***************************************************************************** * 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: St001941 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The evaluation at 1 of the modified Kazhdan--Lusztig R polynomial (as in [1, Section 5.3]) with parameters given by the identity and the permutation. Also the number of paths in the Bruhat order from the identity to the permutation that are increasing with respect to a given reflection ordering as defined in Björner and Brenti [1, Section 5.2]. ----------------------------------------------------------------------------- References: [1] Björner, A., Brenti, F. Combinatorics of Coxeter groups [[MathSciNet:2133266]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- 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] => 2 [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] => 2 [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] => 2 [3,1,2,4] => 1 [3,1,4,2] => 1 [3,2,1,4] => 2 [3,2,4,1] => 2 [3,4,1,2] => 2 [3,4,2,1] => 3 [4,1,2,3] => 1 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 4 [4,3,1,2] => 3 [4,3,2,1] => 5 [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] => 2 [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] => 2 [1,4,2,3,5] => 1 [1,4,2,5,3] => 1 [1,4,3,2,5] => 2 [1,4,3,5,2] => 2 [1,4,5,2,3] => 2 [1,4,5,3,2] => 3 [1,5,2,3,4] => 1 [1,5,2,4,3] => 2 [1,5,3,2,4] => 2 [1,5,3,4,2] => 4 [1,5,4,2,3] => 3 [1,5,4,3,2] => 5 [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] => 2 [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] => 2 [2,4,1,3,5] => 1 [2,4,1,5,3] => 1 [2,4,3,1,5] => 2 [2,4,3,5,1] => 2 [2,4,5,1,3] => 2 [2,4,5,3,1] => 3 [2,5,1,3,4] => 1 [2,5,1,4,3] => 2 [2,5,3,1,4] => 2 [2,5,3,4,1] => 4 [2,5,4,1,3] => 3 [2,5,4,3,1] => 5 [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] => 2 [3,2,1,4,5] => 2 [3,2,1,5,4] => 2 [3,2,4,1,5] => 2 [3,2,4,5,1] => 2 [3,2,5,1,4] => 2 [3,2,5,4,1] => 4 [3,4,1,2,5] => 2 [3,4,1,5,2] => 2 [3,4,2,1,5] => 3 [3,4,2,5,1] => 3 [3,4,5,1,2] => 3 [3,4,5,2,1] => 