,1,4,6,3,2] => 50 [5,1,6,2,3,4] => 50 [5,1,6,2,4,3] => 12 [5,1,6,3,2,4] => 11 [5,1,6,3,4,2] => 50 [5,1,6,4,2,3] => 4 [5,1,6,4,3,2] => 20 [5,2,1,3,4,6] => 6 [5,2,1,3,6,4] => 20 [5,2,1,4,3,6] => 1 [5,2,1,4,6,3] => 6 [5,2,1,6,3,4] => 4 [5,2,1,6,4,3] => 20 [5,2,3,1,4,6] => 1 [5,2,3,1,6,4] => 6 [5,2,3,4,1,6] => 0 [5,2,3,4,6,1] => 1 [5,2,3,6,1,4] => 1 [5,2,3,6,4,1] => 6 [5,2,4,1,3,6] => 6 [5,2,4,1,6,3] => 20 [5,2,4,3,1,6] => 1 [5,2,4,3,6,1] => 4 [5,2,4,6,1,3] => 4 [5,2,4,6,3,1] => 20 [5,2,6,1,3,4] => 20 [5,2,6,1,4,3] => 4 [5,2,6,3,1,4] => 4 [5,2,6,3,4,1] => 20 [5,2,6,4,1,3] => 1 [5,2,6,4,3,1] => 6 [5,3,1,2,4,6] => 20 [5,3,1,2,6,4] => 50 [5,3,1,4,2,6] => 6 [5,3,1,4,6,2] => 20 [5,3,1,6,2,4] => 12 [5,3,1,6,4,2] => 50 [5,3,2,1,4,6] => 4 [5,3,2,1,6,4] => 12 [5,3,2,4,1,6] => 1 [5,3,2,4,6,1] => 4 [5,3,2,6,1,4] => 3 [5,3,2,6,4,1] => 12 [5,3,4,1,2,6] => 20 [5,3,4,1,6,2] => 50 [5,3,4,2,1,6] => 4 [5,3,4,2,6,1] => 11 [5,3,4,6,1,2] => 12 [5,3,4,6,2,1] => 50 [5,3,6,1,2,4] => 50 [5,3,6,1,4,2] => 11 [5,3,6,2,1,4] => 12 [5,3,6,2,4,1] => 50 [5,3,6,4,1,2] => 4 [5,3,6,4,2,1] => 20 [5,4,1,2,3,6] => 4 [5,4,1,2,6,3] => 12 [5,4,1,3,2,6] => 20 [5,4,1,3,6,2] => 50 [5,4,1,6,2,3] => 50 [5,4,1,6,3,2] => 11 [5,4,2,1,3,6] => 20 [5,4,2,1,6,3] => 50 [5,4,2,3,1,6] => 4 [5,4,2,3,6,1] => 11 [5,4,2,6,1,3] => 12 [5,4,2,6,3,1] => 50 [5,4,3,1,2,6] => 6 [5,4,3,1,6,2] => 20 [5,4,3,2,1,6] => 1 [5,4,3,2,6,1] => 4 [5,4,3,6,1,2] => 4 [5,4,3,6,2,1] => 20 [5,4,6,1,2,3] => 12 [5,4,6,1,3,2] => 50 [5,4,6,2,1,3] => 3 [5,4,6,2,3,1] => 12 [5,4,6,3,1,2] => 12 [5,4,6,3,2,1] => 50 [5,6,1,2,3,4] => 11 [5,6,1,2,4,3] => 50 [5,6,1,3,2,4] => 50 [5,6,1,3,4,2] => 12 [5,6,1,4,2,3] => 20 [5,6,1,4,3,2] => 4 [5,6,2,1,3,4] => 50 [5,6,2,1,4,3] => 11 [5,6,2,3,1,4] => 12 [5,6,2,3,4,1] => 50 [5,6,2,4,1,3] => 4 [5,6,2,4,3,1] => 20 [5,6,3,1,2,4] => 20 [5,6,3,1,4,2] => 4 [5,6,3,2,1,4] => 4 [5,6,3,2,4,1] => 20 [5,6,3,4,1,2] => 1 [5,6,3,4,2,1] => 6 [5,6,4,1,2,3] => 50 [5,6,4,1,3,2] => 12 [5,6,4,2,1,3] => 12 [5,6,4,2,3,1] => 50 [5,6,4,3,1,2] => 3 [5,6,4,3,2,1] => 12 [6,1,2,3,4,5] => 50 [6,1,2,3,5,4] => 20 [6,1,2,4,3,5] => 20 [6,1,2,4,5,3] => 6 [6,1,2,5,3,4] => 50 [6,1,2,5,4,3] => 12 [6,1,3,2,4,5] => 20 [6,1,3,2,5,4] => 6 [6,1,3,4,2,5] => 6 [6,1,3,4,5,2] => 1 [6,1,3,5,2,4] => 20 [6,1,3,5,4,2] => 4 [6,1,4,2,3,5] => 50 [6,1,4,2,5,3] => 20 [6,1,4,3,2,5] => 