***************************************************************************** * 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: St000037 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The sign of a permutation. ----------------------------------------------------------------------------- References: [1] Section 1.3 Stanley, R. P. Enumerative combinatorics. Volume 1 [[MathSciNet:2868112]] ----------------------------------------------------------------------------- Code: def statistic(x): return x.sign() ----------------------------------------------------------------------------- Statistic values: [1] => 1 [1,2] => 1 [2,1] => -1 [1,2,3] => 1 [1,3,2] => -1 [2,1,3] => -1 [2,3,1] => 1 [3,1,2] => 1 [3,2,1] => -1 [1,2,3,4] => 1 [1,2,4,3] => -1 [1,3,2,4] => -1 [1,3,4,2] => 1 [1,4,2,3] => 1 [1,4,3,2] => -1 [2,1,3,4] => -1 [2,1,4,3] => 1 [2,3,1,4] => 1 [2,3,4,1] => -1 [2,4,1,3] => -1 [2,4,3,1] => 1 [3,1,2,4] => 1 [3,1,4,2] => -1 [3,2,1,4] => -1 [3,2,4,1] => 1 [3,4,1,2] => 1 [3,4,2,1] => -1 [4,1,2,3] => -1 [4,1,3,2] => 1 [4,2,1,3] => 1 [4,2,3,1] => -1 [4,3,1,2] => -1 [4,3,2,1] => 1 [1,2,3,4,5] => 1 [1,2,3,5,4] => -1 [1,2,4,3,5] => -1 [1,2,4,5,3] => 1 [1,2,5,3,4] => 1 [1,2,5,4,3] => -1 [1,3,2,4,5] => -1 [1,3,2,5,4] => 1 [1,3,4,2,5] => 1 [1,3,4,5,2] => -1 [1,3,5,2,4] => -1 [1,3,5,4,2] => 1 [1,4,2,3,5] => 1 [1,4,2,5,3] => -1 [1,4,3,2,5] => -1 [1,4,3,5,2] => 1 [1,4,5,2,3] => 1 [1,4,5,3,2] => -1 [1,5,2,3,4] => -1 [1,5,2,4,3] => 1 [1,5,3,2,4] => 1 [1,5,3,4,2] => -1 [1,5,4,2,3] => -1 [1,5,4,3,2] => 1 [2,1,3,4,5] => -1 [2,1,3,5,4] => 1 [2,1,4,3,5] => 1 [2,1,4,5,3] => -1 [2,1,5,3,4] => -1 [2,1,5,4,3] => 1 [2,3,1,4,5] => 1 [2,3,1,5,4] => -1 [2,3,4,1,5] => -1 [2,3,4,5,1] => 1 [2,3,5,1,4] => 1 [2,3,5,4,1] => -1 [2,4,1,3,5] => -1 [2,4,1,5,3] => 1 [2,4,3,1,5] => 1 [2,4,3,5,1] => -1 [2,4,5,1,3] => -1 [2,4,5,3,1] => 1 [2,5,1,3,4] => 1 [2,5,1,4,3] => -1 [2,5,3,1,4] => -1 [2,5,3,4,1] => 1 [2,5,4,1,3] => 1 [2,5,4,3,1] => -1 [3,1,2,4,5] => 1 [3,1,2,5,4] => -1 [3,1,4,2,5] => -1 [3,1,4,5,2] => 1 [3,1,5,2,4] => 1 [3,1,5,4,2] => -1 [3,2,1,4,5] => -1 [3,2,1,5,4] => 1 [3,2,4,1,5] => 1 [3,2,4,5,1] => -1 [3,2,5,1,4] => -1 [3,2,5,4,1] => 1 [3,4,1,2,5] => 1 [3,4,1,5,2] => -1 [3,4,2,1,5] => -1 [3,4,2,5,1] => 1 [3,4,5,1,2] => 1 [3,4,5,2,1] => -1 [3,5,1,2,4] => -1 [3,5,1,4,2] => 1 [3,5,2,1,4] => 1 [3,5,2,4,1] => -1 [3,5,4,1,2] => -1 [3,5,4,2,1] => 1 [4,1,2,3,5] => -1 [4,1,2,5,3] => 1 [4,1,3,2,5] => 1 [4,1,3,5,2] => -1 [4,1,5,2,3] => -1 [4,1,5,3,2] => 1 [4,2,1,3,5] => 1 [4,2,1,5,3] => -1 [4,2,3,1,5] => -1 [4,2,3,5,1] => 1 [4,2,5,1,3] => 1 [4,2,5,3,1] => -1 [4,3,1,2,5] => -1 [4,3,1,5,2] => 1 [4,3,2,1,5] => 1 [4,3,2,5,1] => -1 [4,3,5,1,2] => -1 [4,3,5,2,1] => 1 [4,5,1,2,3] => 1 [4,5,1,3,2] => -1 [4,5,2,1,3] => -1 [4,5,2,3,1] => 1 [4,5,3,1,2] => 1 [4,5,3,2,1] => -1 [5,1,2,3,4] => 1 [5,1,2,4,3] => -1 [5,1,3,2,4] => -1 [5,1,3,4,2] => 1 [5,1,4,2,3] => 1 [5,1,4,3,2] => -1 [5,2,1,3,4] => -1 [5,2,1,4,3] => 1 [5,2,3,1,4] => 1 [5,2,3,4,1] => -1 [5,2,4,1,3] => -1 [5,2,4,3,1] => 1 [5,3,1,2,4] => 1 [5,3,1,4,2] => -1 [5,3,2,1,4] => -1 [5,3,2,4,1] => 1 [5,3,4,1,2] => 1 [5,3,4,2,1] => -1 [5,4,1,2,3] => -1 [5,4,1,3,2] => 1 [5,4,2,1,3] => 1 [5,4,2,3,1] => -1 [5,4,3,1,2] => -1 [5,4,3,2,1] => 1 [1,2,3,4,5,6] => 1 [1,2,3,4,6,5] => -1 [1,2,3,5,4,6] => -1 [1,2,3,5,6,4] => 1 [1,2,3,6,4,5] => 1 [1,2,3,6,5,4] => -1 [1,2,4,3,5,6] => -1 [1,2,4,3,6,5] => 1 [1,2,4,5,3,6] => 1 [1,2,4,5,6,3] => -1 [1,2,4,6,3,5] => -1 [1,2,4,6,5,3] => 1 [1,2,5,3,4,6] => 1 [1,2,5,3,6,4] => -1 [1,2,5,4,3,6] => -1 [1,2,5,4,6,3] => 1 [1,2,5,6,3,4] => 1 [1,2,5,6,4,3] => -1 [1,2,6,3,4,5] => -1 [1,2,6,3,5,4] => 1 [1,2,6,4,3,5] => 1 [1,2,6,4,5,3] => -1 [1,2,6,5,3,4] => -1 [1,2,6,5,4,3] => 1 [1,3,2,4,5,6] => -1 [1,3,2,4,6,5] => 1 [1,3,2,5,4,6] => 1 [1,3,2,5,6,4] => -1 [1,3,2,6,4,5] => -1 [1,3,2,6,5,4] => 1 [1,3,4,2,5,6] => 1 [1,3,4,2,6,5] => -1 [1,3,4,5,2,6] => -1 [1,3,4,5,6,2] => 1 [1,3,4,6,2,5] => 1 [1,3,4,6,5,2] => -1 [1,3,5,2,4,6] => -1 [1,3,5,2,6,4] => 1 [1,3,5,4,2,6] => 1 [1,3,5,4,6,2] => -1 [1,3,5,6,2,4] => -1 [1,3,5,6,4,2] => 1 [1,3,6,2,4,5] => 1 [1,3,6,2,5,4] => -1 [1,3,6,4,2,5] => -1 [1,3,6,4,5,2] => 1 [1,3,6,5,2,4] => 1 [1,3,6,5,4,2] => -1 [1,4,2,3,5,6] => 1 [1,4,2,3,6,5] => -1 [1,4,2,5,3,6] => -1 [1,4,2,5,6,3] => 1 [1,4,2,6,3,5] => 1 [1,4,2,6,5,3] => -1 [1,4,3,2,5,6] => -1 [1,4,3,2,6,5] => 1 [1,4,3,5,2,6] => 1 [1,4,3,5,6,2] => -1 [1,4,3,6,2,5] => -1 [1,4,3,6,5,2] => 1 [1,4,5,2,3,6] => 1 [1,4,5,2,6,3] => -1 [1,4,5,3,2,6] => -1 [1,4,5,3,6,2] => 1 [1,4,5,6,2,3] => 1 [1,4,5,6,3,2] => -1 [1,4,6,2,3,5] => -1 [1,4,6,2,5,3] => 1 [1,4,6,3,2,5] => 1 [1,4,6,3,5,2] => -1 [1,4,6,5,2,3] => -1 [1,4,6,5,3,2] => 1 [1,5,2,3,4,6] => -1 [1,5,2,3,6,4] => 1 [1,5,2,4,3,6] => 1 [1,5,2,4,6,3] => -1 [1,5,2,6,3,4] => -1 [1,5,2,6,4,3] => 1 [1,5,3,2,4,6] => 1 [1,5,3,2,6,4] => -1 [1,5,3,4,2,6] => -1 [1,5,3,4,6,2] => 1 [1,5,3,6,2,4] => 1 [1,5,3,6,4,2] => -1 [1,5,4,2,3,6] => -1 [1,5,4,2,6,3] => 1 [1,5,4,3,2,6] => 1 [1,5,4,3,6,2] => -1 [1,5,4,6,2,3] => -1 [1,5,4,6,3,2] => 1 [1,5,6,2,3,4] => 1 [1,5,6,2,4,3] => -1 [1,5,6,3,2,4] => -1 [1,5,6,3,4,2] => 1 [1,5,6,4,2,3] => 1 [1,5,6,4,3,2] => -1 [1,6,2,3,4,5] => 1 [1,6,2,3,5,4] => -1 [1,6,2,4,3,5] => -1 [1,6,2,4,5,3] => 1 [1,6,2,5,3,4] => 1 [1,6,2,5,4,3] => -1 [1,6,3,2,4,5] => -1 [1,6,3,2,5,4] => 1 [1,6,3,4,2,5] => 1 [1,6,3,4,5,2] => -1 [1,6,3,5,2,4] => -1 [1,6,3,5,4,2] => 1 [1,6,4,2,3,5] => 1 [1,6,4,2,5,3] => -1 [1,6,4,3,2,5] => -1 [1,6,4,3,5,2] => 1 [1,6,4,5,2,3] => 1 [1,6,4,5,3,2] => -1 [1,6,5,2,3,4] => -1 [1,6,5,2,4,3] => 1 [1,6,5,3,2,4] => 1 [1,6,5,3,4,2] => -1 [1,6,5,4,2,3] => -1 [1,6,5,4,3,2] => 1 [2,1,3,4,5,6] => -1 [2,1,3,4,6,5] => 1 [2,1,3,5,4,6] => 1 [2,1,3,5,6,4] => -1 [2,1,3,6,4,5] => -1 [2,1,3,6,5,4] => 1 [2,1,4,3,5,6] => 1 [2,1,4,3,6,5] => -1 [2,1,4,5,3,6] => -1 [2,1,4,5,6,3] => 1 [2,1,4,6,3,5] => 1 [2,1,4,6,5,3] => -1 [2,1,5,3,4,6] => -1 [2,1,5,3,6,4] => 1 [2,1,5,4,3,6] => 1 [2,1,5,4,6,3] => -1 [2,1,5,6,3,4] => -1 [2,1,5,6,4,3] => 1 [2,1,6,3,4,5] => 1 [2,1,6,3,5,4] => -1 [2,1,6,4,3,5] => -1 [2,1,6,4,5,3] => 1 [2,1,6,5,3,4] => 1 [2,1,6,5,4,3] => -1 [2,3,1,4,5,6] => 1 [2,3,1,4,6,5] => -1 [2,3,1,5,4,6] => -1 [2,3,1,5,6,4] => 1 [2,3,1,6,4,5] => 1 [2,3,1,6,5,4] => -1 [2,3,4,1,5,6] => -1 [2,3,4,1,6,5] => 1 [2,3,4,5,1,6] => 1 [2,3,4,5,6,1] => -1 [2,3,4,6,1,5] => -1 [2,3,4,6,5,1] => 1 [2,3,5,1,4,6] => 1 [2,3,5,1,6,4] => -1 [2,3,5,4,1,6] => -1 [2,3,5,4,6,1] => 1 [2,3,5,6,1,4] => 1 [2,3,5,6,4,1] => -1 [2,3,6,1,4,5] => -1 [2,3,6,1,5,4] => 1 [2,3,6,4,1,5] => 1 [2,3,6,4,5,1] => -1 [2,3,6,5,1,4] => -1 [2,3,6,5,4,1] => 1 [2,4,1,3,5,6] => -1 [2,4,1,3,6,5] => 1 [2,4,1,5,3,6] => 1 [2,4,1,5,6,3] => -1 [2,4,1,6,3,5] => -1 [2,4,1,6,5,3] => 1 [2,4,3,1,5,6] => 1 [2,4,3,1,6,5] => -1 [2,4,3,5,1,6] => -1 [2,4,3,5,6,1] => 1 [2,4,3,6,1,5] => 1 [2,4,3,6,5,1] => -1 [2,4,5,1,3,6] => -1 [2,4,5,1,6,3] => 1 [2,4,5,3,1,6] => 1 [2,4,5,3,6,1] => -1 [2,4,5,6,1,3] => -1 [2,4,5,6,3,1] => 1 [2,4,6,1,3,5] => 1 [2,4,6,1,5,3] => -1 [2,4,6,3,1,5] => -1 [2,4,6,3,5,1] => 1 [2,4,6,5,1,3] => 1 [2,4,6,5,3,1] => -1 [2,5,1,3,4,6] => 1 [2,5,1,3,6,4] => -1 [2,5,1,4,3,6] => -1 [2,5,1,4,6,3] => 1 [2,5,1,6,3,4] => 1 [2,5,1,6,4,3] => -1 [2,5,3,1,4,6] => -1 [2,5,3,1,6,4] => 1 [2,5,3,4,1,6] => 1 [2,5,3,4,6,1] => -1 [2,5,3,6,1,4] => -1 [2,5,3,6,4,1] => 1 [2,5,4,1,3,6] => 1 [2,5,4,1,6,3] => -1 [2,5,4,3,1,6] => -1 [2,5,4,3,6,1] => 1 [2,5,4,6,1,3] => 1 [2,5,4,6,3,1] => -1 [2,5,6,1,3,4] => -1 [2,5,6,1,4,3] => 1 [2,5,6,3,1,4] => 1 [2,5,6,3,4,1] => -1 [2,5,6,4,1,3] => -1 [2,5,6,4,3,1] => 1 [2,6,1,3,4,5] => -1 [2,6,1,3,5,4] => 1 [2,6,1,4,3,5] => 1 [2,6,1,4,5,3] => -1 [2,6,1,5,3,4] => -1 [2,6,1,5,4,3] => 1 [2,6,3,1,4,5] => 1 [2,6,3,1,5,4] => -1 [2,6,3,4,1,5] => -1 [2,6,3,4,5,1] => 1 [2,6,3,5,1,4] => 1 [2,6,3,5,4,1] => -1 [2,6,4,1,3,5] => -1 [2,6,4,1,5,3] => 1 [2,6,4,3,1,5] => 1 [2,6,4,3,5,1] => -1 [2,6,4,5,1,3] => -1 [2,6,4,5,3,1] => 1 [2,6,5,1,3,4] => 1 [2,6,5,1,4,3] => -1 [2,6,5,3,1,4] => -1 [2,6,5,3,4,1] => 1 [2,6,5,4,1,3] => 1 [2,6,5,4,3,1] => -1 [3,1,2,4,5,6] => 1 [3,1,2,4,6,5] => -1 [3,1,2,5,4,6] => -1 [3,1,2,5,6,4] => 1 [3,1,2,6,4,5] => 1 [3,1,2,6,5,4] => -1 [3,1,4,2,5,6] => -1 [3,1,4,2,6,5] => 1 [3,1,4,5,2,6] => 1 [3,1,4,5,6,2] => -1 [3,1,4,6,2,5] => -1 [3,1,4,6,5,2] => 1 [3,1,5,2,4,6] => 1 [3,1,5,2,6,4] => -1 [3,1,5,4,2,6] => -1 [3,1,5,4,6,2] => 1 [3,1,5,6,2,4] => 1 [3,1,5,6,4,2] => -1 [3,1,6,2,4,5] => -1 [3,1,6,2,5,4] => 1 [3,1,6,4,2,5] => 1 [3,1,6,4,5,2] => -1 [3,1,6,5,2,4] => -1 [3,1,6,5,4,2] => 1 [3,2,1,4,5,6] => -1 [3,2,1,4,6,5] => 1 [3,2,1,5,4,6] => 1 [3,2,1,5,6,4] => -1 [3,2,1,6,4,5] => -1 [3,2,1,6,5,4] => 1 [3,2,4,1,5,6] => 1 [3,2,4,1,6,5] => -1 [3,2,4,5,1,6] => -1 [3,2,4,5,6,1] => 1 [3,2,4,6,1,5] => 1 [3,2,4,6,5,1] => -1 [3,2,5,1,4,6] => -1 [3,2,5,1,6,4] => 1 [3,2,5,4,1,6] => 1 [3,2,5,4,6,1] => -1 [3,2,5,6,1,4] => -1 [3,2,5,6,4,1] => 1 [3,2,6,1,4,5] => 1 [3,2,6,1,5,4] => -1 [3,2,6,4,1,5] => -1 [3,2,6,4,5,1] => 1 [3,2,6,5,1,4] => 1 [3,2,6,5,4,1] => -1 [3,4,1,2,5,6] => 1 [3,4,1,2,6,5] => -1 [3,4,1,5,2,6] => -1 [3,4,1,5,6,2] => 1 [3,4,1,6,2,5] => 1 [3,4,1,6,5,2] => -1 [3,4,2,1,5,6] => -1 [3,4,2,1,6,5] => 1 [3,4,2,5,1,6] => 1 [3,4,2,5,6,1] => -1 [3,4,2,6,1,5] => -1 [3,4,2,6,5,1] => 1 [3,4,5,1,2,6] => 1 [3,4,5,1,6,2] => -1 [3,4,5,2,1,6] => -1 [3,4,5,2,6,1] => 1 [3,4,5,6,1,2] => 1 [3,4,5,6,2,1] => -1 [3,4,6,1,2,5] => -1 [3,4,6,1,5,2] => 1 [3,4,6,2,1,5] => 1 [3,4,6,2,5,1] => -1 [3,4,6,5,1,2] => -1 [3,4,6,5,2,1] => 1 [3,5,1,2,4,6] => -1 [3,5,1,2,6,4] => 1 [3,5,1,4,2,6] => 1 [3,5,1,4,6,2] => -1 [3,5,1,6,2,4] => -1 [3,5,1,6,4,2] => 1 [3,5,2,1,4,6] => 1 [3,5,2,1,6,4] => -1 [3,5,2,4,1,6] => -1 [3,5,2,4,6,1] => 1 [3,5,2,6,1,4] => 1 [3,5,2,6,4,1] => -1 [3,5,4,1,2,6] => -1 [3,5,4,1,6,2] => 1 [3,5,4,2,1,6] => 1 [3,5,4,2,6,1] => -1 [3,5,4,6,1,2] => -1 [3,5,4,6,2,1] => 1 [3,5,6,1,2,4] => 1 [3,5,6,1,4,2] => -1 [3,5,6,2,1,4] => -1 [3,5,6,2,4,1] => 1 [3,5,6,4,1,2] => 1 [3,5,6,4,2,1] => -1 [3,6,1,2,4,5] => 1 [3,6,1,2,5,4] => -1 [3,6,1,4,2,5] => -1 [3,6,1,4,5,2] => 1 [3,6,1,5,2,4] => 1 [3,6,1,5,4,2] => -1 [3,6,2,1,4,5] => -1 [3,6,2,1,5,4] => 1 [3,6,2,4,1,5] => 1 [3,6,2,4,5,1] => -1 [3,6,2,5,1,4] => -1 [3,6,2,5,4,1] => 1 [3,6,4,1,2,5] => 1 [3,6,4,1,5,2] => -1 [3,6,4,2,1,5] => -1 [3,6,4,2,5,1] => 1 [3,6,4,5,1,2] => 1 [3,6,4,5,2,1] => -1 [3,6,5,1,2,4] => -1 [3,6,5,1,4,2] => 1 [3,6,5,2,1,4] => 1 [3,6,5,2,4,1] => -1 [3,6,5,4,1,2] => -1 [3,6,5,4,2,1] => 1 [4,1,2,3,5,6] => -1 [4,1,2,3,6,5] => 1 [4,1,2,5,3,6] => 1 [4,1,2,5,6,3] => -1 [4,1,2,6,3,5] => -1 [4,1,2,6,5,3] => 1 [4,1,3,2,5,6] => 1 [4,1,3,2,6,5] => -1 [4,1,3,5,2,6] => -1 [4,1,3,5,6,2] => 1 [4,1,3,6,2,5] => 1 [4,1,3,6,5,2] => -1 [4,1,5,2,3,6] => -1 [4,1,5,2,6,3] => 1 [4,1,5,3,2,6] => 1 [4,1,5,3,6,2] => -1 [4,1,5,6,2,3] => -1 [4,1,5,6,3,2] => 1 [4,1,6,2,3,5] => 1 [4,1,6,2,5,3] => -1 [4,1,6,3,2,5] => -1 [4,1,6,3,5,2] => 1 [4,1,6,5,2,3] => 1 [4,1,6,5,3,2] => -1 [4,2,1,3,5,6] => 1 [4,2,1,3,6,5] => -1 [4,2,1,5,3,6] => -1 [4,2,1,5,6,3] => 1 [4,2,1,6,3,5] => 1 [4,2,1,6,5,3] => -1 [4,2,3,1,5,6] => -1 [4,2,3,1,6,5] => 1 [4,2,3,5,1,6] => 1 [4,2,3,5,6,1] => -1 [4,2,3,6,1,5] => -1 [4,2,3,6,5,1] => 1 [4,2,5,1,3,6] => 