5 [3,5,1,2,4] => 2 [3,5,1,4,2] => 4 [3,5,2,1,4] => 3 [3,5,2,4,1] => 6 [3,5,4,1,2] => 5 [3,5,4,2,1] => 8 [4,1,2,3,5] => 1 [4,1,2,5,3] => 1 [4,1,3,2,5] => 2 [4,1,3,5,2] => 2 [4,1,5,2,3] => 2 [4,1,5,3,2] => 3 [4,2,1,3,5] => 2 [4,2,1,5,3] => 2 [4,2,3,1,5] => 4 [4,2,3,5,1] => 4 [4,2,5,1,3] => 4 [4,2,5,3,1] => 6 [4,3,1,2,5] => 3 [4,3,1,5,2] => 3 [4,3,2,1,5] => 5 [4,3,2,5,1] => 5 [4,3,5,1,2] => 5 [4,3,5,2,1] => 8 [4,5,1,2,3] => 3 [4,5,1,3,2] => 5 [4,5,2,1,3] => 5 [4,5,2,3,1] => 8 [4,5,3,1,2] => 9 [4,5,3,2,1] => 14 [5,1,2,3,4] => 1 [5,1,2,4,3] => 2 [5,1,3,2,4] => 2 [5,1,3,4,2] => 4 [5,1,4,2,3] => 3 [5,1,4,3,2] => 5 [5,2,1,3,4] => 2 [5,2,1,4,3] => 4 [5,2,3,1,4] => 4 [5,2,3,4,1] => 8 [5,2,4,1,3] => 6 [5,2,4,3,1] => 10 [5,3,1,2,4] => 3 [5,3,1,4,2] => 6 [5,3,2,1,4] => 5 [5,3,2,4,1] => 10 [5,3,4,1,2] => 8 [5,3,4,2,1] => 13 [5,4,1,2,3] => 5 [5,4,1,3,2] => 8 [5,4,2,1,3] => 8 [5,4,2,3,1] => 13 [5,4,3,1,2] => 14 [5,4,3,2,1] => 23 [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] => 2 [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] => 2 [1,2,5,3,4,6] => 1 [1,2,5,3,6,4] => 1 [1,2,5,4,3,6] => 2 [1,2,5,4,6,3] => 2 [1,2,5,6,3,4] => 2 [1,2,5,6,4,3] => 3 [1,2,6,3,4,5] => 1 [1,2,6,3,5,4] => 2 [1,2,6,4,3,5] => 2 [1,2,6,4,5,3] => 4 [1,2,6,5,3,4] => 3 [1,2,6,5,4,3] => 5 [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] => 2 [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] => 2 [1,3,5,2,4,6] => 1 [1,3,5,2,6,4] => 1 [1,3,5,4,2,6] => 2 [1,3,5,4,6,2] => 2 [1,3,5,6,2,4] => 2 [1,3,5,6,4,2] => 3 [1,3,6,2,4,5] => 1 [1,3,6,2,5,4] => 2 [1,3,6,4,2,5] => 2 [1,3,6,4,5,2] => 4 [1,3,6,5,2,4] => 3 [1,3,6,5,4,2] => 5 [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] => 2 [1,4,3,2,5,6] => 2 [1,4,3,2,6,5] => 2 [1,4,3,5,2,6] => 2 [1,4,3,5,6,2] => 2 [1,4,3,6,2,5] => 2 [1,4,3,6,5,2] => 4 [1,4,5,2,3,6] => 2 [1,4,5,2,6,3] => 2 [1,4,5,3,2,6] => 3 [1,4,5,3,6,2] => 3 [1,4,5,6,2,3] => 3 [1,4,5,6,3,2] => 5 [1,4,6,2,3,5] => 2 [1,4,6,2,5,3] => 4 [1,4,6,3,2,5] => 3 [1,4,6,3,5,2] => 6 [1,4,6,5,2,3] => 5 [1,4,6,5,3,2] => 8 [1,5,2,3,4,6] => 1 [1,5,2,3,6,4] => 