***************************************************************************** * 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: St001976 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The bin statistic of a permutation. The '''bin statistic''' of a permutation $\sigma$ is defined as $$ \sum_{i\in Des(\sigma)} \binom{i + 1}{2}, $$ where $Des(\sigma)$ is the set of all indices $i$ such that $\sigma(i) > \sigma(i + 1)$. ----------------------------------------------------------------------------- References: [1] Bright, K. L., Savage, C. D. The geometry of lecture hall partitions and quadratic permutation statistics [[MathSciNet:2673867]] [2] Alfes, C., Maglione, J., Voll, C. Symplectic Hecke eigenbases from Ehrhart polynomials . [3] Savage, C. D. The mathematics of lecture hall partitions [[MathSciNet:3534075]] [[DOI:10.1016/j.jcta.2016.06.006]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,2] => 0 [2,1] => 1 [1,2,3] => 0 [1,3,2] => 3 [2,1,3] => 1 [2,3,1] => 3 [3,1,2] => 1 [3,2,1] => 4 [1,2,3,4] => 0 [1,2,4,3] => 6 [1,3,2,4] => 3 [1,3,4,2] => 6 [1,4,2,3] => 3 [1,4,3,2] => 9 [2,1,3,4] => 1 [2,1,4,3] => 7 [2,3,1,4] => 3 [2,3,4,1] => 6 [2,4,1,3] => 3 [2,4,3,1] => 9 [3,1,2,4] => 1 [3,1,4,2] => 7 [3,2,1,4] => 4 [3,2,4,1] => 7 [3,4,1,2] => 3 [3,4,2,1] => 9 [4,1,2,3] => 1 [4,1,3,2] => 7 [4,2,1,3] => 4 [4,2,3,1] => 7 [4,3,1,2] => 4 [4,3,2,1] => 10 [1,2,3,4,5] => 0 [1,2,3,5,4] => 10 [1,2,4,3,5] => 6 [1,2,4,5,3] => 10 [1,2,5,3,4] => 6 [1,2,5,4,3] => 16 [1,3,2,4,5] => 3 [1,3,2,5,4] => 13 [1,3,4,2,5] => 6 [1,3,4,5,2] => 10 [1,3,5,2,4] => 6 [1,3,5,4,2] => 16 [1,4,2,3,5] => 3 [1,4,2,5,3] => 13 [1,4,3,2,5] => 9 [1,4,3,5,2] => 13 [1,4,5,2,3] => 6 [1,4,5,3,2] => 16 [1,5,2,3,4] => 3 [1,5,2,4,3] => 13 [1,5,3,2,4] => 9 [1,5,3,4,2] => 13 [1,5,4,2,3] => 9 [1,5,4,3,2] => 19 [2,1,3,4,5] => 1 [2,1,3,5,4] => 11 [2,1,4,3,5] => 7 [2,1,4,5,3] => 11 [2,1,5,3,4] => 7 [2,1,5,4,3] => 17 [2,3,1,4,5] => 3 [2,3,1,5,4] => 13 [2,3,4,1,5] => 6 [2,3,4,5,1] => 10 [2,3,5,1,4] => 6 [2,3,5,4,1] => 16 [2,4,1,3,5] => 3 [2,4,1,5,3] => 13 [2,4,3,1,5] => 9 [2,4,3,5,1] => 13 [2,4,5,1,3] => 6 [2,4,5,3,1] => 16 [2,5,1,3,4] => 3 [2,5,1,4,3] => 13 [2,5,3,1,4] => 9 [2,5,3,4,1] => 13 [2,5,4,1,3] => 9 [2,5,4,3,1] => 19 [3,1,2,4,5] => 1 [3,1,2,5,4] => 11 [3,1,4,2,5] => 7 [3,1,4,5,2] => 11 [3,1,5,2,4] => 7 [3,1,5,4,2] => 17 [3,2,1,4,5] => 4 [3,2,1,5,4] => 14 [3,2,4,1,5] => 7 [3,2,4,5,1] => 11 [3,2,5,1,4] => 7 [3,2,5,4,1] => 17 [3,4,1,2,5] => 3 [3,4,1,5,2] => 13 [3,4,2,1,5] => 9 [3,4,2,5,1] => 13 [3,4,5,1,2] => 6 [3,4,5,2,1] => 16 [3,5,1,2,4] => 3 [3,5,1,4,2] => 13 [3,5,2,1,4] => 9 [3,5,2,4,1] => 13 [3,5,4,1,2] => 9 [3,5,4,2,1] => 19 [4,1,2,3,5] => 1 [4,1,2,5,3] => 11 [4,1,3,2,5] => 7 [4,1,3,5,2] => 11 [4,1,5,2,3] => 7 [4,1,5,3,2] => 17 [4,2,1,3,5] => 4 [4,2,1,5,3] => 14 [4,2,3,1,5] => 7 [4,2,3,5,1] => 11 [4,2,5,1,3] => 7 [4,2,5,3,1] => 17 [4,3,1,2,5] => 4 [4,3,1,5,2] => 14 [4,3,2,1,5] => 10 [4,3,2,5,1] => 14 [4,3,5,1,2] => 7 [4,3,5,2,1] => 17 [4,5,1,2,3] => 3 [4,5,1,3,2] => 13 [4,5,2,1,3] => 9 [4,5,2,3,1] => 13 [4,5,3,1,2] => 9 [4,5,3,2,1] => 19 [5,1,2,3,4] => 1 [5,1,2,4,3] => 11 [5,1,3,2,4] => 7 [5,1,3,4,2] => 11 [5,1,4,2,3] => 7 [5,1,4,3,2] => 17 [5,2,1,3,4] => 4 [5,2,1,4,3] => 14 [5,2,3,1,4] => 7 [5,2,3,4,1] => 11 [5,2,4,1,3] => 7 [5,2,4,3,1] => 17 [5,3,1,2,4] => 4 [5,3,1,4,2] => 14 [5,3,2,1,4] => 10 [5,3,2,4,1] => 14 [5,3,4,1,2] => 7 [5,3,4,2,1] => 17 [5,4,1,2,3] => 4 [5,4,1,3,2] => 14 [5,4,2,1,3] => 10 [5,4,2,3,1] => 14 [5,4,3,1,2] => 10 [5,4,3,2,1] => 20 [1,2,3,4,5,6] => 0 [1,2,3,4,6,5] => 15 [1,2,3,5,4,6] => 10 [1,2,3,5,6,4] => 15 [1,2,3,6,4,5] => 10 [1,2,3,6,5,4] => 25 [1,2,4,3,5,6] => 6 [1,2,4,3,6,5] => 21 [1,2,4,5,3,6] => 10 [1,2,4,5,6,3] => 15 [1,2,4,6,3,5] => 10 [1,2,4,6,5,3] => 25 [1,2,5,3,4,6] => 6 [1,2,5,3,6,4] => 21 [1,2,5,4,3,6] => 16 [1,2,5,4,6,3] => 21 [1,2,5,6,3,4] => 10 [1,2,5,6,4,3] => 25 [1,2,6,3,4,5] => 6 [1,2,6,3,5,4] => 21 [1,2,6,4,3,5] => 16 [1,2,6,4,5,3] => 21 [1,2,6,5,3,4] => 16 [1,2,6,5,4,3] => 31 [1,3,2,4,5,6] => 3 [1,3,2,4,6,5] => 18 [1,3,2,5,4,6] => 13 [1,3,2,5,6,4] => 18 [1,3,2,6,4,5] => 13 [1,3,2,6,5,4] => 28 [1,3,4,2,5,6] => 6 [1,3,4,2,6,5] => 21 [1,3,4,5,2,6] => 10 [1,3,4,5,6,2] => 15 [1,3,4,6,2,5] => 10 [1,3,4,6,5,2] => 25 [1,3,5,2,4,6] => 6 [1,3,5,2,6,4] => 21 [1,3,5,4,2,6] => 16 [1,3,5,4,6,2] => 21 [1,3,5,6,2,4] => 10 [1,3,5,6,4,2] => 25 [1,3,6,2,4,5] => 6 [1,3,6,2,5,4] => 21 [1,3,6,4,2,5] => 16 [1,3,6,4,5,2] => 21 [1,3,6,5,2,4] => 16 [1,3,6,5,4,2] => 31 [1,4,2,3,5,6] => 3 [1,4,2,3,6,5] => 18 [1,4,2,5,3,6] => 13 [1,4,2,5,6,3] => 