12 [6,1,4,3,5,2] => 4 [6,1,4,5,2,3] => 50 [6,1,4,5,3,2] => 11 [6,1,5,2,3,4] => 12 [6,1,5,2,4,3] => 50 [6,1,5,3,2,4] => 50 [6,1,5,3,4,2] => 11 [6,1,5,4,2,3] => 20 [6,1,5,4,3,2] => 4 [6,2,1,3,4,5] => 20 [6,2,1,3,5,4] => 6 [6,2,1,4,3,5] => 6 [6,2,1,4,5,3] => 1 [6,2,1,5,3,4] => 20 [6,2,1,5,4,3] => 4 [6,2,3,1,4,5] => 6 [6,2,3,1,5,4] => 1 [6,2,3,4,1,5] => 1 [6,2,3,4,5,1] => 0 [6,2,3,5,1,4] => 6 [6,2,3,5,4,1] => 1 [6,2,4,1,3,5] => 20 [6,2,4,1,5,3] => 6 [6,2,4,3,1,5] => 4 [6,2,4,3,5,1] => 1 [6,2,4,5,1,3] => 20 [6,2,4,5,3,1] => 4 [6,2,5,1,3,4] => 4 [6,2,5,1,4,3] => 20 [6,2,5,3,1,4] => 20 [6,2,5,3,4,1] => 4 [6,2,5,4,1,3] => 6 [6,2,5,4,3,1] => 1 [6,3,1,2,4,5] => 50 [6,3,1,2,5,4] => 20 [6,3,1,4,2,5] => 20 [6,3,1,4,5,2] => 6 [6,3,1,5,2,4] => 50 [6,3,1,5,4,2] => 12 [6,3,2,1,4,5] => 12 [6,3,2,1,5,4] => 4 [6,3,2,4,1,5] => 4 [6,3,2,4,5,1] => 1 [6,3,2,5,1,4] => 12 [6,3,2,5,4,1] => 3 [6,3,4,1,2,5] => 50 [6,3,4,1,5,2] => 20 [6,3,4,2,1,5] => 11 [6,3,4,2,5,1] => 4 [6,3,4,5,1,2] => 50 [6,3,4,5,2,1] => 12 [6,3,5,1,2,4] => 11 [6,3,5,1,4,2] => 50 [6,3,5,2,1,4] => 50 [6,3,5,2,4,1] => 12 [6,3,5,4,1,2] => 20 [6,3,5,4,2,1] => 4 [6,4,1,2,3,5] => 12 [6,4,1,2,5,3] => 4 [6,4,1,3,2,5] => 50 [6,4,1,3,5,2] => 20 [6,4,1,5,2,3] => 11 [6,4,1,5,3,2] => 50 [6,4,2,1,3,5] => 50 [6,4,2,1,5,3] => 20 [6,4,2,3,1,5] => 11 [6,4,2,3,5,1] => 4 [6,4,2,5,1,3] => 50 [6,4,2,5,3,1] => 12 [6,4,3,1,2,5] => 20 [6,4,3,1,5,2] => 6 [6,4,3,2,1,5] => 4 [6,4,3,2,5,1] => 1 [6,4,3,5,1,2] => 20 [6,4,3,5,2,1] => 4 [6,4,5,1,2,3] => 50 [6,4,5,1,3,2] => 12 [6,4,5,2,1,3] => 12 [6,4,5,2,3,1] => 3 [6,4,5,3,1,2] => 50 [6,4,5,3,2,1] => 12 [6,5,1,2,3,4] => 50 [6,5,1,2,4,3] => 11 [6,5,1,3,2,4] => 12 [6,5,1,3,4,2] => 50 [6,5,1,4,2,3] => 4 [6,5,1,4,3,2] => 20 [6,5,2,1,3,4] => 11 [6,5,2,1,4,3] => 50 [6,5,2,3,1,4] => 50 [6,5,2,3,4,1] => 12 [6,5,2,4,1,3] => 20 [6,5,2,4,3,1] => 4 [6,5,3,1,2,4] => 4 [6,5,3,1,4,2] => 20 [6,5,3,2,1,4] => 20 [6,5,3,2,4,1] => 4 [6,5,3,4,1,2] => 6 [6,5,3,4,2,1] => 1 [6,5,4,1,2,3] => 12 [6,5,4,1,3,2] => 50 [6,5,4,2,1,3] => 50 [6,5,4,2,3,1] => 12 [6,5,4,3,1,2] => 12 [6,5,4,3,2,1] => 3 ----------------------------------------------------------------------------- Created: Jul 07, 2021 at 10:23 by Henri Mühle ----------------------------------------------------------------------------- Last Updated: Nov 18, 2024 at 19:29 by Nupur Jain