1 [1,5,2,4,3,6] => 2 [1,5,2,4,6,3] => 2 [1,5,2,6,3,4] => 2 [1,5,2,6,4,3] => 3 [1,5,3,2,4,6] => 2 [1,5,3,2,6,4] => 2 [1,5,3,4,2,6] => 4 [1,5,3,4,6,2] => 4 [1,5,3,6,2,4] => 4 [1,5,3,6,4,2] => 6 [1,5,4,2,3,6] => 3 [1,5,4,2,6,3] => 3 [1,5,4,3,2,6] => 5 [1,5,4,3,6,2] => 5 [1,5,4,6,2,3] => 5 [1,5,4,6,3,2] => 8 [1,5,6,2,3,4] => 3 [1,5,6,2,4,3] => 5 [1,5,6,3,2,4] => 5 [1,5,6,3,4,2] => 8 [1,5,6,4,2,3] => 9 [1,5,6,4,3,2] => 14 [1,6,2,3,4,5] => 1 [1,6,2,3,5,4] => 2 [1,6,2,4,3,5] => 2 [1,6,2,4,5,3] => 4 [1,6,2,5,3,4] => 3 [1,6,2,5,4,3] => 5 [1,6,3,2,4,5] => 2 [1,6,3,2,5,4] => 4 [1,6,3,4,2,5] => 4 [1,6,3,4,5,2] => 8 [1,6,3,5,2,4] => 6 [1,6,3,5,4,2] => 10 [1,6,4,2,3,5] => 3 [1,6,4,2,5,3] => 6 [1,6,4,3,2,5] => 5 [1,6,4,3,5,2] => 10 [1,6,4,5,2,3] => 8 [1,6,4,5,3,2] => 13 [1,6,5,2,3,4] => 5 [1,6,5,2,4,3] => 8 [1,6,5,3,2,4] => 8 [1,6,5,3,4,2] => 13 [1,6,5,4,2,3] => 14 [1,6,5,4,3,2] => 23 [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] => 2 [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] => 2 [2,1,5,3,4,6] => 1 [2,1,5,3,6,4] => 1 [2,1,5,4,3,6] => 2 [2,1,5,4,6,3] => 2 [2,1,5,6,3,4] => 2 [2,1,5,6,4,3] => 3 [2,1,6,3,4,5] => 1 [2,1,6,3,5,4] => 2 [2,1,6,4,3,5] => 2 [2,1,6,4,5,3] => 4 [2,1,6,5,3,4] => 3 [2,1,6,5,4,3] => 5 [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] => 2 [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] => 2 [2,3,5,1,4,6] => 1 [2,3,5,1,6,4] => 1 [2,3,5,4,1,6] => 2 [2,3,5,4,6,1] => 2 [2,3,5,6,1,4] => 2 [2,3,5,6,4,1] => 3 [2,3,6,1,4,5] => 1 [2,3,6,1,5,4] => 2 [2,3,6,4,1,5] => 2 [2,3,6,4,5,1] => 4 [2,3,6,5,1,4] => 3 [2,3,6,5,4,1] => 5 [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] => 2 [2,4,3,1,5,6] => 2 [2,4,3,1,6,5] => 2 [2,4,3,5,1,6] => 2 [2,4,3,5,6,1] => 2 [2,4,3,6,1,5] => 2 [2,4,3,6,5,1] => 4 [2,4,5,1,3,6] => 2 [2,4,5,1,6,3] => 2 [2,4,5,3,1,6] => 3 [2,4,5,3,6,1] => 3 [2,4,5,6,1,3] => 3 [2,4,5,6,3,1] => 5 [2,4,6,1,3,5] => 2 [2,4,6,1,5,3] => 4 [2,4,6,3,1,5] => 3 [2,4,6,3,5,1] => 6 [2,4,6,5,1,3] => 5 [2,4,6,5,3,1] => 8 [2,5,1,3,4,6] => 1 [2,5,1,3,6,4] => 1 [2,5,1,4,3,6] => 2 [2,5,1,4,6,3] => 2 [2,5,1,6,3,4] => 2 [2,5,1,6,4,3] => 3 [2,5,3,1,4,6] => 2 [2,5,3,1,6,4] => 2 [2,5,3,4,1,6] => 4 [2,5,3,4,6,1] => 4 [2,5,3,6,1,4] => 4 [2,5,3,6,4,1] => 6 [2,5,4,1,3,6] => 3 [2,5,4,1,6,3] => 3 [2,5,4,3,1,6] => 5 [2,5,4,3,6,1] => 5 [2,5,4,6,1,3] => 5 [2,5,4,6,3,1] => 8 [2,5,6,1,3,4] => 3 [2,5,6,1,4,3] => 5 [2,5,6,3,1,4] => 5 [2,5,6,3,4,1] => 8 [2,5,6,4,1,3] => 9 [2,5,6,4,3,1] => 14 [2,6,1,3,4,5] => 1 [2,6,1,3,5,4] => 2 [2,6,1,4,3,5] => 2 [2,6,1,4,5,3] => 4 [2,6,1,5,3,4] => 3 [2,6,1,5,4,3] => 5 [2,6,3,1,4,5] => 2 [2,6,3,1,5,4] => 4 [2,6,3,4,1,5] => 4 [2,6,3,4,5,1] => 8 [2,6,3,5,1,4] => 6 [2,6,3,5,4,1] => 10 [2,6,4,1,3,5] => 3 [2,6,4,1,5,3] => 6 [2,6,4,3,1,5] => 5 [2,6,4,3,5,1] => 10 [2,6,4,5,1,3] => 8 [2,6,4,5,3,1] => 13 [2,6,5,1,3,4] => 5 [2,6,5,1,4,3] => 8 [2,6,5,3,1,4] => 8 [2,6,5,3,4,1] => 13 [2,6,5,4,1,3] => 14 [2,6,5,4,3,1] => 23 [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] => 2 [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] => 2 [3,1,5,2,4,6] => 1 [3,1,5,2,6,4] => 1 [3,1,5,4,2,6] => 2 [3,1,5,4,6,2] => 2 [3,1,5,6,2,4] => 2 [3,1,5,6,4,2] => 3 [3,1,6,2,4,5] => 1 [3,1,6,2,5,4] => 2 [3,1,6,4,2,5] => 2 [3,1,6,4,5,2] => 4 [3,1,6,5,2,4] => 3 [3,1,6,5,4,2] => 5 [3,2,1,4,5,6] => 2 [3,2,1,4,6,5] => 2 [3,2,1,5,4,6] => 2 [3,2,1,5,6,4] => 2 [3,2,1,6,4,5] => 2 [3,2,1,6,5,4] => 4 [3,2,4,1,5,6] => 2 [3,2,4,1,6,5] => 2 [3,2,4,5,1,6] => 2 [3,2,4,5,6,1] => 2 [3,2,4,6,1,5] => 2 [3,2,4,6,5,1] => 4 [3,2,5,1,4,6] => 2 [3,2,5,1,6,4] => 2 [3,2,5,4,1,6] => 4 [3,2,5,4,6,1] => 4 [3,2,5,6,1,4] => 4 [3,2,5,6,4,1] => 6 [3,2,6,1,4,5] => 2 [3,2,6,1,5,4] => 4 [3,2,6,4,1,5] => 4 [3,2,6,4,5,1] => 8 [3,2,6,5,1,4] => 6 [3,2,6,5,4,1] => 10 [3,4,1,2,5,6] => 2 [3,4,1,2,6,5] => 2 [3,4,1,5,2,6] => 2 [3,4,1,5,6,2] => 2 [3,4,1,6,2,5] => 2 [3,4,1,6,5,2] => 4 [3,4,2,1,5,6] => 3 [3,4,2,1,6,5] => 3 [3,4,2,5,1,6] => 3 [3,4,2,5,6,1] => 3 [3,4,2,6,1,5] => 3 [3,4,2,6,5,1] => 6 [3,4,5,1,2,6] => 3 [3,4,5,1,6,2] => 3 [3,4,5,2,1,6] => 5 [3,4,5,2,6,1] => 5 [3,4,5,6,1,2] => 5 [3,4,5,6,2,1] => 8 [3,4,6,1,2,5] => 3 [3,4,6,1,5,2] => 6 [3,4,6,2,1,5] => 