1 [4,2,5,1,6,3] => -1 [4,2,5,3,1,6] => -1 [4,2,5,3,6,1] => 1 [4,2,5,6,1,3] => 1 [4,2,5,6,3,1] => -1 [4,2,6,1,3,5] => -1 [4,2,6,1,5,3] => 1 [4,2,6,3,1,5] => 1 [4,2,6,3,5,1] => -1 [4,2,6,5,1,3] => -1 [4,2,6,5,3,1] => 1 [4,3,1,2,5,6] => -1 [4,3,1,2,6,5] => 1 [4,3,1,5,2,6] => 1 [4,3,1,5,6,2] => -1 [4,3,1,6,2,5] => -1 [4,3,1,6,5,2] => 1 [4,3,2,1,5,6] => 1 [4,3,2,1,6,5] => -1 [4,3,2,5,1,6] => -1 [4,3,2,5,6,1] => 1 [4,3,2,6,1,5] => 1 [4,3,2,6,5,1] => -1 [4,3,5,1,2,6] => -1 [4,3,5,1,6,2] => 1 [4,3,5,2,1,6] => 1 [4,3,5,2,6,1] => -1 [4,3,5,6,1,2] => -1 [4,3,5,6,2,1] => 1 [4,3,6,1,2,5] => 1 [4,3,6,1,5,2] => -1 [4,3,6,2,1,5] => -1 [4,3,6,2,5,1] => 1 [4,3,6,5,1,2] => 1 [4,3,6,5,2,1] => -1 [4,5,1,2,3,6] => 1 [4,5,1,2,6,3] => -1 [4,5,1,3,2,6] => -1 [4,5,1,3,6,2] => 1 [4,5,1,6,2,3] => 1 [4,5,1,6,3,2] => -1 [4,5,2,1,3,6] => -1 [4,5,2,1,6,3] => 1 [4,5,2,3,1,6] => 1 [4,5,2,3,6,1] => -1 [4,5,2,6,1,3] => -1 [4,5,2,6,3,1] => 1 [4,5,3,1,2,6] => 1 [4,5,3,1,6,2] => -1 [4,5,3,2,1,6] => -1 [4,5,3,2,6,1] => 1 [4,5,3,6,1,2] => 1 [4,5,3,6,2,1] => -1 [4,5,6,1,2,3] => -1 [4,5,6,1,3,2] => 1 [4,5,6,2,1,3] => 1 [4,5,6,2,3,1] => -1 [4,5,6,3,1,2] => -1 [4,5,6,3,2,1] => 1 [4,6,1,2,3,5] => -1 [4,6,1,2,5,3] => 1 [4,6,1,3,2,5] => 1 [4,6,1,3,5,2] => -1 [4,6,1,5,2,3] => -1 [4,6,1,5,3,2] => 1 [4,6,2,1,3,5] => 1 [4,6,2,1,5,3] => -1 [4,6,2,3,1,5] => -1 [4,6,2,3,5,1] => 1 [4,6,2,5,1,3] => 1 [4,6,2,5,3,1] => -1 [4,6,3,1,2,5] => -1 [4,6,3,1,5,2] => 1 [4,6,3,2,1,5] => 1 [4,6,3,2,5,1] => -1 [4,6,3,5,1,2] => -1 [4,6,3,5,2,1] => 1 [4,6,5,1,2,3] => 1 [4,6,5,1,3,2] => -1 [4,6,5,2,1,3] => -1 [4,6,5,2,3,1] => 1 [4,6,5,3,1,2] => 1 [4,6,5,3,2,1] => -1 [5,1,2,3,4,6] => 1 [5,1,2,3,6,4] => -1 [5,1,2,4,3,6] => -1 [5,1,2,4,6,3] => 1 [5,1,2,6,3,4] => 1 [5,1,2,6,4,3] => -1 [5,1,3,2,4,6] => -1 [5,1,3,2,6,4] => 1 [5,1,3,4,2,6] => 1 [5,1,3,4,6,2] => -1 [5,1,3,6,2,4] => -1 [5,1,3,6,4,2] => 1 [5,1,4,2,3,6] => 1 [5,1,4,2,6,3] => -1 [5,1,4,3,2,6] => -1 [5,1,4,3,6,2] => 1 [5,1,4,6,2,3] => 1 [5,1,4,6,3,2] => -1 [5,1,6,2,3,4] => -1 [5,1,6,2,4,3] => 1 [5,1,6,3,2,4] => 1 [5,1,6,3,4,2] => -1 [5,1,6,4,2,3] => -1 [5,1,6,4,3,2] => 1 [5,2,1,3,4,6] => -1 [5,2,1,3,6,4] => 1 [5,2,1,4,3,6] => 1 [5,2,1,4,6,3] => -1 [5,2,1,6,3,4] => -1 [5,2,1,6,4,3] => 1 [5,2,3,1,4,6] => 1 [5,2,3,1,6,4] => -1 [5,2,3,4,1,6] => -1 [5,2,3,4,6,1] => 1 [5,2,3,6,1,4] => 1 [5,2,3,6,4,1] => -1 [5,2,4,1,3,6] => -1 [5,2,4,1,6,3] => 1 [5,2,4,3,1,6] => 1 [5,2,4,3,6,1] => -1 [5,2,4,6,1,3] => -1 [5,2,4,6,3,1] => 1 [5,2,6,1,3,4] => 1 [5,2,6,1,4,3] => -1 [5,2,6,3,1,4] => -1 [5,2,6,3,4,1] => 1 [5,2,6,4,1,3] => 1 [5,2,6,4,3,1] => -1 [5,3,1,2,4,6] => 1 [5,3,1,2,6,4] => -1 [5,3,1,4,2,6] => -1 [5,3,1,4,6,2] => 1 [5,3,1,6,2,4] => 1 [5,3,1,6,4,2] => -1 [5,3,2,1,4,6] => -1 [5,3,2,1,6,4] => 1 [5,3,2,4,1,6] => 1 [5,3,2,4,6,1] => -1 [5,3,2,6,1,4] => -1 [5,3,2,6,4,1] => 1 [5,3,4,1,2,6] => 1 [5,3,4,1,6,2] => -1 [5,3,4,2,1,6] => -1 [5,3,4,2,6,1] => 1 [5,3,4,6,1,2] => 1 [5,3,4,6,2,1] => -1 [5,3,6,1,2,4] => -1 [5,3,6,1,4,2] => 1 [5,3,6,2,1,4] => 1 [5,3,6,2,4,1] => -1 [5,3,6,4,1,2] => -1 [5,3,6,4,2,1] => 1 [5,4,1,2,3,6] => -1 [5,4,1,2,6,3] => 1 [5,4,1,3,2,6] => 1 [5,4,1,3,6,2] => -1 [5,4,1,6,2,3] => -1 [5,4,1,6,3,2] => 1 [5,4,2,1,3,6] => 1 [5,4,2,1,6,3] => -1 [5,4,2,3,1,6] => -1 [5,4,2,3,6,1] => 1 [5,4,2,6,1,3] => 1 [5,4,2,6,3,1] => -1 [5,4,3,1,2,6] => -1 [5,4,3,1,6,2] => 1 [5,4,3,2,1,6] => 1 [5,4,3,2,6,1] => -1 [5,4,3,6,1,2] => -1 [5,4,3,6,2,1] => 1 [5,4,6,1,2,3] => 1 [5,4,6,1,3,2] => -1 [5,4,6,2,1,3] => -1 [5,4,6,2,3,1] => 1 [5,4,6,3,1,2] => 1 [5,4,6,3,2,1] => -1 [5,6,1,2,3,4] => 1 [5,6,1,2,4,3] => -1 [5,6,1,3,2,4] => -1 [5,6,1,3,4,2] => 1 [5,6,1,4,2,3] => 1 [5,6,1,4,3,2] => -1 [5,6,2,1,3,4] => -1 [5,6,2,1,4,3] => 1 [5,6,2,3,1,4] => 1 [5,6,2,3,4,1] => -1 [5,6,2,4,1,3] => -1 [5,6,2,4,3,1] => 1 [5,6,3,1,2,4] => 1 [5,6,3,1,4,2] => -1 [5,6,3,2,1,4] => -1 [5,6,3,2,4,1] => 1 [5,6,3,4,1,2] => 1 [5,6,3,4,2,1] => -1 [5,6,4,1,2,3] => -1 [5,6,4,1,3,2] => 1 [5,6,4,2,1,3] => 1 [5,6,4,2,3,1] => -1 [5,6,4,3,1,2] => -1 [5,6,4,3,2,1] => 1 [6,1,2,3,4,5] => -1 [6,1,2,3,5,4] => 1 [6,1,2,4,3,5] => 1 [6,1,2,4,5,3] => -1 [6,1,2,5,3,4] => -1 [6,1,2,5,4,3] => 1 [6,1,3,2,4,5] => 1 [6,1,3,2,5,4] => -1 [6,1,3,4,2,5] => -1 [6,1,3,4,5,2] => 1 [6,1,3,5,2,4] => 1 [6,1,3,5,4,2] => -1 [6,1,4,2,3,5] => -1 [6,1,4,2,5,3] => 1 [6,1,4,3,2,5] => 1 [6,1,4,3,5,2] => -1 [6,1,4,5,2,3] => -1 [6,1,4,5,3,2] => 1 [6,1,5,2,3,4] => 1 [6,1,5,2,4,3] => -1 [6,1,5,3,2,4] => -1 [6,1,5,3,4,2] => 1 [6,1,5,4,2,3] => 1 [6,1,5,4,3,2] => -1 [6,2,1,3,4,5] => 1 [6,2,1,3,5,4] => -1 [6,2,1,4,3,5] => -1 [6,2,1,4,5,3] => 1 [6,2,1,5,3,4] => 1 [6,2,1,5,4,3] => -1 [6,2,3,1,4,5] => -1 [6,2,3,1,5,4] => 1 [6,2,3,4,1,5] => 1 [6,2,3,4,5,1] => -1 [6,2,3,5,1,4] => -1 [6,2,3,5,4,1] => 1 [6,2,4,1,3,5] => 1 [6,2,4,1,5,3] => -1 [6,2,4,3,1,5] => -1 [6,2,4,3,5,1] => 1 [6,2,4,5,1,3] => 1 [6,2,4,5,3,1] => -1 [6,2,5,1,3,4] => -1 [6,2,5,1,4,3] => 1 [6,2,5,3,1,4] => 1 [6,2,5,3,4,1] => -1 [6,2,5,4,1,3] => -1 [6,2,5,4,3,1] => 1 [6,3,1,2,4,5] => -1 [6,3,1,2,5,4] => 1 [6,3,1,4,2,5] => 1 [6,3,1,4,5,2] => -1 [6,3,1,5,2,4] => -1 [6,3,1,5,4,2] => 1 [6,3,2,1,4,5] => 1 [6,3,2,1,5,4] => -1 [6,3,2,4,1,5] => -1 [6,3,2,4,5,1] => 1 [6,3,2,5,1,4] => 1 [6,3,2,5,4,1] => -1 [6,3,4,1,2,5] => -1 [6,3,4,1,5,2] => 1 [6,3,4,2,1,5] => 1 [6,3,4,2,5,1] => -1 [6,3,4,5,1,2] => -1 [6,3,4,5,2,1] => 1 [6,3,5,1,2,4] => 1 [6,3,5,1,4,2] => -1 [6,3,5,2,1,4] => -1 [6,3,5,2,4,1] => 1 [6,3,5,4,1,2] => 1 [6,3,5,4,2,1] => -1 [6,4,1,2,3,5] => 1 [6,4,1,2,5,3] => -1 [6,4,1,3,2,5] => -1 [6,4,1,3,5,2] => 1 [6,4,1,5,2,3] => 1 [6,4,1,5,3,2] => -1 [6,4,2,1,3,5] => -1 [6,4,2,1,5,3] => 1 [6,4,2,3,1,5] => 1 [6,4,2,3,5,1] => -1 [6,4,2,5,1,3] => -1 [6,4,2,5,3,1] => 1 [6,4,3,1,2,5] => 1 [6,4,3,1,5,2] => -1 [6,4,3,2,1,5] => -1 [6,4,3,2,5,1] => 1 [6,4,3,5,1,2] => 1 [6,4,3,5,2,1] => -1 [6,4,5,1,2,3] => -1 [6,4,5,1,3,2] => 1 [6,4,5,2,1,3] => 1 [6,4,5,2,3,1] => -1 [6,4,5,3,1,2] => -1 [6,4,5,3,2,1] => 1 [6,5,1,2,3,4] => -1 [6,5,1,2,4,3] => 1 [6,5,1,3,2,4] => 1 [6,5,1,3,4,2] => -1 [6,5,1,4,2,3] => -1 [6,5,1,4,3,2] => 1 [6,5,2,1,3,4] => 1 [6,5,2,1,4,3] => -1 [6,5,2,3,1,4] => -1 [6,5,2,3,4,1] => 1 [6,5,2,4,1,3] => 1 [6,5,2,4,3,1] => -1 [6,5,3,1,2,4] => -1 [6,5,3,1,4,2] => 1 [6,5,3,2,1,4] => 1 [6,5,3,2,4,1] => -1 [6,5,3,4,1,2] => -1 [6,5,3,4,2,1] => 1 [6,5,4,1,2,3] => 1 [6,5,4,1,3,2] => -1 [6,5,4,2,1,3] => -1 [6,5,4,2,3,1] => 1 [6,5,4,3,1,2] => 1 [6,5,4,3,2,1] => -1 ----------------------------------------------------------------------------- Created: Feb 14, 2013 at 04:32 by Sara Billey ----------------------------------------------------------------------------- Last Updated: May 27, 2022 at 09:39 by Martin Rubey