18 [1,4,2,6,3,5] => 13 [1,4,2,6,5,3] => 28 [1,4,3,2,5,6] => 9 [1,4,3,2,6,5] => 24 [1,4,3,5,2,6] => 13 [1,4,3,5,6,2] => 18 [1,4,3,6,2,5] => 13 [1,4,3,6,5,2] => 28 [1,4,5,2,3,6] => 6 [1,4,5,2,6,3] => 21 [1,4,5,3,2,6] => 16 [1,4,5,3,6,2] => 21 [1,4,5,6,2,3] => 10 [1,4,5,6,3,2] => 25 [1,4,6,2,3,5] => 6 [1,4,6,2,5,3] => 21 [1,4,6,3,2,5] => 16 [1,4,6,3,5,2] => 21 [1,4,6,5,2,3] => 16 [1,4,6,5,3,2] => 31 [1,5,2,3,4,6] => 3 [1,5,2,3,6,4] => 18 [1,5,2,4,3,6] => 13 [1,5,2,4,6,3] => 18 [1,5,2,6,3,4] => 13 [1,5,2,6,4,3] => 28 [1,5,3,2,4,6] => 9 [1,5,3,2,6,4] => 24 [1,5,3,4,2,6] => 13 [1,5,3,4,6,2] => 18 [1,5,3,6,2,4] => 13 [1,5,3,6,4,2] => 28 [1,5,4,2,3,6] => 9 [1,5,4,2,6,3] => 24 [1,5,4,3,2,6] => 19 [1,5,4,3,6,2] => 24 [1,5,4,6,2,3] => 13 [1,5,4,6,3,2] => 28 [1,5,6,2,3,4] => 6 [1,5,6,2,4,3] => 21 [1,5,6,3,2,4] => 16 [1,5,6,3,4,2] => 21 [1,5,6,4,2,3] => 16 [1,5,6,4,3,2] => 31 [1,6,2,3,4,5] => 3 [1,6,2,3,5,4] => 18 [1,6,2,4,3,5] => 13 [1,6,2,4,5,3] => 18 [1,6,2,5,3,4] => 13 [1,6,2,5,4,3] => 28 [1,6,3,2,4,5] => 9 [1,6,3,2,5,4] => 24 [1,6,3,4,2,5] => 13 [1,6,3,4,5,2] => 18 [1,6,3,5,2,4] => 13 [1,6,3,5,4,2] => 28 [1,6,4,2,3,5] => 9 [1,6,4,2,5,3] => 24 [1,6,4,3,2,5] => 19 [1,6,4,3,5,2] => 24 [1,6,4,5,2,3] => 13 [1,6,4,5,3,2] => 28 [1,6,5,2,3,4] => 9 [1,6,5,2,4,3] => 24 [1,6,5,3,2,4] => 19 [1,6,5,3,4,2] => 24 [1,6,5,4,2,3] => 19 [1,6,5,4,3,2] => 34 [2,1,3,4,5,6] => 1 [2,1,3,4,6,5] => 16 [2,1,3,5,4,6] => 11 [2,1,3,5,6,4] => 16 [2,1,3,6,4,5] => 11 [2,1,3,6,5,4] => 26 [2,1,4,3,5,6] => 7 [2,1,4,3,6,5] => 22 [2,1,4,5,3,6] => 11 [2,1,4,5,6,3] => 16 [2,1,4,6,3,5] => 11 [2,1,4,6,5,3] => 26 [2,1,5,3,4,6] => 7 [2,1,5,3,6,4] => 22 [2,1,5,4,3,6] => 17 [2,1,5,4,6,3] => 22 [2,1,5,6,3,4] => 11 [2,1,5,6,4,3] => 26 [2,1,6,3,4,5] => 7 [2,1,6,3,5,4] => 22 [2,1,6,4,3,5] => 17 [2,1,6,4,5,3] => 22 [2,1,6,5,3,4] => 17 [2,1,6,5,4,3] => 32 [2,3,1,4,5,6] => 3 [2,3,1,4,6,5] => 18 [2,3,1,5,4,6] => 13 [2,3,1,5,6,4] => 18 [2,3,1,6,4,5] => 13 [2,3,1,6,5,4] => 28 [2,3,4,1,5,6] => 6 [2,3,4,1,6,5] => 21 [2,3,4,5,1,6] => 10 [2,3,4,5,6,1] => 15 [2,3,4,6,1,5] => 10 [2,3,4,6,5,1] => 25 [2,3,5,1,4,6] => 6 [2,3,5,1,6,4] => 21 [2,3,5,4,1,6] => 16 [2,3,5,4,6,1] => 21 [2,3,5,6,1,4] => 10 [2,3,5,6,4,1] => 25 [2,3,6,1,4,5] => 6 [2,3,6,1,5,4] => 21 [2,3,6,4,1,5] => 16 [2,3,6,4,5,1] => 21 [2,3,6,5,1,4] => 16 [2,3,6,5,4,1] => 31 [2,4,1,3,5,6] => 3 [2,4,1,3,6,5] => 18 [2,4,1,5,3,6] => 13 [2,4,1,5,6,3] => 18 [2,4,1,6,3,5] => 13 [2,4,1,6,5,3] => 28 [2,4,3,1,5,6] => 9 [2,4,3,1,6,5] => 24 [2,4,3,5,1,6] => 13 [2,4,3,5,6,1] => 18 [2,4,3,6,1,5] => 13 [2,4,3,6,5,1] => 28 [2,4,5,1,3,6] => 6 [2,4,5,1,6,3] => 21 [2,4,5,3,1,6] => 16 [2,4,5,3,6,1] => 21 [2,4,5,6,1,3] => 10 [2,4,5,6,3,1] => 25 [2,4,6,1,3,5] => 6 [2,4,6,1,5,3] => 21 [2,4,6,3,1,5] => 16 [2,4,6,3,5,1] => 21 [2,4,6,5,1,3] => 16 [2,4,6,5,3,1] => 31 [2,5,1,3,4,6] => 3 [2,5,1,3,6,4] => 18 [2,5,1,4,3,6] => 13 [2,5,1,4,6,3] => 18 [2,5,1,6,3,4] => 13 [2,5,1,6,4,3] => 28 [2,5,3,1,4,6] => 9 [2,5,3,1,6,4] => 24 [2,5,3,4,1,6] => 13 [2,5,3,4,6,1] => 18 [2,5,3,6,1,4] => 13 [2,5,3,6,4,1] => 28 [2,5,4,1,3,6] => 9 [2,5,4,1,6,3] => 24 [2,5,4,3,1,6] => 19 [2,5,4,3,6,1] => 24 [2,5,4,6,1,3] => 13 [2,5,4,6,3,1] => 28 [2,5,6,1,3,4] => 6 [2,5,6,1,4,3] => 21 [2,5,6,3,1,4] => 16 [2,5,6,3,4,1] => 21 [2,5,6,4,1,3] => 16 [2,5,6,4,3,1] => 31 [2,6,1,3,4,5] => 3 [2,6,1,3,5,4] => 18 [2,6,1,4,3,5] => 13 [2,6,1,4,5,3] => 18 [2,6,1,5,3,4] => 13 [2,6,1,5,4,3] => 28 [2,6,3,1,4,5] => 9 [2,6,3,1,5,4] => 24 [2,6,3,4,1,5] => 13 [2,6,3,4,5,1] => 18 [2,6,3,5,1,4] => 13 [2,6,3,5,4,1] => 28 [2,6,4,1,3,5] => 9 [2,6,4,1,5,3] => 24 [2,6,4,3,1,5] => 19 [2,6,4,3,5,1] => 24 [2,6,4,5,1,3] => 13 [2,6,4,5,3,1] => 28 [2,6,5,1,3,4] => 9 [2,6,5,1,4,3] => 24 [2,6,5,3,1,4] => 19 [2,6,5,3,4,1] => 24 [2,6,5,4,1,3] => 19 [2,6,5,4,3,1] => 34 [3,1,2,4,5,6] => 1 [3,1,2,4,6,5] => 16 [3,1,2,5,4,6] => 11 [3,1,2,5,6,4] => 16 [3,1,2,6,4,5] => 11 [3,1,2,6,5,4] => 26 [3,1,4,2,5,6] => 7 [3,1,4,2,6,5] => 22 [3,1,4,5,2,6] => 11 [3,1,4,5,6,2] => 16 [3,1,4,6,2,5] => 11 [3,1,4,6,5,2] => 26 [3,1,5,2,4,6] => 7 [3,1,5,2,6,4] => 22 [3,1,5,4,2,6] => 17 [3,1,5,4,6,2] => 22 [3,1,5,6,2,4] => 11 [3,1,5,6,4,2] => 26 [3,1,6,2,4,5] => 7 [3,1,6,2,5,4] => 22 [3,1,6,4,2,5] => 17 [3,1,6,4,5,2] => 22 [3,1,6,5,2,4] => 17 [3,1,6,5,4,2] => 32 [3,2,1,4,5,6] => 4 [3,2,1,4,6,5] => 19 [3,2,1,5,4,6] => 14 [3,2,1,5,6,4] => 19 [3,2,1,6,4,5] => 14 [3,2,1,6,5,4] => 29 [3,2,4,1,5,6] => 7 [3,2,4,1,6,5] => 22 [3,2,4,5,1,6] => 11 [3,2,4,5,6,1] => 16 [3,2,4,6,1,5] => 11 [3,2,4,6,5,1] => 26 [3,2,5,1,4,6] => 7 [3,2,5,1,6,4] => 22 [3,2,5,4,1,6] => 17 [3,2,5,4,6,1] => 22 [3,2,5,6,1,4] => 11 [3,2,5,6,4,1] => 26 [3,2,6,1,4,5] => 7 [3,2,6,1,5,4] => 22 [3,2,6,4,1,5] => 17 [3,2,6,4,5,1] => 22 [3,2,6,5,1,4] => 17 [3,2,6,5,4,1] => 32 [3,4,1,2,5,6] => 3 [3,4,1,2,6,5] => 18 [3,4,1,5,2,6] => 13 [3,4,1,5,6,2] => 18 [3,4,1,6,2,5] => 13 [3,4,1,6,5,2] => 28 [3,4,2,1,5,6] => 9 [3,4,2,1,6,5] => 24 [3,4,2,5,1,6] => 13 [3,4,2,5,6,1] => 18 [3,4,2,6,1,5] => 13 [3,4,2,6,5,1] => 28 [3,4,5,1,2,6] => 6 [3,4,5,1,6,2] => 21 [3,4,5,2,1,6] => 16 [3,4,5,2,6,1] => 21 [3,4,5,6,1,2] => 10 [3,4,5,6,2,1] => 25 [3,4,6,1,2,5] => 6 [3,4,6,1,5,2] => 21 [3,4,6,2,1,5] => 16 [3,4,6,2,5,1] => 21 [3,4,6,5,1,2] => 16 [3,4,6,5,2,1] => 31 [3,5,1,2,4,6] => 3 [3,5,1,2,6,4] => 18 [3,5,1,4,2,6] => 13 [3,5,1,4,6,2] => 18 [3,5,1,6,2,4] => 13 [3,5,1,6,4,2] => 28 [3,5,2,1,4,6] => 9 [3,5,2,1,6,4] => 24 [3,5,2,4,1,6] => 13 [3,5,2,4,6,1] => 18 [3,5,2,6,1,4] => 13 [3,5,2,6,4,1] => 28 [3,5,4,1,2,6] => 9 [3,5,4,1,6,2] => 24 [3,5,4,2,1,6] => 19 [3,5,4,2,6,1] => 24 [3,5,4,6,1,2] => 13 [3,5,4,6,2,1] => 28 [3,5,6,1,2,4] => 6 [3,5,6,1,4,2] => 21 [3,5,6,2,1,4] => 16 [3,5,6,2,4,1] => 21 [3,5,6,4,1,2] => 16 [3,5,6,4,2,1] => 31 [3,6,1,2,4,5] => 3 [3,6,1,2,5,4] => 18 [3,6,1,4,2,5] => 13 [3,6,1,4,5,2] => 18 [3,6,1,5,2,4] => 13 [3,6,1,5,4,2] => 28 [3,6,2,1,4,5] => 9 [3,6,2,1,5,4] => 24 [3,6,2,4,1,5] => 13 [3,6,2,4,5,1] => 18 [3,6,2,5,1,4] => 13 [3,6,2,5,4,1] => 28 [3,6,4,1,2,5] => 9 [3,6,4,1,5,2] => 24 [3,6,4,2,1,5] => 19 [3,6,4,2,5,1] => 24 [3,6,4,5,1,2] => 13 [3,6,4,5,2,1] => 28 [3,6,5,1,2,4] => 9 [3,6,5,1,4,2] => 24 [3,6,5,2,1,4] => 19 [3,6,5,2,4,1] => 24 [3,6,5,4,1,2] => 19 [3,6,5,4,2,1] => 34 [4,1,2,3,5,6] => 1 [4,1,2,3,6,5] => 16 [4,1,2,5,3,6] => 11 [4,1,2,5,6,3] => 16 [4,1,2,6,3,5] => 11 [4,1,2,6,5,3] => 26 [4,1,3,2,5,6] => 7 [4,1,3,2,6,5] => 22 [4,1,3,5,2,6] => 11 [4,1,3,5,6,2] => 16 [4,1,3,6,2,5] => 11 [4,1,3,6,5,2] => 26 [4,1,5,2,3,6] => 7 [4,1,5,2,6,3] => 22 [4,1,5,3,2,6] => 17 [4,1,5,3,6,2] => 22 [4,1,5,6,2,3] => 11 [4,1,5,6,3,2] => 26 [4,1,6,2,3,5] => 7 [4,1,6,2,5,3] => 22 [4,1,6,3,2,5] => 17 [4,1,6,3,5,2] => 22 [4,1,6,5,2,3] => 17 [4,1,6,5,3,2] => 32 [4,2,1,3,5,6] => 4 [4,2,1,3,6,5] => 19 [4,2,1,5,3,6] => 14 [4,2,1,5,6,3] => 19 [4,2,1,6,3,5] => 14 [4,2,1,6,5,3] => 29 [4,2,3,1,5,6] => 7 [4,2,3,1,6,5] => 22 [4,2,3,5,1,6] => 