5 [3,4,6,2,5,1] => 10 [3,4,6,5,1,2] => 8 [3,4,6,5,2,1] => 13 [3,5,1,2,4,6] => 2 [3,5,1,2,6,4] => 2 [3,5,1,4,2,6] => 4 [3,5,1,4,6,2] => 4 [3,5,1,6,2,4] => 4 [3,5,1,6,4,2] => 6 [3,5,2,1,4,6] => 3 [3,5,2,1,6,4] => 3 [3,5,2,4,1,6] => 6 [3,5,2,4,6,1] => 6 [3,5,2,6,1,4] => 6 [3,5,2,6,4,1] => 9 [3,5,4,1,2,6] => 5 [3,5,4,1,6,2] => 5 [3,5,4,2,1,6] => 8 [3,5,4,2,6,1] => 8 [3,5,4,6,1,2] => 8 [3,5,4,6,2,1] => 13 [3,5,6,1,2,4] => 5 [3,5,6,1,4,2] => 8 [3,5,6,2,1,4] => 8 [3,5,6,2,4,1] => 13 [3,5,6,4,1,2] => 14 [3,5,6,4,2,1] => 23 [3,6,1,2,4,5] => 2 [3,6,1,2,5,4] => 4 [3,6,1,4,2,5] => 4 [3,6,1,4,5,2] => 8 [3,6,1,5,2,4] => 6 [3,6,1,5,4,2] => 10 [3,6,2,1,4,5] => 3 [3,6,2,1,5,4] => 6 [3,6,2,4,1,5] => 6 [3,6,2,4,5,1] => 12 [3,6,2,5,1,4] => 9 [3,6,2,5,4,1] => 15 [3,6,4,1,2,5] => 5 [3,6,4,1,5,2] => 10 [3,6,4,2,1,5] => 8 [3,6,4,2,5,1] => 16 [3,6,4,5,1,2] => 13 [3,6,4,5,2,1] => 21 [3,6,5,1,2,4] => 8 [3,6,5,1,4,2] => 13 [3,6,5,2,1,4] => 13 [3,6,5,2,4,1] => 21 [3,6,5,4,1,2] => 23 [3,6,5,4,2,1] => 37 [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] => 2 [4,1,3,2,5,6] => 2 [4,1,3,2,6,5] => 2 [4,1,3,5,2,6] => 2 [4,1,3,5,6,2] => 2 [4,1,3,6,2,5] => 2 [4,1,3,6,5,2] => 4 [4,1,5,2,3,6] => 2 [4,1,5,2,6,3] => 2 [4,1,5,3,2,6] => 3 [4,1,5,3,6,2] => 3 [4,1,5,6,2,3] => 3 [4,1,5,6,3,2] => 5 [4,1,6,2,3,5] => 2 [4,1,6,2,5,3] => 4 [4,1,6,3,2,5] => 3 [4,1,6,3,5,2] => 6 [4,1,6,5,2,3] => 5 [4,1,6,5,3,2] => 8 [4,2,1,3,5,6] => 2 [4,2,1,3,6,5] => 2 [4,2,1,5,3,6] => 2 [4,2,1,5,6,3] => 2 [4,2,1,6,3,5] => 2 [4,2,1,6,5,3] => 4 [4,2,3,1,5,6] => 4 [4,2,3,1,6,5] => 4 [4,2,3,5,1,6] => 4 [4,2,3,5,6,1] => 4 [4,2,3,6,1,5] => 4 [4,2,3,6,5,1] => 8 [4,2,5,1,3,6] => 4 [4,2,5,1,6,3] => 4 [4,2,5,3,1,6] => 6 [4,2,5,3,6,1] => 6 [4,2,5,6,1,3] => 6 [4,2,5,6,3,1] => 10 [4,2,6,1,3,5] => 4 [4,2,6,1,5,3] => 8 [4,2,6,3,1,5] => 6 [4,2,6,3,5,1] => 12 [4,2,6,5,1,3] => 10 [4,2,6,5,3,1] => 16 [4,3,1,2,5,6] => 3 [4,3,1,2,6,5] => 3 [4,3,1,5,2,6] => 3 [4,3,1,5,6,2] => 3 [4,3,1,6,2,5] => 3 [4,3,1,6,5,2] => 6 [4,3,2,1,5,6] => 5 [4,3,2,1,6,5] => 5 [4,3,2,5,1,6] => 5 [4,3,2,5,6,1] => 5 [4,3,2,6,1,5] => 