***************************************************************************** * 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: St000188 ----------------------------------------------------------------------------- Collection: Parking functions ----------------------------------------------------------------------------- Description: The area of the Dyck path corresponding to a parking function. For a parking function $p_1,\ldots,p_n$ of length $n$, this is given by $\binom{n+1}{2} - \sum_i p_i$. ----------------------------------------------------------------------------- References: [1] Triangle of coefficients of polynomials enumerating trees with n labeled nodes by inversions. [[OEIS:A052121]] ----------------------------------------------------------------------------- Code: def statistic(p): return p.area() ----------------------------------------------------------------------------- Statistic values: [1] => 0 [1,1] => 1 [1,2] => 0 [2,1] => 0 [1,1,1] => 3 [1,1,2] => 2 [1,2,1] => 2 [2,1,1] => 2 [1,1,3] => 1 [1,3,1] => 1 [3,1,1] => 1 [1,2,2] => 1 [2,1,2] => 1 [2,2,1] => 1 [1,2,3] => 0 [1,3,2] => 0 [2,1,3] => 0 [2,3,1] => 0 [3,1,2] => 0 [3,2,1] => 0 [1,1,1,1] => 6 [1,1,1,2] => 5 [1,1,2,1] => 5 [1,2,1,1] => 5 [2,1,1,1] => 5 [1,1,1,3] => 4 [1,1,3,1] => 4 [1,3,1,1] => 4 [3,1,1,1] => 4 [1,1,1,4] => 3 [1,1,4,1] => 3 [1,4,1,1] => 3 [4,1,1,1] => 3 [1,1,2,2] => 4 [1,2,1,2] => 4 [1,2,2,1] => 4 [2,1,1,2] => 4 [2,1,2,1] => 4 [2,2,1,1] => 4 [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] => 2 [1,1,4,2] => 2 [1,2,1,4] => 2 [1,2,4,1] => 2 [1,4,1,2] => 2 [1,4,2,1] => 2 [2,1,1,4] => 2 [2,1,4,1] => 2 [2,4,1,1] => 2 [4,1,1,2] => 2 [4,1,2,1] => 2 [4,2,1,1] => 2 [1,1,3,3] => 2 [1,3,1,3] => 2 [1,3,3,1] => 2 [3,1,1,3] => 2 [3,1,3,1] => 2 [3,3,1,1] => 2 [1,1,3,4] => 1 [1,1,4,3] => 1 [1,3,1,4] => 1 [1,3,4,1] => 1 [1,4,1,3] => 1 [1,4,3,1] => 1 [3,1,1,4] => 1 [3,1,4,1] => 1 [3,4,1,1] => 1 [4,1,1,3] => 1 [4,1,3,1] => 1 [4,3,1,1] => 1 [1,2,2,2] => 3 [2,1,2,2] => 3 [2,2,1,2] => 3 [2,2,2,1] => 3 [1,2,2,3] => 2 [1,2,3,2] => 2 [1,3,2,2] => 2 [2,1,2,3] => 2 [2,1,3,2] => 2 [2,2,1,3] => 2 [2,2,3,1] => 2 [2,3,1,2] => 2 [2,3,2,1] => 2 [3,1,2,2] => 2 [3,2,1,2] => 2 [3,2,2,1] => 2 [1,2,2,4] => 1 [1,2,4,2] => 1 [1,4,2,2] => 1 [2,1,2,4] => 1 [2,1,4,2] => 1 [2,2,1,4] => 1 [2,2,4,1] => 1 [2,4,1,2] => 1 [2,4,2,1] => 1 [4,1,2,2] => 1 [4,2,1,2] => 1 [4,2,2,1] => 1 [1,2,3,3] => 1 [1,3,2,3] => 1 [1,3,3,2] => 1 [2,1,3,3] => 1 [2,3,1,3] => 1 [2,3,3,1] => 1 [3,1,2,3] => 1 [3,1,3,2] => 1 [3,2,1,3] => 1 [3,2,3,1] => 1 [3,3,1,2] => 1 [3,3,2,1] => 1 [1,2,3,4] => 0 [1,2,4,3] => 0 [1,3,2,4] => 0 [1,3,4,2] => 0 [1,4,2,3] => 0 [1,4,3,2] => 0 [2,1,3,4] => 0 [2,1,4,3] => 0 [2,3,1,4] => 0 [2,3,4,1] => 0 [2,4,1,3] => 0 [2,4,3,1] => 0 [3,1,2,4] => 0 [3,1,4,2] => 0 [3,2,1,4] => 0 [3,2,4,1] => 0 [3,4,1,2] => 0 [3,4,2,1] => 0 [4,1,2,3] => 0 [4,1,3,2] => 0 [4,2,1,3] => 0 [4,2,3,1] => 0 [4,3,1,2] => 0 [4,3,2,1] => 0 [1,1,1,1,1] => 10 [1,1,1,1,2] => 9 [1,1,1,2,1] => 9 [1,1,2,1,1] => 9 [1,2,1,1,1] => 9 [2,1,1,1,1] => 9 [1,1,1,1,3] => 8 [1,1,1,3,1] => 8 [1,1,3,1,1] => 8 [1,3,1,1,1] => 8 [3,1,1,1,1] => 8 [1,1,1,1,4] => 7 [1,1,1,4,1] => 7 [1,1,4,1,1] => 7 [1,4,1,1,1] => 7 [4,1,1,1,1] => 7 [1,1,1,1,5] => 6 [1,1,1,5,1] => 6 [1,1,5,1,1] => 6 [1,5,1,1,1] => 6 [5,1,1,1,1] => 6 [1,1,1,2,2] => 8 [1,1,2,1,2] => 8 [1,1,2,2,1] => 8 [1,2,1,1,2] => 8 [1,2,1,2,1] => 8 [1,2,2,1,1] => 8 [2,1,1,1,2] => 8 [2,1,1,2,1] => 8 [2,1,2,1,1] => 8 [2,2,1,1,1] => 8 [1,1,1,2,3] => 7 [1,1,1,3,2] => 7 [1,1,2,1,3] => 7 [1,1,2,3,1] => 7 [1,1,3,1,2] => 7 [1,1,3,2,1] => 7 [1,2,1,1,3] => 7 [1,2,1,3,1] => 7 [1,2,3,1,1] => 7 [1,3,1,1,2] => 7 [1,3,1,2,1] => 7 [1,3,2,1,1] => 7 [2,1,1,1,3] => 7 [2,1,1,3,1] => 7 [2,1,3,1,1] => 7 [2,3,1,1,1] => 7 [3,1,1,1,2] => 7 [3,1,1,2,1] => 7 [3,1,2,1,1] => 7 [3,2,1,1,1] => 7 [1,1,1,2,4] => 6 [1,1,1,4,2] => 6 [1,1,2,1,4] => 6 [1,1,2,4,1] => 6 [1,1,4,1,2] => 6 [1,1,4,2,1] => 6 [1,2,1,1,4] => 6 [1,2,1,4,1] => 6 [1,2,4,1,1] => 6 [1,4,1,1,2] => 6 [1,4,1,2,1] => 6 [1,4,2,1,1] => 6 [2,1,1,1,4] => 6 [2,1,1,4,1] => 6 [2,1,4,1,1] => 6 [2,4,1,1,1] => 6 [4,1,1,1,2] => 6 [4,1,1,2,1] => 6 [4,1,2,1,1] => 6 [4,2,1,1,1] => 6 [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] => 6 [1,1,3,1,3] => 6 [1,1,3,3,1] => 6 [1,3,1,1,3] => 6 [1,3,1,3,1] => 6 [1,3,3,1,1] => 6 [3,1,1,1,3] => 6 [3,1,1,3,1] => 6 [3,1,3,1,1] => 6 [3,3,1,1,1] => 6 [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] => 4 [1,1,1,5,3] => 4 [1,1,3,1,5] => 4 [1,1,3,5,1] => 4 [1,1,5,1,3] => 4 [1,1,5,3,1] => 4 [1,3,1,1,5] => 4 [1,3,1,5,1] => 4 [1,3,5,1,1] => 4 [1,5,1,1,3] => 4 [1,5,1,3,1] => 4 [1,5,3,1,1] => 4 [3,1,1,1,5] => 4 [3,1,1,5,1] => 4 [3,1,5,1,1] => 4 [3,5,1,1,1] => 4 [5,1,1,1,3] => 4 [5,1,1,3,1] => 4 [5,1,3,1,1] => 4 [5,3,1,1,1] => 4 [1,1,1,4,4] => 4 [1,1,4,1,4] => 4 [1,1,4,4,1] => 4 [1,4,1,1,4] => 4 [1,4,1,4,1] => 4 [1,4,4,1,1] => 4 [4,1,1,1,4] => 4 [4,1,1,4,1] => 4 [4,1,4,1,1] => 4 [4,4,1,1,1] => 4 [1,1,1,4,5] => 3 [1,1,1,5,4] => 3 [1,1,4,1,5] => 3 [1,1,4,5,1] => 3 [1,1,5,1,4] => 3 [1,1,5,4,1] => 3 [1,4,1,1,5] => 3 [1,4,1,5,1] => 3 [1,4,5,1,1] => 3 [1,5,1,1,4] => 3 [1,5,1,4,1] => 3 [1,5,4,1,1] => 3 [4,1,1,1,5] => 3 [4,1,1,5,1] => 3 [4,1,5,1,1] => 3 [4,5,1,1,1] => 3 [5,1,1,1,4] => 3 [5,1,1,4,1] => 3 [5,1,4,1,1] => 3 [5,4,1,1,1] => 3 [1,1,2,2,2] => 7 [1,2,1,2,2] => 7 [1,2,2,1,2] => 7 [1,2,2,2,1] => 7 [2,1,1,2,2] => 7 [2,1,2,1,2] => 7 [2,1,2,2,1] => 7 [2,2,1,1,2] => 7 [2,2,1,2,1] => 7 [2,2,2,1,1] => 7 [1,1,2,2,3] => 6 [1,1,2,3,2] => 6 [1,1,3,2,2] => 6 [1,2,1,2,3] => 6 [1,2,1,3,2] => 6 [1,2,2,1,3] => 6 [1,2,2,3,1] => 6 [1,2,3,1,2] => 6 [1,2,3,2,1] => 6 [1,3,1,2,2] => 6 [1,3,2,1,2] => 6 [1,3,2,2,1] => 6 [2,1,1,2,3] => 6 [2,1,1,3,2] => 6 [2,1,2,1,3] => 6 [2,1,2,3,1] => 6 [2,1,3,1,2] => 6 [2,1,3,2,1] => 6 [2,2,1,1,3] => 6 [2,2,1,3,1] => 6 [2,2,3,1,1] => 6 [2,3,1,1,2] => 6 [2,3,1,2,1] => 6 [2,3,2,1,1] => 6 [3,1,1,2,2] => 6 [3,1,2,1,2] => 6 [3,1,2,2,1] => 6 [3,2,1,1,2] => 6 [3,2,1,2,1] => 6 [3,2,2,1,1] => 6 [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] => 4 [1,1,2,5,2] => 4 [1,1,5,2,2] => 4 [1,2,1,2,5] => 4 [1,2,1,5,2] => 4 [1,2,2,1,5] => 4 [1,2,2,5,1] => 4 [1,2,5,1,2] => 4 [1,2,5,2,1] => 4 [1,5,1,2,2] => 4 [1,5,2,1,2] => 4 [1,5,2,2,1] => 4 [2,1,1,2,5] => 4 [2,1,1,5,2] => 4 [2,1,2,1,5] => 4 [2,1,2,5,1] => 4 [2,1,5,1,2] => 4 [2,1,5,2,1] => 4 [2,2,1,1,5] => 4 [2,2,1,5,1] => 4 [2,2,5,1,1] => 4 [2,5,1,1,2] => 4 [2,5,1,2,1] => 4 [2,5,2,1,1] => 4 [5,1,1,2,2] => 4 [5,1,2,1,2] => 4 [5,1,2,2,1] => 4 [5,2,1,1,2] => 4 [5,2,1,2,1] => 4 [5,2,2,1,1] => 4 [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] => 4 [1,1,2,4,3] => 4 [1,1,3,2,4] => 4 [1,1,3,4,2] => 4 [1,1,4,2,3] => 4 [1,1,4,3,2] => 4 [1,2,1,3,4] => 4 [1,2,1,4,3] => 4 [1,2,3,1,4] => 4 [1,2,3,4,1] => 4 [1,2,4,1,3] => 4 [1,2,4,3,1] => 4 [1,3,1,2,4] => 4 [1,3,1,4,2] => 4 [1,3,2,1,4] => 4 [1,3,2,4,1] => 4 [1,3,4,1,2] => 4 [1,3,4,2,1] => 4 [1,4,1,2,3] => 4 [1,4,1,3,2] => 4 [1,4,2,1,3] => 4 [1,4,2,3,1] => 4 [1,4,3,1,2] => 4 [1,4,3,2,1] => 4 [2,1,1,3,4] => 4 [2,1,1,4,3] => 4 [2,1,3,1,4] => 4 [2,1,3,4,1] => 4 [2,1,4,1,3] => 4 [2,1,4,3,1] => 4 [2,3,1,1,4] => 4 [2,3,1,4,1] => 4 [2,3,4,1,1] => 4 [2,4,1,1,3] => 4 [2,4,1,3,1] => 4 [2,4,3,1,1] => 4 [3,1,1,2,4] => 4 [3,1,1,4,2] => 4 [3,1,2,1,4] => 4 [3,1,2,4,1] => 4 [3,1,4,1,2] => 4 [3,1,4,2,1] => 4 [3,2,1,1,4] => 4 [3,2,1,4,1] => 4 [3,2,4,1,1] => 4 [3,4,1,1,2] => 4 [3,4,1,2,1] => 4 [3,4,2,1,1] => 4 [4,1,1,2,3] => 4 [4,1,1,3,2] => 4 [4,1,2,1,3] => 4 [4,1,2,3,1] => 4 [4,1,3,1,2] => 4 [4,1,3,2,1] => 4 [4,2,1,1,3] => 4 [4,2,1,3,1] => 4 [4,2,3,1,1] => 4 [4,3,1,1,2] => 4 [4,3,1,2,1] => 4 [4,3,2,1,1] => 4 [1,1,2,3,5] => 3 [1,1,2,5,3] => 3 [1,1,3,2,5] => 3 [1,1,3,5,2] => 3 [1,1,5,2,3] => 3 [1,1,5,3,2] => 3 [1,2,1,3,5] => 3 [1,2,1,5,3] => 3 [1,2,3,1,5] => 3 [1,2,3,5,1] => 3 [1,2,5,1,3] => 3 [1,2,5,3,1] => 3 [1,3,1,2,5] => 3 [1,3,1,5,2] => 3 [1,3,2,1,5] => 3 [1,3,2,5,1] => 3 [1,3,5,1,2] => 3 [1,3,5,2,1] => 3 [1,5,1,2,3] => 3 [1,5,1,3,2] => 3 [1,5,2,1,3] => 3 [1,5,2,3,1] => 3 [1,5,3,1,2] => 3 [1,5,3,2,1] => 3 [2,1,1,3,5] => 3 [2,1,1,5,3] => 3 [2,1,3,1,5] => 3 [2,1,3,5,1] => 3 [2,1,5,1,3] => 3 [2,1,5,3,1] => 3 [2,3,1,1,5] => 3 [2,3,1,5,1] => 3 [2,3,5,1,1] => 3 [2,5,1,1,3] => 3 [2,5,1,3,1] => 3 [2,5,3,1,1] => 3 [3,1,1,2,5] => 3 [3,1,1,5,2] => 3 [3,1,2,1,5] => 3 [3,1,2,5,1] => 3 [3,1,5,1,2] => 3 [3,1,5,2,1] => 3 [3,2,1,1,5] => 3 [3,2,1,5,1] => 3 [3,2,5,1,1] => 3 [3,5,1,1,2] => 3 [3,5,1,2,1] => 3 [3,5,2,1,1] => 3 [5,1,1,2,3] => 3 [5,1,1,3,2] => 3 [5,1,2,1,3] => 3 [5,1,2,3,1] => 3 [5,1,3,1,2] => 3 [5,1,3,2,1] => 3 [5,2,1,1,3] => 3 [5,2,1,3,1] => 3 [5,2,3,1,1] => 3 [5,3,1,1,2] => 3 [5,3,1,2,1] => 3 [5,3,2,1,1] => 3 [1,1,2,4,4] => 3 [1,1,4,2,4] => 3 [1,1,4,4,2] => 3 [1,2,1,4,4] => 3 [1,2,4,1,4] => 3 [1,2,4,4,1] => 3 [1,4,1,2,4] => 3 [1,4,1,4,2] => 3 [1,4,2,1,4] => 3 [1,4,2,4,1] => 3 [1,4,4,1,2] => 3 [1,4,4,2,1] => 3 [2,1,1,4,4] => 3 [2,1,4,1,4] => 3 [2,1,4,4,1] => 3 [2,4,1,1,4] => 3 [2,4,1,4,1] => 3 [2,4,4,1,1] => 3 [4,1,1,2,4] => 3 [4,1,1,4,2] => 3 [4,1,2,1,4] => 3 [4,1,2,4,1] => 3 [4,1,4,1,2] => 3 [4,1,4,2,1] => 3 [4,2,1,1,4] => 3 [4,2,1,4,1] => 3 [4,2,4,1,1] => 3 [4,4,1,1,2] => 3 [4,4,1,2,1] => 3 [4,4,2,1,1] => 3 [1,1,2,4,5] => 2 [1,1,2,5,4] => 2 [1,1,4,2,5] => 2 [1,1,4,5,2] => 2 [1,1,5,2,4] => 2 [1,1,5,4,2] => 2 [1,2,1,4,5] => 2 [1,2,1,5,4] => 2 [1,2,4,1,5] => 2 [1,2,4,5,1] => 2 [1,2,5,1,4] => 2 [1,2,5,4,1] => 2 [1,4,1,2,5] => 2 [1,4,1,5,2] => 2 [1,4,2,1,5] => 2 [1,4,2,5,1] => 2 [1,4,5,1,2] => 