11 [4,2,3,5,6,1] => 16 [4,2,3,6,1,5] => 11 [4,2,3,6,5,1] => 26 [4,2,5,1,3,6] => 7 [4,2,5,1,6,3] => 22 [4,2,5,3,1,6] => 17 [4,2,5,3,6,1] => 22 [4,2,5,6,1,3] => 11 [4,2,5,6,3,1] => 26 [4,2,6,1,3,5] => 7 [4,2,6,1,5,3] => 22 [4,2,6,3,1,5] => 17 [4,2,6,3,5,1] => 22 [4,2,6,5,1,3] => 17 [4,2,6,5,3,1] => 32 [4,3,1,2,5,6] => 4 [4,3,1,2,6,5] => 19 [4,3,1,5,2,6] => 14 [4,3,1,5,6,2] => 19 [4,3,1,6,2,5] => 14 [4,3,1,6,5,2] => 29 [4,3,2,1,5,6] => 10 [4,3,2,1,6,5] => 25 [4,3,2,5,1,6] => 14 [4,3,2,5,6,1] => 19 [4,3,2,6,1,5] => 14 [4,3,2,6,5,1] => 29 [4,3,5,1,2,6] => 7 [4,3,5,1,6,2] => 22 [4,3,5,2,1,6] => 17 [4,3,5,2,6,1] => 22 [4,3,5,6,1,2] => 11 [4,3,5,6,2,1] => 26 [4,3,6,1,2,5] => 7 [4,3,6,1,5,2] => 22 [4,3,6,2,1,5] => 17 [4,3,6,2,5,1] => 22 [4,3,6,5,1,2] => 17 [4,3,6,5,2,1] => 32 [4,5,1,2,3,6] => 3 [4,5,1,2,6,3] => 18 [4,5,1,3,2,6] => 13 [4,5,1,3,6,2] => 18 [4,5,1,6,2,3] => 13 [4,5,1,6,3,2] => 28 [4,5,2,1,3,6] => 9 [4,5,2,1,6,3] => 24 [4,5,2,3,1,6] => 13 [4,5,2,3,6,1] => 18 [4,5,2,6,1,3] => 13 [4,5,2,6,3,1] => 28 [4,5,3,1,2,6] => 9 [4,5,3,1,6,2] => 24 [4,5,3,2,1,6] => 19 [4,5,3,2,6,1] => 24 [4,5,3,6,1,2] => 13 [4,5,3,6,2,1] => 28 [4,5,6,1,2,3] => 6 [4,5,6,1,3,2] => 21 [4,5,6,2,1,3] => 16 [4,5,6,2,3,1] => 21 [4,5,6,3,1,2] => 16 [4,5,6,3,2,1] => 31 [4,6,1,2,3,5] => 3 [4,6,1,2,5,3] => 18 [4,6,1,3,2,5] => 13 [4,6,1,3,5,2] => 18 [4,6,1,5,2,3] => 13 [4,6,1,5,3,2] => 28 [4,6,2,1,3,5] => 9 [4,6,2,1,5,3] => 24 [4,6,2,3,1,5] => 13 [4,6,2,3,5,1] => 18 [4,6,2,5,1,3] => 13 [4,6,2,5,3,1] => 28 [4,6,3,1,2,5] => 9 [4,6,3,1,5,2] => 24 [4,6,3,2,1,5] => 19 [4,6,3,2,5,1] => 24 [4,6,3,5,1,2] => 13 [4,6,3,5,2,1] => 28 [4,6,5,1,2,3] => 9 [4,6,5,1,3,2] => 24 [4,6,5,2,1,3] => 19 [4,6,5,2,3,1] => 24 [4,6,5,3,1,2] => 19 [4,6,5,3,2,1] => 34 [5,1,2,3,4,6] => 1 [5,1,2,3,6,4] => 16 [5,1,2,4,3,6] => 11 [5,1,2,4,6,3] => 16 [5,1,2,6,3,4] => 11 [5,1,2,6,4,3] => 26 [5,1,3,2,4,6] => 7 [5,1,3,2,6,4] => 22 [5,1,3,4,2,6] => 11 [5,1,3,4,6,2] => 16 [5,1,3,6,2,4] => 11 [5,1,3,6,4,2] => 26 [5,1,4,2,3,6] => 7 [5,1,4,2,6,3] => 22 [5,1,4,3,2,6] => 17 [5,1,4,3,6,2] => 22 [5,1,4,6,2,3] => 11 [5,1,4,6,3,2] => 26 [5,1,6,2,3,4] => 7 [5,1,6,2,4,3] => 22 [5,1,6,3,2,4] => 17 [5,1,6,3,4,2] => 22 [5,1,6,4,2,3] => 17 [5,1,6,4,3,2] => 32 [5,2,1,3,4,6] => 4 [5,2,1,3,6,4] => 19 [5,2,1,4,3,6] => 14 [5,2,1,4,6,3] => 19 [5,2,1,6,3,4] => 14 [5,2,1,6,4,3] => 29 [5,2,3,1,4,6] => 7 [5,2,3,1,6,4] => 22 [5,2,3,4,1,6] => 11 [5,2,3,4,6,1] => 16 [5,2,3,6,1,4] => 11 [5,2,3,6,4,1] => 26 [5,2,4,1,3,6] => 7 [5,2,4,1,6,3] => 22 [5,2,4,3,1,6] => 17 [5,2,4,3,6,1] => 22 [5,2,4,6,1,3] => 11 [5,2,4,6,3,1] => 26 [5,2,6,1,3,4] => 7 [5,2,6,1,4,3] => 22 [5,2,6,3,1,4] => 17 [5,2,6,3,4,1] => 22 [5,2,6,4,1,3] => 17 [5,2,6,4,3,1] => 32 [5,3,1,2,4,6] => 4 [5,3,1,2,6,4] => 19 [5,3,1,4,2,6] => 14 [5,3,1,4,6,2] => 19 [5,3,1,6,2,4] => 14 [5,3,1,6,4,2] => 29 [5,3,2,1,4,6] => 10 [5,3,2,1,6,4] => 25 [5,3,2,4,1,6] => 14 [5,3,2,4,6,1] => 19 [5,3,2,6,1,4] => 14 [5,3,2,6,4,1] => 29 [5,3,4,1,2,6] => 7 [5,3,4,1,6,2] => 22 [5,3,4,2,1,6] => 17 [5,3,4,2,6,1] => 22 [5,3,4,6,1,2] => 11 [5,3,4,6,2,1] => 26 [5,3,6,1,2,4] => 7 [5,3,6,1,4,2] => 22 [5,3,6,2,1,4] => 17 [5,3,6,2,4,1] => 22 [5,3,6,4,1,2] => 17 [5,3,6,4,2,1] => 32 [5,4,1,2,3,6] => 4 [5,4,1,2,6,3] => 19 [5,4,1,3,2,6] => 14 [5,4,1,3,6,2] => 19 [5,4,1,6,2,3] => 14 [5,4,1,6,3,2] => 29 [5,4,2,1,3,6] => 10 [5,4,2,1,6,3] => 25 [5,4,2,3,1,6] => 14 [5,4,2,3,6,1] => 19 [5,4,2,6,1,3] => 14 [5,4,2,6,3,1] => 29 [5,4,3,1,2,6] => 10 [5,4,3,1,6,2] => 25 [5,4,3,2,1,6] => 20 [5,4,3,2,6,1] => 25 [5,4,3,6,1,2] => 14 [5,4,3,6,2,1] => 29 [5,4,6,1,2,3] => 7 [5,4,6,1,3,2] => 22 [5,4,6,2,1,3] => 17 [5,4,6,2,3,1] => 22 [5,4,6,3,1,2] => 17 [5,4,6,3,2,1] => 32 [5,6,1,2,3,4] => 3 [5,6,1,2,4,3] => 18 [5,6,1,3,2,4] => 13 [5,6,1,3,4,2] => 18 [5,6,1,4,2,3] => 13 [5,6,1,4,3,2] => 28 [5,6,2,1,3,4] => 9 [5,6,2,1,4,3] => 24 [5,6,2,3,1,4] => 13 [5,6,2,3,4,1] => 18 [5,6,2,4,1,3] => 13 [5,6,2,4,3,1] => 28 [5,6,3,1,2,4] => 9 [5,6,3,1,4,2] => 24 [5,6,3,2,1,4] => 19 [5,6,3,2,4,1] => 24 [5,6,3,4,1,2] => 13 [5,6,3,4,2,1] => 28 [5,6,4,1,2,3] => 9 [5,6,4,1,3,2] => 24 [5,6,4,2,1,3] => 19 [5,6,4,2,3,1] => 24 [5,6,4,3,1,2] => 19 [5,6,4,3,2,1] => 34 [6,1,2,3,4,5] => 1 [6,1,2,3,5,4] => 16 [6,1,2,4,3,5] => 11 [6,1,2,4,5,3] => 16 [6,1,2,5,3,4] => 11 [6,1,2,5,4,3] => 26 [6,1,3,2,4,5] => 7 [6,1,3,2,5,4] => 22 [6,1,3,4,2,5] => 11 [6,1,3,4,5,2] => 16 [6,1,3,5,2,4] => 11 [6,1,3,5,4,2] => 26 [6,1,4,2,3,5] => 7 [6,1,4,2,5,3] => 22 [6,1,4,3,2,5] => 17 [6,1,4,3,5,2] => 22 [6,1,4,5,2,3] => 11 [6,1,4,5,3,2] => 26 [6,1,5,2,3,4] => 7 [6,1,5,2,4,3] => 