***************************************************************************** * 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: St000540 ----------------------------------------------------------------------------- Collection: Parking functions ----------------------------------------------------------------------------- Description: The sum of the entries of a parking function minus its length. Under the standard map to labelled rooted forests, this statistic is sent to the number of inversions. ----------------------------------------------------------------------------- References: [1] Stanley, R. P. Hyperplane arrangements, parking functions and tree inversions [[MathSciNet:1627378]] ----------------------------------------------------------------------------- Code: def statistic(PF): return sum(PF) - len(PF) ----------------------------------------------------------------------------- Statistic values: [1] => 0 [1,1] => 0 [1,2] => 1 [2,1] => 1 [1,1,1] => 0 [1,1,2] => 1 [1,2,1] => 1 [2,1,1] => 1 [1,1,3] => 2 [1,3,1] => 2 [3,1,1] => 2 [1,2,2] => 2 [2,1,2] => 2 [2,2,1] => 2 [1,2,3] => 3 [1,3,2] => 3 [2,1,3] => 3 [2,3,1] => 3 [3,1,2] => 3 [3,2,1] => 3 [1,1,1,1] => 0 [1,1,1,2] => 1 [1,1,2,1] => 1 [1,2,1,1] => 1 [2,1,1,1] => 1 [1,1,1,3] => 2 [1,1,3,1] => 2 [1,3,1,1] => 2 [3,1,1,1] => 2 [1,1,1,4] => 3 [1,1,4,1] => 3 [1,4,1,1] => 3 [4,1,1,1] => 3 [1,1,2,2] => 2 [1,2,1,2] => 2 [1,2,2,1] => 2 [2,1,1,2] => 2 [2,1,2,1] => 2 [2,2,1,1] => 2 [1,1,2,3] => 3 [1,1,3,2] => 3 [1,2,1,3] => 3 [1,2,3,1] => 3 [1,3,1,2] => 3 [1,3,2,1] => 3 [2,1,1,3] => 3 [2,1,3,1] => 3 [2,3,1,1] => 3 [3,1,1,2] => 3 [3,1,2,1] => 3 [3,2,1,1] => 3 [1,1,2,4] => 4 [1,1,4,2] => 4 [1,2,1,4] => 4 [1,2,4,1] => 4 [1,4,1,2] => 4 [1,4,2,1] => 4 [2,1,1,4] => 4 [2,1,4,1] => 4 [2,4,1,1] => 4 [4,1,1,2] => 4 [4,1,2,1] => 4 [4,2,1,1] => 4 [1,1,3,3] => 4 [1,3,1,3] => 4 [1,3,3,1] => 4 [3,1,1,3] => 4 [3,1,3,1] => 4 [3,3,1,1] => 4 [1,1,3,4] => 5 [1,1,4,3] => 5 [1,3,1,4] => 5 [1,3,4,1] => 5 [1,4,1,3] => 5 [1,4,3,1] => 5 [3,1,1,4] => 5 [3,1,4,1] => 5 [3,4,1,1] => 5 [4,1,1,3] => 5 [4,1,3,1] => 5 [4,3,1,1] => 5 [1,2,2,2] => 3 [2,1,2,2] => 3 [2,2,1,2] => 3 [2,2,2,1] => 3 [1,2,2,3] => 4 [1,2,3,2] => 4 [1,3,2,2] => 4 [2,1,2,3] => 4 [2,1,3,2] => 4 [2,2,1,3] => 4 [2,2,3,1] => 4 [2,3,1,2] => 4 [2,3,2,1] => 4 [3,1,2,2] => 4 [3,2,1,2] => 4 [3,2,2,1] => 4 [1,2,2,4] => 5 [1,2,4,2] => 5 [1,4,2,2] => 5 [2,1,2,4] => 5 [2,1,4,2] => 5 [2,2,1,4] => 5 [2,2,4,1] => 5 [2,4,1,2] => 5 [2,4,2,1] => 5 [4,1,2,2] => 5 [4,2,1,2] => 5 [4,2,2,1] => 5 [1,2,3,3] => 5 [1,3,2,3] => 5 [1,3,3,2] => 5 [2,1,3,3] => 5 [2,3,1,3] => 5 [2,3,3,1] => 5 [3,1,2,3] => 5 [3,1,3,2] => 5 [3,2,1,3] => 5 [3,2,3,1] => 5 [3,3,1,2] => 5 [3,3,2,1] => 5 [1,2,3,4] => 6 [1,2,4,3] => 6 [1,3,2,4] => 6 [1,3,4,2] => 6 [1,4,2,3] => 6 [1,4,3,2] => 6 [2,1,3,4] => 6 [2,1,4,3] => 6 [2,3,1,4] => 6 [2,3,4,1] => 6 [2,4,1,3] => 6 [2,4,3,1] => 6 [3,1,2,4] => 6 [3,1,4,2] => 6 [3,2,1,4] => 6 [3,2,4,1] => 6 [3,4,1,2] => 6 [3,4,2,1] => 6 [4,1,2,3] => 6 [4,1,3,2] => 6 [4,2,1,3] => 6 [4,2,3,1] => 6 [4,3,1,2] => 6 [4,3,2,1] => 6 [1,1,1,1,1] => 0 [1,1,1,1,2] => 1 [1,1,1,2,1] => 1 [1,1,2,1,1] => 1 [1,2,1,1,1] => 1 [2,1,1,1,1] => 1 [1,1,1,1,3] => 2 [1,1,1,3,1] => 2 [1,1,3,1,1] => 2 [1,3,1,1,1] => 2 [3,1,1,1,1] => 2 [1,1,1,1,4] => 3 [1,1,1,4,1] => 3 [1,1,4,1,1] => 3 [1,4,1,1,1] => 3 [4,1,1,1,1] => 3 [1,1,1,1,5] => 4 [1,1,1,5,1] => 4 [1,1,5,1,1] => 4 [1,5,1,1,1] => 4 [5,1,1,1,1] => 4 [1,1,1,2,2] => 2 [1,1,2,1,2] => 2 [1,1,2,2,1] => 2 [1,2,1,1,2] => 2 [1,2,1,2,1] => 2 [1,2,2,1,1] => 2 [2,1,1,1,2] => 2 [2,1,1,2,1] => 2 [2,1,2,1,1] => 2 [2,2,1,1,1] => 2 [1,1,1,2,3] => 3 [1,1,1,3,2] => 3 [1,1,2,1,3] => 3 [1,1,2,3,1] => 3 [1,1,3,1,2] => 3 [1,1,3,2,1] => 3 [1,2,1,1,3] => 3 [1,2,1,3,1] => 3 [1,2,3,1,1] => 3 [1,3,1,1,2] => 3 [1,3,1,2,1] => 3 [1,3,2,1,1] => 3 [2,1,1,1,3] => 3 [2,1,1,3,1] => 3 [2,1,3,1,1] => 3 [2,3,1,1,1] => 3 [3,1,1,1,2] => 3 [3,1,1,2,1] => 3 [3,1,2,1,1] => 3 [3,2,1,1,1] => 3 [1,1,1,2,4] => 4 [1,1,1,4,2] => 4 [1,1,2,1,4] => 4 [1,1,2,4,1] => 4 [1,1,4,1,2] => 4 [1,1,4,2,1] => 4 [1,2,1,1,4] => 4 [1,2,1,4,1] => 4 [1,2,4,1,1] => 4 [1,4,1,1,2] => 4 [1,4,1,2,1] => 4 [1,4,2,1,1] => 4 [2,1,1,1,4] => 4 [2,1,1,4,1] => 4 [2,1,4,1,1] => 4 [2,4,1,1,1] => 4 [4,1,1,1,2] => 4 [4,1,1,2,1] => 4 [4,1,2,1,1] => 4 [4,2,1,1,1] => 4 [1,1,1,2,5] => 5 [1,1,1,5,2] => 5 [1,1,2,1,5] => 5 [1,1,2,5,1] => 5 [1,1,5,1,2] => 5 [1,1,5,2,1] => 5 [1,2,1,1,5] => 5 [1,2,1,5,1] => 5 [1,2,5,1,1] => 5 [1,5,1,1,2] => 5 [1,5,1,2,1] => 5 [1,5,2,1,1] => 5 [2,1,1,1,5] => 5 [2,1,1,5,1] => 5 [2,1,5,1,1] => 5 [2,5,1,1,1] => 5 [5,1,1,1,2] => 5 [5,1,1,2,1] => 5 [5,1,2,1,1] => 5 [5,2,1,1,1] => 5 [1,1,1,3,3] => 4 [1,1,3,1,3] => 4 [1,1,3,3,1] => 4 [1,3,1,1,3] => 4 [1,3,1,3,1] => 4 [1,3,3,1,1] => 4 [3,1,1,1,3] => 4 [3,1,1,3,1] => 4 [3,1,3,1,1] => 4 [3,3,1,1,1] => 4 [1,1,1,3,4] => 5 [1,1,1,4,3] => 5 [1,1,3,1,4] => 5 [1,1,3,4,1] => 5 [1,1,4,1,3] => 5 [1,1,4,3,1] => 5 [1,3,1,1,4] => 5 [1,3,1,4,1] => 5 [1,3,4,1,1] => 5 [1,4,1,1,3] => 5 [1,4,1,3,1] => 5 [1,4,3,1,1] => 5 [3,1,1,1,4] => 5 [3,1,1,4,1] => 5 [3,1,4,1,1] => 5 [3,4,1,1,1] => 5 [4,1,1,1,3] => 5 [4,1,1,3,1] => 5 [4,1,3,1,1] => 5 [4,3,1,1,1] => 5 [1,1,1,3,5] => 6 [1,1,1,5,3] => 6 [1,1,3,1,5] => 6 [1,1,3,5,1] => 6 [1,1,5,1,3] => 6 [1,1,5,3,1] => 6 [1,3,1,1,5] => 6 [1,3,1,5,1] => 6 [1,3,5,1,1] => 6 [1,5,1,1,3] => 6 [1,5,1,3,1] => 6 [1,5,3,1,1] => 6 [3,1,1,1,5] => 6 [3,1,1,5,1] => 6 [3,1,5,1,1] => 6 [3,5,1,1,1] => 6 [5,1,1,1,3] => 6 [5,1,1,3,1] => 6 [5,1,3,1,1] => 6 [5,3,1,1,1] => 6 [1,1,1,4,4] => 6 [1,1,4,1,4] => 6 [1,1,4,4,1] => 6 [1,4,1,1,4] => 6 [1,4,1,4,1] => 6 [1,4,4,1,1] => 6 [4,1,1,1,4] => 6 [4,1,1,4,1] => 6 [4,1,4,1,1] => 6 [4,4,1,1,1] => 6 [1,1,1,4,5] => 7 [1,1,1,5,4] => 7 [1,1,4,1,5] => 7 [1,1,4,5,1] => 7 [1,1,5,1,4] => 7 [1,1,5,4,1] => 7 [1,4,1,1,5] => 7 [1,4,1,5,1] => 7 [1,4,5,1,1] => 7 [1,5,1,1,4] => 7 [1,5,1,4,1] => 7 [1,5,4,1,1] => 7 [4,1,1,1,5] => 7 [4,1,1,5,1] => 7 [4,1,5,1,1] => 7 [4,5,1,1,1] => 7 [5,1,1,1,4] => 7 [5,1,1,4,1] => 7 [5,1,4,1,1] => 7 [5,4,1,1,1] => 7 [1,1,2,2,2] => 3 [1,2,1,2,2] => 3 [1,2,2,1,2] => 3 [1,2,2,2,1] => 3 [2,1,1,2,2] => 3 [2,1,2,1,2] => 3 [2,1,2,2,1] => 3 [2,2,1,1,2] => 3 [2,2,1,2,1] => 3 [2,2,2,1,1] => 3 [1,1,2,2,3] => 4 [1,1,2,3,2] => 4 [1,1,3,2,2] => 4 [1,2,1,2,3] => 4 [1,2,1,3,2] => 4 [1,2,2,1,3] => 4 [1,2,2,3,1] => 4 [1,2,3,1,2] => 4 [1,2,3,2,1] => 4 [1,3,1,2,2] => 4 [1,3,2,1,2] => 4 [1,3,2,2,1] => 4 [2,1,1,2,3] => 4 [2,1,1,3,2] => 4 [2,1,2,1,3] => 4 [2,1,2,3,1] => 4 [2,1,3,1,2] => 4 [2,1,3,2,1] => 4 [2,2,1,1,3] => 4 [2,2,1,3,1] => 4 [2,2,3,1,1] => 4 [2,3,1,1,2] => 4 [2,3,1,2,1] => 4 [2,3,2,1,1] => 4 [3,1,1,2,2] => 4 [3,1,2,1,2] => 4 [3,1,2,2,1] => 4 [3,2,1,1,2] => 4 [3,2,1,2,1] => 4 [3,2,2,1,1] => 4 [1,1,2,2,4] => 5 [1,1,2,4,2] => 5 [1,1,4,2,2] => 5 [1,2,1,2,4] => 5 [1,2,1,4,2] => 5 [1,2,2,1,4] => 5 [1,2,2,4,1] => 5 [1,2,4,1,2] => 5 [1,2,4,2,1] => 5 [1,4,1,2,2] => 5 [1,4,2,1,2] => 5 [1,4,2,2,1] => 5 [2,1,1,2,4] => 5 [2,1,1,4,2] => 5 [2,1,2,1,4] => 5 [2,1,2,4,1] => 5 [2,1,4,1,2] => 5 [2,1,4,2,1] => 5 [2,2,1,1,4] => 5 [2,2,1,4,1] => 5 [2,2,4,1,1] => 5 [2,4,1,1,2] => 5 [2,4,1,2,1] => 5 [2,4,2,1,1] => 5 [4,1,1,2,2] => 5 [4,1,2,1,2] => 5 [4,1,2,2,1] => 5 [4,2,1,1,2] => 5 [4,2,1,2,1] => 5 [4,2,2,1,1] => 5 [1,1,2,2,5] => 6 [1,1,2,5,2] => 6 [1,1,5,2,2] => 6 [1,2,1,2,5] => 6 [1,2,1,5,2] => 6 [1,2,2,1,5] => 6 [1,2,2,5,1] => 6 [1,2,5,1,2] => 6 [1,2,5,2,1] => 6 [1,5,1,2,2] => 6 [1,5,2,1,2] => 6 [1,5,2,2,1] => 6 [2,1,1,2,5] => 6 [2,1,1,5,2] => 6 [2,1,2,1,5] => 6 [2,1,2,5,1] => 6 [2,1,5,1,2] => 6 [2,1,5,2,1] => 6 [2,2,1,1,5] => 6 [2,2,1,5,1] => 6 [2,2,5,1,1] => 6 [2,5,1,1,2] => 6 [2,5,1,2,1] => 6 [2,5,2,1,1] => 6 [5,1,1,2,2] => 6 [5,1,2,1,2] => 6 [5,1,2,2,1] => 6 [5,2,1,1,2] => 6 [5,2,1,2,1] => 6 [5,2,2,1,1] => 6 [1,1,2,3,3] => 5 [1,1,3,2,3] => 5 [1,1,3,3,2] => 5 [1,2,1,3,3] => 5 [1,2,3,1,3] => 5 [1,2,3,3,1] => 5 [1,3,1,2,3] => 5 [1,3,1,3,2] => 5 [1,3,2,1,3] => 5 [1,3,2,3,1] => 5 [1,3,3,1,2] => 5 [1,3,3,2,1] => 5 [2,1,1,3,3] => 5 [2,1,3,1,3] => 5 [2,1,3,3,1] => 5 [2,3,1,1,3] => 5 [2,3,1,3,1] => 