2 [1,4,5,2,1] => 2 [1,5,1,2,4] => 2 [1,5,1,4,2] => 2 [1,5,2,1,4] => 2 [1,5,2,4,1] => 2 [1,5,4,1,2] => 2 [1,5,4,2,1] => 2 [2,1,1,4,5] => 2 [2,1,1,5,4] => 2 [2,1,4,1,5] => 2 [2,1,4,5,1] => 2 [2,1,5,1,4] => 2 [2,1,5,4,1] => 2 [2,4,1,1,5] => 2 [2,4,1,5,1] => 2 [2,4,5,1,1] => 2 [2,5,1,1,4] => 2 [2,5,1,4,1] => 2 [2,5,4,1,1] => 2 [4,1,1,2,5] => 2 [4,1,1,5,2] => 2 [4,1,2,1,5] => 2 [4,1,2,5,1] => 2 [4,1,5,1,2] => 2 [4,1,5,2,1] => 2 [4,2,1,1,5] => 2 [4,2,1,5,1] => 2 [4,2,5,1,1] => 2 [4,5,1,1,2] => 2 [4,5,1,2,1] => 2 [4,5,2,1,1] => 2 [5,1,1,2,4] => 2 [5,1,1,4,2] => 2 [5,1,2,1,4] => 2 [5,1,2,4,1] => 2 [5,1,4,1,2] => 2 [5,1,4,2,1] => 2 [5,2,1,1,4] => 2 [5,2,1,4,1] => 2 [5,2,4,1,1] => 2 [5,4,1,1,2] => 2 [5,4,1,2,1] => 2 [5,4,2,1,1] => 2 [1,1,3,3,3] => 4 [1,3,1,3,3] => 4 [1,3,3,1,3] => 4 [1,3,3,3,1] => 4 [3,1,1,3,3] => 4 [3,1,3,1,3] => 4 [3,1,3,3,1] => 4 [3,3,1,1,3] => 4 [3,3,1,3,1] => 4 [3,3,3,1,1] => 4 [1,1,3,3,4] => 3 [1,1,3,4,3] => 3 [1,1,4,3,3] => 3 [1,3,1,3,4] => 3 [1,3,1,4,3] => 3 [1,3,3,1,4] => 3 [1,3,3,4,1] => 3 [1,3,4,1,3] => 3 [1,3,4,3,1] => 3 [1,4,1,3,3] => 3 [1,4,3,1,3] => 3 [1,4,3,3,1] => 3 [3,1,1,3,4] => 3 [3,1,1,4,3] => 3 [3,1,3,1,4] => 3 [3,1,3,4,1] => 3 [3,1,4,1,3] => 3 [3,1,4,3,1] => 3 [3,3,1,1,4] => 3 [3,3,1,4,1] => 3 [3,3,4,1,1] => 3 [3,4,1,1,3] => 3 [3,4,1,3,1] => 3 [3,4,3,1,1] => 3 [4,1,1,3,3] => 3 [4,1,3,1,3] => 3 [4,1,3,3,1] => 3 [4,3,1,1,3] => 3 [4,3,1,3,1] => 3 [4,3,3,1,1] => 3 [1,1,3,3,5] => 2 [1,1,3,5,3] => 2 [1,1,5,3,3] => 2 [1,3,1,3,5] => 2 [1,3,1,5,3] => 2 [1,3,3,1,5] => 2 [1,3,3,5,1] => 2 [1,3,5,1,3] => 2 [1,3,5,3,1] => 2 [1,5,1,3,3] => 2 [1,5,3,1,3] => 2 [1,5,3,3,1] => 2 [3,1,1,3,5] => 2 [3,1,1,5,3] => 2 [3,1,3,1,5] => 2 [3,1,3,5,1] => 2 [3,1,5,1,3] => 2 [3,1,5,3,1] => 2 [3,3,1,1,5] => 2 [3,3,1,5,1] => 2 [3,3,5,1,1] => 2 [3,5,1,1,3] => 2 [3,5,1,3,1] => 2 [3,5,3,1,1] => 2 [5,1,1,3,3] => 2 [5,1,3,1,3] => 2 [5,1,3,3,1] => 2 [5,3,1,1,3] => 2 [5,3,1,3,1] => 2 [5,3,3,1,1] => 2 [1,1,3,4,4] => 2 [1,1,4,3,4] => 2 [1,1,4,4,3] => 2 [1,3,1,4,4] => 2 [1,3,4,1,4] => 2 [1,3,4,4,1] => 2 [1,4,1,3,4] => 2 [1,4,1,4,3] => 2 [1,4,3,1,4] => 2 [1,4,3,4,1] => 2 [1,4,4,1,3] => 2 [1,4,4,3,1] => 2 [3,1,1,4,4] => 2 [3,1,4,1,4] => 2 [3,1,4,4,1] => 2 [3,4,1,1,4] => 2 [3,4,1,4,1] => 2 [3,4,4,1,1] => 2 [4,1,1,3,4] => 2 [4,1,1,4,3] => 2 [4,1,3,1,4] => 2 [4,1,3,4,1] => 2 [4,1,4,1,3] => 2 [4,1,4,3,1] => 2 [4,3,1,1,4] => 2 [4,3,1,4,1] => 2 [4,3,4,1,1] => 2 [4,4,1,1,3] => 2 [4,4,1,3,1] => 2 [4,4,3,1,1] => 2 [1,1,3,4,5] => 1 [1,1,3,5,4] => 1 [1,1,4,3,5] => 1 [1,1,4,5,3] => 1 [1,1,5,3,4] => 1 [1,1,5,4,3] => 1 [1,3,1,4,5] => 1 [1,3,1,5,4] => 1 [1,3,4,1,5] => 1 [1,3,4,5,1] => 1 [1,3,5,1,4] => 1 [1,3,5,4,1] => 1 [1,4,1,3,5] => 1 [1,4,1,5,3] => 1 [1,4,3,1,5] => 1 [1,4,3,5,1] => 1 [1,4,5,1,3] => 1 [1,4,5,3,1] => 1 [1,5,1,3,4] => 1 [1,5,1,4,3] => 1 [1,5,3,1,4] => 1 [1,5,3,4,1] => 1 [1,5,4,1,3] => 1 [1,5,4,3,1] => 1 [3,1,1,4,5] => 1 [3,1,1,5,4] => 1 [3,1,4,1,5] => 1 [3,1,4,5,1] => 1 [3,1,5,1,4] => 1 [3,1,5,4,1] => 1 [3,4,1,1,5] => 1 [3,4,1,5,1] => 1 [3,4,5,1,1] => 1 [3,5,1,1,4] => 1 [3,5,1,4,1] => 1 [3,5,4,1,1] => 1 [4,1,1,3,5] => 1 [4,1,1,5,3] => 1 [4,1,3,1,5] => 1 [4,1,3,5,1] => 1 [4,1,5,1,3] => 1 [4,1,5,3,1] => 1 [4,3,1,1,5] => 1 [4,3,1,5,1] => 1 [4,3,5,1,1] => 1 [4,5,1,1,3] => 1 [4,5,1,3,1] => 1 [4,5,3,1,1] => 1 [5,1,1,3,4] => 1 [5,1,1,4,3] => 1 [5,1,3,1,4] => 1 [5,1,3,4,1] => 1 [5,1,4,1,3] => 1 [5,1,4,3,1] => 1 [5,3,1,1,4] => 1 [5,3,1,4,1] => 1 [5,3,4,1,1] => 1 [5,4,1,1,3] => 1 [5,4,1,3,1] => 1 [5,4,3,1,1] => 1 [1,2,2,2,2] => 6 [2,1,2,2,2] => 6 [2,2,1,2,2] => 6 [2,2,2,1,2] => 6 [2,2,2,2,1] => 6 [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] => 4 [1,2,2,4,2] => 4 [1,2,4,2,2] => 4 [1,4,2,2,2] => 4 [2,1,2,2,4] => 4 [2,1,2,4,2] => 4 [2,1,4,2,2] => 4 [2,2,1,2,4] => 4 [2,2,1,4,2] => 4 [2,2,2,1,4] => 4 [2,2,2,4,1] => 4 [2,2,4,1,2] => 4 [2,2,4,2,1] => 4 [2,4,1,2,2] => 4 [2,4,2,1,2] => 4 [2,4,2,2,1] => 4 [4,1,2,2,2] => 4 [4,2,1,2,2] => 4 [4,2,2,1,2] => 4 [4,2,2,2,1] => 4 [1,2,2,2,5] => 3 [1,2,2,5,2] => 3 [1,2,5,2,2] => 3 [1,5,2,2,2] => 3 [2,1,2,2,5] => 3 [2,1,2,5,2] => 3 [2,1,5,2,2] => 3 [2,2,1,2,5] => 3 [2,2,1,5,2] => 3 [2,2,2,1,5] => 3 [2,2,2,5,1] => 3 [2,2,5,1,2] => 3 [2,2,5,2,1] => 3 [2,5,1,2,2] => 3 [2,5,2,1,2] => 3 [2,5,2,2,1] => 3 [5,1,2,2,2] => 3 [5,2,1,2,2] => 3 [5,2,2,1,2] => 3 [5,2,2,2,1] => 3 [1,2,2,3,3] => 4 [1,2,3,2,3] => 4 [1,2,3,3,2] => 4 [1,3,2,2,3] => 4 [1,3,2,3,2] => 4 [1,3,3,2,2] => 4 [2,1,2,3,3] => 4 [2,1,3,2,3] => 4 [2,1,3,3,2] => 4 [2,2,1,3,3] => 4 [2,2,3,1,3] => 4 [2,2,3,3,1] => 4 [2,3,1,2,3] => 4 [2,3,1,3,2] => 4 [2,3,2,1,3] => 4 [2,3,2,3,1] => 4 [2,3,3,1,2] => 4 [2,3,3,2,1] => 4 [3,1,2,2,3] => 4 [3,1,2,3,2] => 4 [3,1,3,2,2] => 4 [3,2,1,2,3] => 4 [3,2,1,3,2] => 4 [3,2,2,1,3] => 4 [3,2,2,3,1] => 4 [3,2,3,1,2] => 4 [3,2,3,2,1] => 4 [3,3,1,2,2] => 4 [3,3,2,1,2] => 4 [3,3,2,2,1] => 4 [1,2,2,3,4] => 3 [1,2,2,4,3] => 3 [1,2,3,2,4] => 3 [1,2,3,4,2] => 3 [1,2,4,2,3] => 3 [1,2,4,3,2] => 3 [1,3,2,2,4] => 3 [1,3,2,4,2] => 3 [1,3,4,2,2] => 3 [1,4,2,2,3] => 3 [1,4,2,3,2] => 3 [1,4,3,2,2] => 3 [2,1,2,3,4] => 3 [2,1,2,4,3] => 3 [2,1,3,2,4] => 3 [2,1,3,4,2] => 3 [2,1,4,2,3] => 3 [2,1,4,3,2] => 3 [2,2,1,3,4] => 3 [2,2,1,4,3] => 3 [2,2,3,1,4] => 3 [2,2,3,4,1] => 3 [2,2,4,1,3] => 3 [2,2,4,3,1] => 3 [2,3,1,2,4] => 3 [2,3,1,4,2] => 3 [2,3,2,1,4] => 3 [2,3,2,4,1] => 3 [2,3,4,1,2] => 3 [2,3,4,2,1] => 3 [2,4,1,2,3] => 3 [2,4,1,3,2] => 3 [2,4,2,1,3] => 3 [2,4,2,3,1] => 3 [2,4,3,1,2] => 3 [2,4,3,2,1] => 3 [3,1,2,2,4] => 3 [3,1,2,4,2] => 3 [3,1,4,2,2] => 3 [3,2,1,2,4] => 3 [3,2,1,4,2] => 3 [3,2,2,1,4] => 3 [3,2,2,4,1] => 3 [3,2,4,1,2] => 3 [3,2,4,2,1] => 3 [3,4,1,2,2] => 3 [3,4,2,1,2] => 3 [3,4,2,2,1] => 3 [4,1,2,2,3] => 3 [4,1,2,3,2] => 3 [4,1,3,2,2] => 3 [4,2,1,2,3] => 3 [4,2,1,3,2] => 3 [4,2,2,1,3] => 3 [4,2,2,3,1] => 3 [4,2,3,1,2] => 3 [4,2,3,2,1] => 3 [4,3,1,2,2] => 3 [4,3,2,1,2] => 3 [4,3,2,2,1] => 3 [1,2,2,3,5] => 2 [1,2,2,5,3] => 2 [1,2,3,2,5] => 2 [1,2,3,5,2] => 2 [1,2,5,2,3] => 2 [1,2,5,3,2] => 2 [1,3,2,2,5] => 2 [1,3,2,5,2] => 2 [1,3,5,2,2] => 2 [1,5,2,2,3] => 2 [1,5,2,3,2] => 2 [1,5,3,2,2] => 2 [2,1,2,3,5] => 2 [2,1,2,5,3] => 2 [2,1,3,2,5] => 2 [2,1,3,5,2] => 2 [2,1,5,2,3] => 2 [2,1,5,3,2] => 2 [2,2,1,3,5] => 2 [2,2,1,5,3] => 2 [2,2,3,1,5] => 2 [2,2,3,5,1] => 2 [2,2,5,1,3] => 2 [2,2,5,3,1] => 2 [2,3,1,2,5] => 2 [2,3,1,5,2] => 2 [2,3,2,1,5] => 2 [2,3,2,5,1] => 2 [2,3,5,1,2] => 2 [2,3,5,2,1] => 2 [2,5,1,2,3] => 2 [2,5,1,3,2] => 2 [2,5,2,1,3] => 2 [2,5,2,3,1] => 2 [2,5,3,1,2] => 2 [2,5,3,2,1] => 2 [3,1,2,2,5] => 2 [3,1,2,5,2] => 2 [3,1,5,2,2] => 2 [3,2,1,2,5] => 2 [3,2,1,5,2] => 2 [3,2,2,1,5] => 2 [3,2,2,5,1] => 2 [3,2,5,1,2] => 2 [3,2,5,2,1] => 2 [3,5,1,2,2] => 2 [3,5,2,1,2] => 2 [3,5,2,2,1] => 2 [5,1,2,2,3] => 2 [5,1,2,3,2] => 2 [5,1,3,2,2] => 2 [5,2,1,2,3] => 2 [5,2,1,3,2] => 2 [5,2,2,1,3] => 2 [5,2,2,3,1] => 2 [5,2,3,1,2] => 2 [5,2,3,2,1] => 2 [5,3,1,2,2] => 2 [5,3,2,1,2] => 2 [5,3,2,2,1] => 2 [1,2,2,4,4] => 2 [1,2,4,2,4] => 2 [1,2,4,4,2] => 2 [1,4,2,2,4] => 2 [1,4,2,4,2] => 2 [1,4,4,2,2] => 2 [2,1,2,4,4] => 2 [2,1,4,2,4] => 2 [2,1,4,4,2] => 2 [2,2,1,4,4] => 2 [2,2,4,1,4] => 2 [2,2,4,4,1] => 