5 [4,3,2,6,5,1] => 10 [4,3,5,1,2,6] => 5 [4,3,5,1,6,2] => 5 [4,3,5,2,1,6] => 8 [4,3,5,2,6,1] => 8 [4,3,5,6,1,2] => 8 [4,3,5,6,2,1] => 13 [4,3,6,1,2,5] => 5 [4,3,6,1,5,2] => 10 [4,3,6,2,1,5] => 8 [4,3,6,2,5,1] => 16 [4,3,6,5,1,2] => 13 [4,3,6,5,2,1] => 21 [4,5,1,2,3,6] => 3 [4,5,1,2,6,3] => 3 [4,5,1,3,2,6] => 5 [4,5,1,3,6,2] => 5 [4,5,1,6,2,3] => 5 [4,5,1,6,3,2] => 8 [4,5,2,1,3,6] => 5 [4,5,2,1,6,3] => 5 [4,5,2,3,1,6] => 8 [4,5,2,3,6,1] => 8 [4,5,2,6,1,3] => 8 [4,5,2,6,3,1] => 13 [4,5,3,1,2,6] => 9 [4,5,3,1,6,2] => 9 [4,5,3,2,1,6] => 14 [4,5,3,2,6,1] => 14 [4,5,3,6,1,2] => 14 [4,5,3,6,2,1] => 23 [4,5,6,1,2,3] => 9 [4,5,6,1,3,2] => 14 [4,5,6,2,1,3] => 14 [4,5,6,2,3,1] => 22 [4,5,6,3,1,2] => 22 [4,5,6,3,2,1] => 36 [4,6,1,2,3,5] => 3 [4,6,1,2,5,3] => 6 [4,6,1,3,2,5] => 5 [4,6,1,3,5,2] => 10 [4,6,1,5,2,3] => 8 [4,6,1,5,3,2] => 13 [4,6,2,1,3,5] => 5 [4,6,2,1,5,3] => 10 [4,6,2,3,1,5] => 8 [4,6,2,3,5,1] => 16 [4,6,2,5,1,3] => 13 [4,6,2,5,3,1] => 21 [4,6,3,1,2,5] => 9 [4,6,3,1,5,2] => 18 [4,6,3,2,1,5] => 14 [4,6,3,2,5,1] => 28 [4,6,3,5,1,2] => 23 [4,6,3,5,2,1] => 37 [4,6,5,1,2,3] => 14 [4,6,5,1,3,2] => 23 [4,6,5,2,1,3] => 22 [4,6,5,2,3,1] => 36 [4,6,5,3,1,2] => 36 [4,6,5,3,2,1] => 58 [5,1,2,3,4,6] => 1 [5,1,2,3,6,4] => 1 [5,1,2,4,3,6] => 2 [5,1,2,4,6,3] => 2 [5,1,2,6,3,4] => 2 [5,1,2,6,4,3] => 3 [5,1,3,2,4,6] => 2 [5,1,3,2,6,4] => 2 [5,1,3,4,2,6] => 4 [5,1,3,4,6,2] => 4 [5,1,3,6,2,4] => 4 [5,1,3,6,4,2] => 6 [5,1,4,2,3,6] => 3 [5,1,4,2,6,3] => 3 [5,1,4,3,2,6] => 5 [5,1,4,3,6,2] => 5 [5,1,4,6,2,3] => 5 [5,1,4,6,3,2] => 8 [5,1,6,2,3,4] => 3 [5,1,6,2,4,3] => 5 [5,1,6,3,2,4] => 5 [5,1,6,3,4,2] => 8 [5,1,6,4,2,3] => 9 [5,1,6,4,3,2] => 14 [5,2,1,3,4,6] => 2 [5,2,1,3,6,4] => 2 [5,2,1,4,3,6] => 4 [5,2,1,4,6,3] => 4 [5,2,1,6,3,4] => 4 [5,2,1,6,4,3] => 6 [5,2,3,1,4,6] => 4 [5,2,3,1,6,4] => 4 [5,2,3,4,1,6] => 8 [5,2,3,4,6,1] => 8 [5,2,3,6,1,4] => 8 [5,2,3,6,4,1] => 12 [5,2,4,1,3,6] => 6 [5,2,4,1,6,3] => 6 [5,2,4,3,1,6] => 10 [5,2,4,3,6,1] => 10 [5,2,4,6,1,3] => 10 [5,2,4,6,3,1] => 16 [5,2,6,1,3,4] => 6 [5,2,6,1,4,3] => 10 [5,2,6,3,1,4] => 10 [5,2,6,3,4,1] => 16 [5,2,6,4,1,3] => 18 [5,2,6,4,3,1] => 28 [5,3,1,2,4,6] => 3 [5,3,1,2,6,4] => 3 [5,3,1,4,2,6] => 6 [5,3,1,4,6,2] => 6 [5,3,1,6,2,4] => 6 [5,3,1,6,4,2] => 9 [5,3,2,1,4,6] => 5 [5,3,2,1,6,4] => 5 [5,3,2,4,1,6] => 10 [5,3,2,4,6,1] => 10 [5,3,2,6,1,4] => 10 [5,3,2,6,4,1] => 15 [5,3,4,1,2,6] => 8 [5,3,4,1,6,2] => 8 [5,3,4,2,1,6] => 13 [5,3,4,2,6,1] => 13 [5,3,4,6,1,2] => 13 [5,3,4,6,2,1] => 21 [5,3,6,1,2,4] => 8 [5,3,6,1,4,2] => 13 [5,3,6,2,1,4] => 13 [5,3,6,2,4,1] => 21 [5,3,6,4,1,2] => 23 [5,3,6,4,2,1] => 37 [5,4,1,2,3,6] => 5 [5,4,1,2,6,3] => 5 [5,4,1,3,2,6] => 8 [5,4,1,3,6,2] => 8 [5,4,1,6,2,3] => 8 [5,4,1,6,3,2] => 13 [5,4,2,1,3,6] => 8 [5,4,2,1,6,3] => 8 [5,4,2,3,1,6] => 13 [5,4,2,3,6,1] => 13 [5,4,2,6,1,3] => 13 [5,4,2,6,3,1] => 21 [5,4,3,1,2,6] => 14 [5,4,3,1,6,2] => 14 [5,4,3,2,1,6] => 23 [5,4,3,2,6,1] => 23 [5,4,3,6,1,2] => 23 [5,4,3,6,2,1] => 37 [5,4,6,1,2,3] => 14 [5,4,6,1,3,2] => 22 [5,4,6,2,1,3] => 23 [5,4,6,2,3,1] => 36 [5,4,6,3,1,2] => 36 [5,4,6,3,2,1] => 58 [5,6,1,2,3,4] => 5 [5,6,1,2,4,3] => 8 [5,6,1,3,2,4] => 8 [5,6,1,3,4,2] => 13 [5,6,1,4,2,3] => 14 [5,6,1,4,3,2] => 23 [5,6,2,1,3,4] => 8 [5,6,2,1,4,3] => 13 [5,6,2,3,1,4] => 13 [5,6,2,3,4,1] => 21 [5,6,2,4,1,3] => 23 [5,6,2,4,3,1] => 37 [5,6,3,1,2,4] => 14 [5,6,3,1,4,2] => 23 [5,6,3,2,1,4] => 23 [5,6,3,2,4,1] => 37 [5,6,3,4,1,2] => 41 [5,6,3,4,2,1] => 65 [5,6,4,1,2,3] => 22 [5,6,4,1,3,2] => 36 [5,6,4,2,1,3] => 36 [5,6,4,2,3,1] => 58 [5,6,4,3,1,2] => 59 [5,6,4,3,2,1] => 94 [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] => 4 [6,1,2,5,3,4] => 3 [6,1,2,5,4,3] => 5 [6,1,3,2,4,5] => 2 [6,1,3,2,5,4] => 4 [6,1,3,4,2,5] => 4 [6,1,3,4,5,2] => 8 [6,1,3,5,2,4] => 6 [6,1,3,5,4,2] => 10 [6,1,4,2,3,5] => 3 [6,1,4,2,5,3] => 6 [6,1,4,3,2,5] => 5 [6,1,4,3,5,2] => 10 [6,1,4,5,2,3] => 8 [6,1,4,5,3,2] => 13 [6,1,5,2,3,4] => 5 [6,1,5,2,4,3] => 8 [6,1,5,3,2,4] => 8 [6,1,5,3,4,2] => 13 [6,1,5,4,2,3] => 14 [6,1,5,4,3,2] => 23 [6,2,1,3,4,5] => 2 [6,2,1,3,5,4] => 4 [6,2,1,4,3,5] => 4 [6,2,1,4,5,3] => 8 [6,2,1,5,3,4] => 6 [6,2,1,5,4,3] => 10 [6,2,3,1,4,5] => 4 [6,2,3,1,5,4] => 8 [6,2,3,4,1,5] => 8 [6,2,3,4,5,1] => 16 [6,2,3,5,1,4] => 12 [6,2,3,5,4,1] => 20 [6,2,4,1,3,5] => 6 [6,2,4,1,5,3] => 12 [6,2,4,3,1,5] => 10 [6,2,4,3,5,1] => 20 [6,2,4,5,1,3] => 16 [6,2,4,5,3,1] => 26 [6,2,5,1,3,4] => 10 [6,2,5,1,4,3] => 16 [6,2,5,3,1,4] => 16 [6,2,5,3,4,1] => 26 [6,2,5,4,1,3] => 28 [6,2,5,4,3,1] => 46 [6,3,1,2,4,5] => 3 [6,3,1,2,5,4] => 6 [6,3,1,4,2,5] => 6 [6,3,1,4,5,2] => 12 [6,3,1,5,2,4] => 9 [6,3,1,5,4,2] => 15 [6,3,2,1,4,5] => 5 [6,3,2,1,5,4] => 10 [6,3,2,4,1,5] => 10 [6,3,2,4,5,1] => 20 [6,3,2,5,1,4] => 15 [6,3,2,5,4,1] => 25 [6,3,4,1,2,5] => 8 [6,3,4,1,5,2] => 16 [6,3,4,2,1,5] => 13 [6,3,4,2,5,1] => 26 [6,3,4,5,1,2] => 21 [6,3,4,5,2,1] => 34 [6,3,5,1,2,4] => 13 [6,3,5,1,4,2] => 21 [6,3,5,2,1,4] => 21 [6,3,5,2,4,1] => 34 [6,3,5,4,1,2] => 37 [6,3,5,4,2,1] => 60 [6,4,1,2,3,5] => 5 [6,4,1,2,5,3] => 10 [6,4,1,3,2,5] => 8 [6,4,1,3,5,2] => 16 [6,4,1,5,2,3] => 13 [6,4,1,5,3,2] => 21 [6,4,2,1,3,5] => 8 [6,4,2,1,5,3] => 16 [6,4,2,3,1,5] => 13 [6,4,2,3,5,1] => 26 [6,4,2,5,1,3] => 21 [6,4,2,5,3,1] => 34 [6,4,3,1,2,5] => 14 [6,4,3,1,5,2] => 28 [6,4,3,2,1,5] => 23 [6,4,3,2,5,1] => 46 [6,4,3,5,1,2] => 37 [6,4,3,5,2,1] => 60 [6,4,5,1,2,3] => 22 [6,4,5,1,3,2] => 36 [6,4,5,2,1,3] => 36 [6,4,5,2,3,1] => 59 [6,4,5,3,1,2] => 58 [6,4,5,3,2,1] => 94 [6,5,1,2,3,4] => 8 [6,5,1,2,4,3] => 13 [6,5,1,3,2,4] => 13 [6,5,1,3,4,2] => 21 [6,5,1,4,2,3] => 23 [6,5,1,4,3,2] => 37 [6,5,2,1,3,4] => 13 [6,5,2,1,4,3] => 21 [6,5,2,3,1,4] => 21 [6,5,2,3,4,1] => 34 [6,5,2,4,1,3] => 37 [6,5,2,4,3,1] => 60 [6,5,3,1,2,4] => 23 [6,5,3,1,4,2] => 37 [6,5,3,2,1,4] => 37 [6,5,3,2,4,1] => 60 [6,5,3,4,1,2] => 65 [6,5,3,4,2,1] => 106 [6,5,4,1,2,3] => 36 [6,5,4,1,3,2] => 58 [6,5,4,2,1,3] => 58 [6,5,4,2,3,1] => 94 [6,5,4,3,1,2] => 94 [6,5,4,3,2,1] => 153 ----------------------------------------------------------------------------- Created: Jan 31, 2024 at 16:32 by Joel Lewis, Alejandro H. Morales ----------------------------------------------------------------------------- Last Updated: Jan 31, 2024 at 17:22 by Joel Lewis, Alejandro Morales