5 [2,3,3,1,1] => 5 [3,1,1,2,3] => 5 [3,1,1,3,2] => 5 [3,1,2,1,3] => 5 [3,1,2,3,1] => 5 [3,1,3,1,2] => 5 [3,1,3,2,1] => 5 [3,2,1,1,3] => 5 [3,2,1,3,1] => 5 [3,2,3,1,1] => 5 [3,3,1,1,2] => 5 [3,3,1,2,1] => 5 [3,3,2,1,1] => 5 [1,1,2,3,4] => 6 [1,1,2,4,3] => 6 [1,1,3,2,4] => 6 [1,1,3,4,2] => 6 [1,1,4,2,3] => 6 [1,1,4,3,2] => 6 [1,2,1,3,4] => 6 [1,2,1,4,3] => 6 [1,2,3,1,4] => 6 [1,2,3,4,1] => 6 [1,2,4,1,3] => 6 [1,2,4,3,1] => 6 [1,3,1,2,4] => 6 [1,3,1,4,2] => 6 [1,3,2,1,4] => 6 [1,3,2,4,1] => 6 [1,3,4,1,2] => 6 [1,3,4,2,1] => 6 [1,4,1,2,3] => 6 [1,4,1,3,2] => 6 [1,4,2,1,3] => 6 [1,4,2,3,1] => 6 [1,4,3,1,2] => 6 [1,4,3,2,1] => 6 [2,1,1,3,4] => 6 [2,1,1,4,3] => 6 [2,1,3,1,4] => 6 [2,1,3,4,1] => 6 [2,1,4,1,3] => 6 [2,1,4,3,1] => 6 [2,3,1,1,4] => 6 [2,3,1,4,1] => 6 [2,3,4,1,1] => 6 [2,4,1,1,3] => 6 [2,4,1,3,1] => 6 [2,4,3,1,1] => 6 [3,1,1,2,4] => 6 [3,1,1,4,2] => 6 [3,1,2,1,4] => 6 [3,1,2,4,1] => 6 [3,1,4,1,2] => 6 [3,1,4,2,1] => 6 [3,2,1,1,4] => 6 [3,2,1,4,1] => 6 [3,2,4,1,1] => 6 [3,4,1,1,2] => 6 [3,4,1,2,1] => 6 [3,4,2,1,1] => 6 [4,1,1,2,3] => 6 [4,1,1,3,2] => 6 [4,1,2,1,3] => 6 [4,1,2,3,1] => 6 [4,1,3,1,2] => 6 [4,1,3,2,1] => 6 [4,2,1,1,3] => 6 [4,2,1,3,1] => 6 [4,2,3,1,1] => 6 [4,3,1,1,2] => 6 [4,3,1,2,1] => 6 [4,3,2,1,1] => 6 [1,1,2,3,5] => 7 [1,1,2,5,3] => 7 [1,1,3,2,5] => 7 [1,1,3,5,2] => 7 [1,1,5,2,3] => 7 [1,1,5,3,2] => 7 [1,2,1,3,5] => 7 [1,2,1,5,3] => 7 [1,2,3,1,5] => 7 [1,2,3,5,1] => 7 [1,2,5,1,3] => 7 [1,2,5,3,1] => 7 [1,3,1,2,5] => 7 [1,3,1,5,2] => 7 [1,3,2,1,5] => 7 [1,3,2,5,1] => 7 [1,3,5,1,2] => 7 [1,3,5,2,1] => 7 [1,5,1,2,3] => 7 [1,5,1,3,2] => 7 [1,5,2,1,3] => 7 [1,5,2,3,1] => 7 [1,5,3,1,2] => 7 [1,5,3,2,1] => 7 [2,1,1,3,5] => 7 [2,1,1,5,3] => 7 [2,1,3,1,5] => 7 [2,1,3,5,1] => 7 [2,1,5,1,3] => 7 [2,1,5,3,1] => 7 [2,3,1,1,5] => 7 [2,3,1,5,1] => 7 [2,3,5,1,1] => 7 [2,5,1,1,3] => 7 [2,5,1,3,1] => 7 [2,5,3,1,1] => 7 [3,1,1,2,5] => 7 [3,1,1,5,2] => 7 [3,1,2,1,5] => 7 [3,1,2,5,1] => 7 [3,1,5,1,2] => 7 [3,1,5,2,1] => 7 [3,2,1,1,5] => 7 [3,2,1,5,1] => 7 [3,2,5,1,1] => 7 [3,5,1,1,2] => 7 [3,5,1,2,1] => 7 [3,5,2,1,1] => 7 [5,1,1,2,3] => 7 [5,1,1,3,2] => 7 [5,1,2,1,3] => 7 [5,1,2,3,1] => 7 [5,1,3,1,2] => 7 [5,1,3,2,1] => 7 [5,2,1,1,3] => 7 [5,2,1,3,1] => 7 [5,2,3,1,1] => 7 [5,3,1,1,2] => 7 [5,3,1,2,1] => 7 [5,3,2,1,1] => 7 [1,1,2,4,4] => 7 [1,1,4,2,4] => 7 [1,1,4,4,2] => 7 [1,2,1,4,4] => 7 [1,2,4,1,4] => 7 [1,2,4,4,1] => 7 [1,4,1,2,4] => 7 [1,4,1,4,2] => 7 [1,4,2,1,4] => 7 [1,4,2,4,1] => 7 [1,4,4,1,2] => 7 [1,4,4,2,1] => 7 [2,1,1,4,4] => 7 [2,1,4,1,4] => 7 [2,1,4,4,1] => 7 [2,4,1,1,4] => 7 [2,4,1,4,1] => 7 [2,4,4,1,1] => 7 [4,1,1,2,4] => 7 [4,1,1,4,2] => 7 [4,1,2,1,4] => 7 [4,1,2,4,1] => 7 [4,1,4,1,2] => 