2 [2,4,1,2,4] => 2 [2,4,1,4,2] => 2 [2,4,2,1,4] => 2 [2,4,2,4,1] => 2 [2,4,4,1,2] => 2 [2,4,4,2,1] => 2 [4,1,2,2,4] => 2 [4,1,2,4,2] => 2 [4,1,4,2,2] => 2 [4,2,1,2,4] => 2 [4,2,1,4,2] => 2 [4,2,2,1,4] => 2 [4,2,2,4,1] => 2 [4,2,4,1,2] => 2 [4,2,4,2,1] => 2 [4,4,1,2,2] => 2 [4,4,2,1,2] => 2 [4,4,2,2,1] => 2 [1,2,2,4,5] => 1 [1,2,2,5,4] => 1 [1,2,4,2,5] => 1 [1,2,4,5,2] => 1 [1,2,5,2,4] => 1 [1,2,5,4,2] => 1 [1,4,2,2,5] => 1 [1,4,2,5,2] => 1 [1,4,5,2,2] => 1 [1,5,2,2,4] => 1 [1,5,2,4,2] => 1 [1,5,4,2,2] => 1 [2,1,2,4,5] => 1 [2,1,2,5,4] => 1 [2,1,4,2,5] => 1 [2,1,4,5,2] => 1 [2,1,5,2,4] => 1 [2,1,5,4,2] => 1 [2,2,1,4,5] => 1 [2,2,1,5,4] => 1 [2,2,4,1,5] => 1 [2,2,4,5,1] => 1 [2,2,5,1,4] => 1 [2,2,5,4,1] => 1 [2,4,1,2,5] => 1 [2,4,1,5,2] => 1 [2,4,2,1,5] => 1 [2,4,2,5,1] => 1 [2,4,5,1,2] => 1 [2,4,5,2,1] => 1 [2,5,1,2,4] => 1 [2,5,1,4,2] => 1 [2,5,2,1,4] => 1 [2,5,2,4,1] => 1 [2,5,4,1,2] => 1 [2,5,4,2,1] => 1 [4,1,2,2,5] => 1 [4,1,2,5,2] => 1 [4,1,5,2,2] => 1 [4,2,1,2,5] => 1 [4,2,1,5,2] => 1 [4,2,2,1,5] => 1 [4,2,2,5,1] => 1 [4,2,5,1,2] => 1 [4,2,5,2,1] => 1 [4,5,1,2,2] => 1 [4,5,2,1,2] => 1 [4,5,2,2,1] => 1 [5,1,2,2,4] => 1 [5,1,2,4,2] => 1 [5,1,4,2,2] => 1 [5,2,1,2,4] => 1 [5,2,1,4,2] => 1 [5,2,2,1,4] => 1 [5,2,2,4,1] => 1 [5,2,4,1,2] => 1 [5,2,4,2,1] => 1 [5,4,1,2,2] => 1 [5,4,2,1,2] => 1 [5,4,2,2,1] => 1 [1,2,3,3,3] => 3 [1,3,2,3,3] => 3 [1,3,3,2,3] => 3 [1,3,3,3,2] => 3 [2,1,3,3,3] => 3 [2,3,1,3,3] => 3 [2,3,3,1,3] => 3 [2,3,3,3,1] => 3 [3,1,2,3,3] => 3 [3,1,3,2,3] => 3 [3,1,3,3,2] => 3 [3,2,1,3,3] => 3 [3,2,3,1,3] => 3 [3,2,3,3,1] => 3 [3,3,1,2,3] => 3 [3,3,1,3,2] => 3 [3,3,2,1,3] => 3 [3,3,2,3,1] => 3 [3,3,3,1,2] => 3 [3,3,3,2,1] => 3 [1,2,3,3,4] => 2 [1,2,3,4,3] => 2 [1,2,4,3,3] => 2 [1,3,2,3,4] => 2 [1,3,2,4,3] => 2 [1,3,3,2,4] => 2 [1,3,3,4,2] => 2 [1,3,4,2,3] => 2 [1,3,4,3,2] => 2 [1,4,2,3,3] => 2 [1,4,3,2,3] => 2 [1,4,3,3,2] => 2 [2,1,3,3,4] => 2 [2,1,3,4,3] => 2 [2,1,4,3,3] => 2 [2,3,1,3,4] => 2 [2,3,1,4,3] => 2 [2,3,3,1,4] => 2 [2,3,3,4,1] => 2 [2,3,4,1,3] => 2 [2,3,4,3,1] => 2 [2,4,1,3,3] => 2 [2,4,3,1,3] => 2 [2,4,3,3,1] => 2 ----------------------------------------------------------------------------- Created: May 08, 2014 at 23:40 by Joanna Heppner ----------------------------------------------------------------------------- Last Updated: Jun 14, 2018 at 11:16 by Christian Stump