22 [6,1,5,3,2,4] => 17 [6,1,5,3,4,2] => 22 [6,1,5,4,2,3] => 17 [6,1,5,4,3,2] => 32 [6,2,1,3,4,5] => 4 [6,2,1,3,5,4] => 19 [6,2,1,4,3,5] => 14 [6,2,1,4,5,3] => 19 [6,2,1,5,3,4] => 14 [6,2,1,5,4,3] => 29 [6,2,3,1,4,5] => 7 [6,2,3,1,5,4] => 22 [6,2,3,4,1,5] => 11 [6,2,3,4,5,1] => 16 [6,2,3,5,1,4] => 11 [6,2,3,5,4,1] => 26 [6,2,4,1,3,5] => 7 [6,2,4,1,5,3] => 22 [6,2,4,3,1,5] => 17 [6,2,4,3,5,1] => 22 [6,2,4,5,1,3] => 11 [6,2,4,5,3,1] => 26 [6,2,5,1,3,4] => 7 [6,2,5,1,4,3] => 22 [6,2,5,3,1,4] => 17 [6,2,5,3,4,1] => 22 [6,2,5,4,1,3] => 17 [6,2,5,4,3,1] => 32 [6,3,1,2,4,5] => 4 [6,3,1,2,5,4] => 19 [6,3,1,4,2,5] => 14 [6,3,1,4,5,2] => 19 [6,3,1,5,2,4] => 14 [6,3,1,5,4,2] => 29 [6,3,2,1,4,5] => 10 [6,3,2,1,5,4] => 25 [6,3,2,4,1,5] => 14 [6,3,2,4,5,1] => 19 [6,3,2,5,1,4] => 14 [6,3,2,5,4,1] => 29 [6,3,4,1,2,5] => 7 [6,3,4,1,5,2] => 22 [6,3,4,2,1,5] => 17 [6,3,4,2,5,1] => 22 [6,3,4,5,1,2] => 11 [6,3,4,5,2,1] => 26 [6,3,5,1,2,4] => 7 [6,3,5,1,4,2] => 22 [6,3,5,2,1,4] => 17 [6,3,5,2,4,1] => 22 [6,3,5,4,1,2] => 17 [6,3,5,4,2,1] => 32 [6,4,1,2,3,5] => 4 [6,4,1,2,5,3] => 19 [6,4,1,3,2,5] => 14 [6,4,1,3,5,2] => 19 [6,4,1,5,2,3] => 14 [6,4,1,5,3,2] => 29 [6,4,2,1,3,5] => 10 [6,4,2,1,5,3] => 25 [6,4,2,3,1,5] => 14 [6,4,2,3,5,1] => 19 [6,4,2,5,1,3] => 14 [6,4,2,5,3,1] => 29 [6,4,3,1,2,5] => 10 [6,4,3,1,5,2] => 25 [6,4,3,2,1,5] => 20 [6,4,3,2,5,1] => 25 [6,4,3,5,1,2] => 14 [6,4,3,5,2,1] => 29 [6,4,5,1,2,3] => 7 [6,4,5,1,3,2] => 22 [6,4,5,2,1,3] => 17 [6,4,5,2,3,1] => 22 [6,4,5,3,1,2] => 17 [6,4,5,3,2,1] => 32 [6,5,1,2,3,4] => 4 [6,5,1,2,4,3] => 19 [6,5,1,3,2,4] => 14 [6,5,1,3,4,2] => 19 [6,5,1,4,2,3] => 14 [6,5,1,4,3,2] => 29 [6,5,2,1,3,4] => 10 [6,5,2,1,4,3] => 25 [6,5,2,3,1,4] => 14 [6,5,2,3,4,1] => 19 [6,5,2,4,1,3] => 14 [6,5,2,4,3,1] => 29 [6,5,3,1,2,4] => 10 [6,5,3,1,4,2] => 25 [6,5,3,2,1,4] => 20 [6,5,3,2,4,1] => 25 [6,5,3,4,1,2] => 14 [6,5,3,4,2,1] => 29 [6,5,4,1,2,3] => 10 [6,5,4,1,3,2] => 25 [6,5,4,2,1,3] => 20 [6,5,4,2,3,1] => 25 [6,5,4,3,1,2] => 20 [6,5,4,3,2,1] => 35 ----------------------------------------------------------------------------- Created: Sep 07, 2025 at 08:26 by Joshua Maglione ----------------------------------------------------------------------------- Last Updated: Sep 07, 2025 at 08:26 by Joshua Maglione