7 [4,1,4,2,1] => 7 [4,2,1,1,4] => 7 [4,2,1,4,1] => 7 [4,2,4,1,1] => 7 [4,4,1,1,2] => 7 [4,4,1,2,1] => 7 [4,4,2,1,1] => 7 [1,1,2,4,5] => 8 [1,1,2,5,4] => 8 [1,1,4,2,5] => 8 [1,1,4,5,2] => 8 [1,1,5,2,4] => 8 [1,1,5,4,2] => 8 [1,2,1,4,5] => 8 [1,2,1,5,4] => 8 [1,2,4,1,5] => 8 [1,2,4,5,1] => 8 [1,2,5,1,4] => 8 [1,2,5,4,1] => 8 [1,4,1,2,5] => 8 [1,4,1,5,2] => 8 [1,4,2,1,5] => 8 [1,4,2,5,1] => 8 [1,4,5,1,2] => 8 [1,4,5,2,1] => 8 [1,5,1,2,4] => 8 [1,5,1,4,2] => 8 [1,5,2,1,4] => 8 [1,5,2,4,1] => 8 [1,5,4,1,2] => 8 [1,5,4,2,1] => 8 [2,1,1,4,5] => 8 [2,1,1,5,4] => 8 [2,1,4,1,5] => 8 [2,1,4,5,1] => 8 [2,1,5,1,4] => 8 [2,1,5,4,1] => 8 [2,4,1,1,5] => 8 [2,4,1,5,1] => 8 [2,4,5,1,1] => 8 [2,5,1,1,4] => 8 [2,5,1,4,1] => 8 [2,5,4,1,1] => 8 [4,1,1,2,5] => 8 [4,1,1,5,2] => 8 [4,1,2,1,5] => 8 [4,1,2,5,1] => 8 [4,1,5,1,2] => 8 [4,1,5,2,1] => 8 [4,2,1,1,5] => 8 [4,2,1,5,1] => 8 [4,2,5,1,1] => 8 [4,5,1,1,2] => 8 [4,5,1,2,1] => 8 [4,5,2,1,1] => 8 [5,1,1,2,4] => 8 [5,1,1,4,2] => 8 [5,1,2,1,4] => 8 [5,1,2,4,1] => 8 [5,1,4,1,2] => 8 [5,1,4,2,1] => 8 [5,2,1,1,4] => 8 [5,2,1,4,1] => 8 [5,2,4,1,1] => 8 [5,4,1,1,2] => 8 [5,4,1,2,1] => 8 [5,4,2,1,1] => 8 [1,1,3,3,3] => 6 [1,3,1,3,3] => 6 [1,3,3,1,3] => 6 [1,3,3,3,1] => 6 [3,1,1,3,3] => 6 [3,1,3,1,3] => 6 [3,1,3,3,1] => 6 [3,3,1,1,3] => 6 [3,3,1,3,1] => 6 [3,3,3,1,1] => 6 [1,1,3,3,4] => 7 [1,1,3,4,3] => 7 [1,1,4,3,3] => 7 [1,3,1,3,4] => 7 [1,3,1,4,3] => 7 [1,3,3,1,4] => 7 [1,3,3,4,1] => 7 [1,3,4,1,3] => 7 [1,3,4,3,1] => 7 [1,4,1,3,3] => 7 [1,4,3,1,3] => 7 [1,4,3,3,1] => 7 [3,1,1,3,4] => 7 [3,1,1,4,3] => 7 [3,1,3,1,4] => 7 [3,1,3,4,1] => 7 [3,1,4,1,3] => 7 [3,1,4,3,1] => 7 [3,3,1,1,4] => 7 [3,3,1,4,1] => 7 [3,3,4,1,1] => 7 [3,4,1,1,3] => 7 [3,4,1,3,1] => 7 [3,4,3,1,1] => 7 [4,1,1,3,3] => 7 [4,1,3,1,3] => 7 [4,1,3,3,1] => 7 [4,3,1,1,3] => 7 [4,3,1,3,1] => 7 [4,3,3,1,1] => 7 [1,1,3,3,5] => 8 [1,1,3,5,3] => 8 [1,1,5,3,3] => 8 [1,3,1,3,5] => 8 [1,3,1,5,3] => 8 [1,3,3,1,5] => 8 [1,3,3,5,1] => 8 [1,3,5,1,3] => 8 [1,3,5,3,1] => 8 [1,5,1,3,3] => 8 [1,5,3,1,3] => 8 [1,5,3,3,1] => 8 [3,1,1,3,5] => 8 [3,1,1,5,3] => 8 [3,1,3,1,5] => 8 [3,1,3,5,1] => 8 [3,1,5,1,3] => 8 [3,1,5,3,1] => 8 [3,3,1,1,5] => 8 [3,3,1,5,1] => 8 [3,3,5,1,1] => 8 [3,5,1,1,3] => 8 [3,5,1,3,1] => 8 [3,5,3,1,1] => 8 [5,1,1,3,3] => 8 [5,1,3,1,3] => 8 [5,1,3,3,1] => 8 [5,3,1,1,3] => 8 [5,3,1,3,1] => 8 [5,3,3,1,1] => 8 [1,1,3,4,4] => 8 [1,1,4,3,4] => 8 [1,1,4,4,3] => 8 [1,3,1,4,4] => 8 [1,3,4,1,4] => 8 [1,3,4,4,1] => 8 [1,4,1,3,4] => 8 [1,4,1,4,3] => 8 [1,4,3,1,4] => 8 [1,4,3,4,1] => 8 [1,4,4,1,3] => 8 [1,4,4,3,1] => 8 [3,1,1,4,4] => 8 [3,1,4,1,4] => 8 [3,1,4,4,1] => 8 [3,4,1,1,4] => 8 [3,4,1,4,1] => 8 [3,4,4,1,1] => 8 [4,1,1,3,4] => 8 [4,1,1,4,3] => 8 [4,1,3,1,4] => 8 [4,1,3,4,1] => 8 [4,1,4,1,3] => 8 [4,1,4,3,1] => 8 [4,3,1,1,4] => 8 [4,3,1,4,1] => 8 [4,3,4,1,1] => 8 [4,4,1,1,3] => 8 [4,4,1,3,1] => 8 [4,4,3,1,1] => 8 [1,1,3,4,5] => 9 [1,1,3,5,4] => 9 [1,1,4,3,5] => 9 [1,1,4,5,3] => 9 [1,1,5,3,4] => 9 [1,1,5,4,3] => 9 [1,3,1,4,5] => 9 [1,3,1,5,4] => 9 [1,3,4,1,5] => 9 [1,3,4,5,1] => 9 [1,3,5,1,4] => 9 [1,3,5,4,1] => 9 [1,4,1,3,5] => 9 [1,4,1,5,3] => 9 [1,4,3,1,5] => 9 [1,4,3,5,1] => 9 [1,4,5,1,3] => 9 [1,4,5,3,1] => 9 [1,5,1,3,4] => 9 [1,5,1,4,3] => 9 [1,5,3,1,4] => 9 [1,5,3,4,1] => 9 [1,5,4,1,3] => 9 [1,5,4,3,1] => 9 [3,1,1,4,5] => 9 [3,1,1,5,4] => 9 [3,1,4,1,5] => 9 [3,1,4,5,1] => 9 [3,1,5,1,4] => 9 [3,1,5,4,1] => 9 [3,4,1,1,5] => 9 [3,4,1,5,1] => 9 [3,4,5,1,1] => 9 [3,5,1,1,4] => 9 [3,5,1,4,1] => 9 [3,5,4,1,1] => 9 [4,1,1,3,5] => 9 [4,1,1,5,3] => 9 [4,1,3,1,5] => 9 [4,1,3,5,1] => 9 [4,1,5,1,3] => 9 [4,1,5,3,1] => 9 [4,3,1,1,5] => 9 [4,3,1,5,1] => 9 [4,3,5,1,1] => 9 [4,5,1,1,3] => 9 [4,5,1,3,1] => 9 [4,5,3,1,1] => 9 [5,1,1,3,4] => 9 [5,1,1,4,3] => 9 [5,1,3,1,4] => 9 [5,1,3,4,1] => 9 [5,1,4,1,3] => 9 [5,1,4,3,1] => 9 [5,3,1,1,4] => 9 [5,3,1,4,1] => 9 [5,3,4,1,1] => 9 [5,4,1,1,3] => 9 [5,4,1,3,1] => 9 [5,4,3,1,1] => 9 [1,2,2,2,2] => 4 [2,1,2,2,2] => 4 [2,2,1,2,2] => 4 [2,2,2,1,2] => 4 [2,2,2,2,1] => 4 [1,2,2,2,3] => 5 [1,2,2,3,2] => 5 [1,2,3,2,2] => 5 [1,3,2,2,2] => 5 [2,1,2,2,3] => 5 [2,1,2,3,2] => 5 [2,1,3,2,2] => 5 [2,2,1,2,3] => 5 [2,2,1,3,2] => 5 [2,2,2,1,3] => 5 [2,2,2,3,1] => 5 [2,2,3,1,2] => 5 [2,2,3,2,1] => 5 [2,3,1,2,2] => 5 [2,3,2,1,2] => 5 [2,3,2,2,1] => 5 [3,1,2,2,2] => 5 [3,2,1,2,2] => 5 [3,2,2,1,2] => 5 [3,2,2,2,1] => 5 [1,2,2,2,4] => 6 [1,2,2,4,2] => 6 [1,2,4,2,2] => 6 [1,4,2,2,2] => 6 [2,1,2,2,4] => 6 [2,1,2,4,2] => 6 [2,1,4,2,2] => 6 [2,2,1,2,4] => 6 [2,2,1,4,2] => 6 [2,2,2,1,4] => 6 [2,2,2,4,1] => 6 [2,2,4,1,2] => 6 [2,2,4,2,1] => 6 [2,4,1,2,2] => 6 [2,4,2,1,2] => 6 [2,4,2,2,1] => 6 [4,1,2,2,2] => 6 [4,2,1,2,2] => 6 [4,2,2,1,2] => 6 [4,2,2,2,1] => 6 [1,2,2,2,5] => 7 [1,2,2,5,2] => 7 [1,2,5,2,2] => 7 [1,5,2,2,2] => 7 [2,1,2,2,5] => 7 [2,1,2,5,2] => 7 [2,1,5,2,2] => 7 [2,2,1,2,5] => 7 [2,2,1,5,2] => 7 [2,2,2,1,5] => 7 [2,2,2,5,1] => 7 [2,2,5,1,2] => 7 [2,2,5,2,1] => 7 [2,5,1,2,2] => 7 [2,5,2,1,2] => 7 [2,5,2,2,1] => 7 [5,1,2,2,2] => 7 [5,2,1,2,2] => 7 [5,2,2,1,2] => 7 [5,2,2,2,1] => 7 [1,2,2,3,3] => 6 [1,2,3,2,3] => 6 [1,2,3,3,2] => 6 [1,3,2,2,3] => 6 [1,3,2,3,2] => 6 [1,3,3,2,2] => 6 [2,1,2,3,3] => 6 [2,1,3,2,3] => 6 [2,1,3,3,2] => 6 [2,2,1,3,3] => 6 [2,2,3,1,3] => 6 [2,2,3,3,1] => 6 [2,3,1,2,3] => 6 [2,3,1,3,2] => 6 [2,3,2,1,3] => 6 [2,3,2,3,1] => 6 [2,3,3,1,2] => 6 [2,3,3,2,1] => 6 [3,1,2,2,3] => 6 [3,1,2,3,2] => 6 [3,1,3,2,2] => 6 [3,2,1,2,3] => 6 [3,2,1,3,2] => 6 [3,2,2,1,3] => 6 [3,2,2,3,1] => 6 [3,2,3,1,2] => 6 [3,2,3,2,1] => 6 [3,3,1,2,2] => 6 [3,3,2,1,2] => 6 [3,3,2,2,1] => 6 [1,2,2,3,4] => 7 [1,2,2,4,3] => 7 [1,2,3,2,4] => 7 [1,2,3,4,2] => 7 [1,2,4,2,3] => 7 [1,2,4,3,2] => 7 [1,3,2,2,4] => 7 [1,3,2,4,2] => 7 [1,3,4,2,2] => 7 [1,4,2,2,3] => 7 [1,4,2,3,2] => 7 [1,4,3,2,2] => 7 [2,1,2,3,4] => 7 [2,1,2,4,3] => 7 [2,1,3,2,4] => 7 [2,1,3,4,2] => 7 [2,1,4,2,3] => 7 [2,1,4,3,2] => 7 [2,2,1,3,4] => 7 [2,2,1,4,3] => 7 [2,2,3,1,4] => 7 [2,2,3,4,1] => 7 [2,2,4,1,3] => 7 [2,2,4,3,1] => 7 [2,3,1,2,4] => 7 [2,3,1,4,2] => 7 [2,3,2,1,4] => 7 [2,3,2,4,1] => 7 [2,3,4,1,2] => 7 [2,3,4,2,1] => 7 [2,4,1,2,3] => 7 [2,4,1,3,2] => 7 [2,4,2,1,3] => 7 [2,4,2,3,1] => 7 [2,4,3,1,2] => 7 [2,4,3,2,1] => 7 [3,1,2,2,4] => 7 [3,1,2,4,2] => 7 [3,1,4,2,2] => 7 [3,2,1,2,4] => 7 [3,2,1,4,2] => 7 [3,2,2,1,4] => 7 [3,2,2,4,1] => 7 [3,2,4,1,2] => 7 [3,2,4,2,1] => 7 [3,4,1,2,2] => 7 [3,4,2,1,2] => 7 [3,4,2,2,1] => 7 [4,1,2,2,3] => 7 [4,1,2,3,2] => 7 [4,1,3,2,2] => 7 [4,2,1,2,3] => 7 [4,2,1,3,2] => 7 [4,2,2,1,3] => 7 [4,2,2,3,1] => 7 [4,2,3,1,2] => 7 [4,2,3,2,1] => 7 [4,3,1,2,2] => 7 [4,3,2,1,2] => 7 [4,3,2,2,1] => 7 [1,2,2,3,5] => 8 [1,2,2,5,3] => 8 [1,2,3,2,5] => 8 [1,2,3,5,2] => 8 [1,2,5,2,3] => 8 [1,2,5,3,2] => 8 [1,3,2,2,5] => 8 [1,3,2,5,2] => 8 [1,3,5,2,2] => 8 [1,5,2,2,3] => 8 [1,5,2,3,2] => 8 [1,5,3,2,2] => 8 [2,1,2,3,5] => 8 [2,1,2,5,3] => 8 [2,1,3,2,5] => 8 [2,1,3,5,2] => 8 [2,1,5,2,3] => 8 [2,1,5,3,2] => 8 [2,2,1,3,5] => 8 [2,2,1,5,3] => 8 [2,2,3,1,5] => 8 [2,2,3,5,1] => 8 [2,2,5,1,3] => 8 [2,2,5,3,1] => 8 [2,3,1,2,5] => 8 [2,3,1,5,2] => 8 [2,3,2,1,5] => 8 [2,3,2,5,1] => 8 [2,3,5,1,2] => 8 [2,3,5,2,1] => 8 [2,5,1,2,3] => 8 [2,5,1,3,2] => 8 [2,5,2,1,3] => 8 [2,5,2,3,1] => 8 [2,5,3,1,2] => 8 [2,5,3,2,1] => 8 [3,1,2,2,5] => 8 [3,1,2,5,2] => 8 [3,1,5,2,2] => 8 [3,2,1,2,5] => 8 [3,2,1,5,2] => 8 [3,2,2,1,5] => 8 [3,2,2,5,1] => 8 [3,2,5,1,2] => 8 [3,2,5,2,1] => 8 [3,5,1,2,2] => 8 [3,5,2,1,2] => 8 [3,5,2,2,1] => 8 [5,1,2,2,3] => 8 [5,1,2,3,2] => 8 [5,1,3,2,2] => 8 [5,2,1,2,3] => 8 [5,2,1,3,2] => 8 [5,2,2,1,3] => 8 [5,2,2,3,1] => 8 [5,2,3,1,2] => 8 [5,2,3,2,1] => 8 [5,3,1,2,2] => 8 [5,3,2,1,2] => 8 [5,3,2,2,1] => 8 [1,2,2,4,4] => 8 [1,2,4,2,4] => 8 [1,2,4,4,2] => 8 [1,4,2,2,4] => 8 [1,4,2,4,2] => 8 [1,4,4,2,2] => 8 [2,1,2,4,4] => 8 [2,1,4,2,4] => 8 [2,1,4,4,2] => 8 [2,2,1,4,4] => 8 [2,2,4,1,4] => 8 [2,2,4,4,1] => 8 [2,4,1,2,4] => 8 [2,4,1,4,2] => 8 [2,4,2,1,4] => 8 [2,4,2,4,1] => 8 [2,4,4,1,2] => 8 [2,4,4,2,1] => 8 [4,1,2,2,4] => 8 [4,1,2,4,2] => 8 [4,1,4,2,2] => 8 [4,2,1,2,4] => 8 [4,2,1,4,2] => 8 [4,2,2,1,4] => 8 [4,2,2,4,1] => 8 [4,2,4,1,2] => 8 [4,2,4,2,1] => 8 [4,4,1,2,2] => 8 [4,4,2,1,2] => 8 [4,4,2,2,1] => 8 [1,2,2,4,5] => 9 [1,2,2,5,4] => 9 [1,2,4,2,5] => 9 [1,2,4,5,2] => 9 [1,2,5,2,4] => 9 [1,2,5,4,2] => 9 [1,4,2,2,5] => 9 [1,4,2,5,2] => 9 [1,4,5,2,2] => 9 [1,5,2,2,4] => 9 [1,5,2,4,2] => 9 [1,5,4,2,2] => 9 [2,1,2,4,5] => 9 [2,1,2,5,4] => 9 [2,1,4,2,5] => 9 [2,1,4,5,2] => 9 [2,1,5,2,4] => 9 [2,1,5,4,2] => 9 [2,2,1,4,5] => 9 [2,2,1,5,4] => 9 [2,2,4,1,5] => 9 [2,2,4,5,1] => 9 [2,2,5,1,4] => 9 [2,2,5,4,1] => 9 [2,4,1,2,5] => 9 [2,4,1,5,2] => 9 [2,4,2,1,5] => 9 [2,4,2,5,1] => 9 [2,4,5,1,2] => 9 [2,4,5,2,1] => 9 [2,5,1,2,4] => 9 [2,5,1,4,2] => 9 [2,5,2,1,4] => 9 [2,5,2,4,1] => 9 [2,5,4,1,2] => 9 [2,5,4,2,1] => 9 [4,1,2,2,5] => 9 [4,1,2,5,2] => 9 [4,1,5,2,2] => 9 [4,2,1,2,5] => 9 [4,2,1,5,2] => 9 [4,2,2,1,5] => 9 [4,2,2,5,1] => 9 [4,2,5,1,2] => 9 [4,2,5,2,1] => 9 [4,5,1,2,2] => 9 [4,5,2,1,2] => 9 [4,5,2,2,1] => 9 [5,1,2,2,4] => 9 [5,1,2,4,2] => 9 [5,1,4,2,2] => 9 [5,2,1,2,4] => 9 [5,2,1,4,2] => 9 [5,2,2,1,4] => 9 [5,2,2,4,1] => 9 [5,2,4,1,2] => 9 [5,2,4,2,1] => 9 [5,4,1,2,2] => 9 [5,4,2,1,2] => 9 [5,4,2,2,1] => 9 [1,2,3,3,3] => 7 [1,3,2,3,3] => 7 [1,3,3,2,3] => 7 [1,3,3,3,2] => 7 [2,1,3,3,3] => 7 [2,3,1,3,3] => 7 [2,3,3,1,3] => 7 [2,3,3,3,1] => 7 [3,1,2,3,3] => 7 [3,1,3,2,3] => 7 [3,1,3,3,2] => 7 [3,2,1,3,3] => 7 [3,2,3,1,3] => 7 [3,2,3,3,1] => 7 [3,3,1,2,3] => 7 [3,3,1,3,2] => 7 [3,3,2,1,3] => 7 [3,3,2,3,1] => 7 [3,3,3,1,2] => 7 [3,3,3,2,1] => 7 [1,2,3,3,4] => 8 [1,2,3,4,3] => 8 [1,2,4,3,3] => 8 [1,3,2,3,4] => 8 [1,3,2,4,3] => 8 [1,3,3,2,4] => 8 [1,3,3,4,2] => 8 [1,3,4,2,3] => 8 [1,3,4,3,2] => 8 [1,4,2,3,3] => 8 [1,4,3,2,3] => 8 [1,4,3,3,2] => 8 [2,1,3,3,4] => 8 [2,1,3,4,3] => 8 [2,1,4,3,3] => 8 [2,3,1,3,4] => 8 [2,3,1,4,3] => 8 [2,3,3,1,4] => 8 [2,3,3,4,1] => 8 [2,3,4,1,3] => 8 [2,3,4,3,1] => 8 [2,4,1,3,3] => 8 [2,4,3,1,3] => 8 [2,4,3,3,1] => 8 [3,1,2,3,4] => 8 [3,1,2,4,3] => 8 [3,1,3,2,4] => 8 [3,1,3,4,2] => 8 [3,1,4,2,3] => 8 [3,1,4,3,2] => 8 [3,2,1,3,4] => 8 [3,2,1,4,3] => 8 [3,2,3,1,4] => 8 [3,2,3,4,1] => 8 [3,2,4,1,3] => 8 [3,2,4,3,1] => 8 [3,3,1,2,4] => 8 [3,3,1,4,2] => 8 [3,3,2,1,4] => 8 [3,3,2,4,1] => 8 [3,3,4,1,2] => 8 [3,3,4,2,1] => 8 [3,4,1,2,3] => 8 [3,4,1,3,2] => 8 [3,4,2,1,3] => 8 [3,4,2,3,1] => 8 [3,4,3,1,2] => 8 [3,4,3,2,1] => 8 [4,1,2,3,3] => 8 [4,1,3,2,3] => 8 [4,1,3,3,2] => 8 [4,2,1,3,3] => 8 [4,2,3,1,3] => 8 [4,2,3,3,1] => 8 [4,3,1,2,3] => 8 [4,3,1,3,2] => 8 [4,3,2,1,3] => 8 [4,3,2,3,1] => 8 [4,3,3,1,2] => 8 ----------------------------------------------------------------------------- Created: Jun 26, 2016 at 21:01 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Jun 26, 2016 at 21:01 by Christian Stump