***************************************************************************** * 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: St000221 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of strong fixed points of a permutation. $i$ is called a strong fixed point of $\pi$ if 1. $j < i$ implies $\pi_j < \pi_i$, and 2. $j > i$ implies $\pi_j > \pi_i$ This can be described as an occurrence of the mesh pattern ([1], {(0,1),(1,0)}), i.e., the upper left and the lower right quadrants are shaded, see [3]. The generating function for the joint-distribution (RLmin, LRmax, strong fixed points) has a continued fraction expression as given in [4, Lemma 3.2], for LRmax see [[St000314]]. ----------------------------------------------------------------------------- References: [1] Triangle read by rows: T(n,k) is the number of permutations of [n] having k strong fixed points (0<=k<=n). A permutation p of 1,2,...,n is said to have j as a strong fixed point (splitter) if p(k)j for k>j. [[OEIS:A145878]] [2] Ex 1.128b Stanley, R. P. Enumerative combinatorics. Volume 1 [[MathSciNet:2868112]] [3] Brändén, P., Claesson, A. Mesh patterns and the expansion of permutation statistics as sums of permutation patterns [[arXiv:1102.4226]] [4] Kim, J. S., Stanton, D. The Combinatorics of Associated Laguerre Polynomials [[arXiv:1501.03880]] ----------------------------------------------------------------------------- Code: def strong_fixed_point(x, i): v = x[i] for j in range(i): if x[j] >= v: return False for j in range(i+1, len(x)): if x[j] <= v: return False return True def statistic(x): return len([1 for i in range(len(x)) if strong_fixed_point(x, i)]) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [1,2] => 2 [2,1] => 0 [1,2,3] => 3 [1,3,2] => 1 [2,1,3] => 1 [2,3,1] => 0 [3,1,2] => 0 [3,2,1] => 0 [1,2,3,4] => 4 [1,2,4,3] => 2 [1,3,2,4] => 2 [1,3,4,2] => 1 [1,4,2,3] => 1 [1,4,3,2] => 1 [2,1,3,4] => 2 [2,1,4,3] => 0 [2,3,1,4] => 1 [2,3,4,1] => 0 [2,4,1,3] => 0 [2,4,3,1] => 0 [3,1,2,4] => 1 [3,1,4,2] => 0 [3,2,1,4] => 1 [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 [1,2,3,4,5] => 5 [1,2,3,5,4] => 3 [1,2,4,3,5] => 3 [1,2,4,5,3] => 2 [1,2,5,3,4] => 2 [1,2,5,4,3] => 2 [1,3,2,4,5] => 3 [1,3,2,5,4] => 1 [1,3,4,2,5] => 2 [1,3,4,5,2] => 1 [1,3,5,2,4] => 1 [1,3,5,4,2] => 1 [1,4,2,3,5] => 2 [1,4,2,5,3] => 1 [1,4,3,2,5] => 2 [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] => 3 [2,1,3,5,4] => 1 [2,1,4,3,5] => 1 [2,1,4,5,3] => 0 [2,1,5,3,4] => 0 [2,1,5,4,3] => 0 [2,3,1,4,5] => 2 [2,3,1,5,4] => 0 [2,3,4,1,5] => 1 [2,3,4,5,1] => 0 [2,3,5,1,4] => 0 [2,3,5,4,1] => 0 [2,4,1,3,5] => 1 [2,4,1,5,3] => 0 [2,4,3,1,5] => 1 [2,4,3,5,1] => 0 [2,4,5,1,3] => 0 [2,4,5,3,1] => 0 [2,5,1,3,4] => 0 [2,5,1,4,3] => 0 [2,5,3,1,4] => 0 [2,5,3,4,1] => 0 [2,5,4,1,3] => 0 [2,5,4,3,1] => 0 [3,1,2,4,5] => 2 [3,1,2,5,4] => 0 [3,1,4,2,5] => 1 [3,1,4,5,2] => 0 [3,1,5,2,4] => 0 [3,1,5,4,2] => 0 [3,2,1,4,5] => 2 [3,2,1,5,4] => 0 [3,2,4,1,5] => 1 [3,2,4,5,1] => 0 [3,2,5,1,4] => 0 [3,2,5,4,1] => 0 [3,4,1,2,5] => 1 [3,4,1,5,2] => 0 [3,4,2,1,5] => 1 [3,4,2,5,1] => 0 [3,4,5,1,2] => 0 [3,4,5,2,1] => 0 [3,5,1,2,4] => 0 [3,5,1,4,2] => 0 [3,5,2,1,4] => 0 [3,5,2,4,1] => 0 [3,5,4,1,2] => 0 [3,5,4,2,1] => 0 [4,1,2,3,5] => 1 [4,1,2,5,3] => 0 [4,1,3,2,5] => 1 [4,1,3,5,2] => 0 [4,1,5,2,3] => 0 [4,1,5,3,2] => 0 [4,2,1,3,5] => 1 [4,2,1,5,3] => 0 [4,2,3,1,5] => 1 [4,2,3,5,1] => 0 [4,2,5,1,3] => 0 [4,2,5,3,1] => 0 [4,3,1,2,5] => 1 [4,3,1,5,2] => 0 [4,3,2,1,5] => 1 [4,3,2,5,1] => 0 [4,3,5,1,2] => 0 [4,3,5,2,1] => 0 [4,5,1,2,3] => 0 [4,5,1,3,2] => 0 [4,5,2,1,3] => 0 [4,5,2,3,1] => 0 [4,5,3,1,2] => 0 [4,5,3,2,1] => 0 [5,1,2,3,4] => 0 [5,1,2,4,3] => 0 [5,1,3,2,4] => 0 [5,1,3,4,2] => 0 [5,1,4,2,3] => 0 [5,1,4,3,2] => 0 [5,2,1,3,4] => 0 [5,2,1,4,3] => 0 [5,2,3,1,4] => 0 [5,2,3,4,1] => 0 [5,2,4,1,3] => 0 [5,2,4,3,1] => 0 [5,3,1,2,4] => 0 [5,3,1,4,2] => 0 [5,3,2,1,4] => 0 [5,3,2,4,1] => 0 [5,3,4,1,2] => 0 [5,3,4,2,1] => 0 [5,4,1,2,3] => 0 [5,4,1,3,2] => 0 [5,4,2,1,3] => 0 [5,4,2,3,1] => 0 [5,4,3,1,2] => 0 [5,4,3,2,1] => 0 [1,2,3,4,5,6] => 6 [1,2,3,4,6,5] => 4 [1,2,3,5,4,6] => 4 [1,2,3,5,6,4] => 3 [1,2,3,6,4,5] => 3 [1,2,3,6,5,4] => 3 [1,2,4,3,5,6] => 4 [1,2,4,3,6,5] => 2 [1,2,4,5,3,6] => 3 [1,2,4,5,6,3] => 2 [1,2,4,6,3,5] => 2 [1,2,4,6,5,3] => 2 [1,2,5,3,4,6] => 3 [1,2,5,3,6,4] => 2 [1,2,5,4,3,6] => 3 [1,2,5,4,6,3] => 2 [1,2,5,6,3,4] => 2 [1,2,5,6,4,3] => 2 [1,2,6,3,4,5] => 2 [1,2,6,3,5,4] => 2 [1,2,6,4,3,5] => 2 [1,2,6,4,5,3] => 2 [1,2,6,5,3,4] => 2 [1,2,6,5,4,3] => 2 [1,3,2,4,5,6] => 4 [1,3,2,4,6,5] => 2 [1,3,2,5,4,6] => 2 [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] => 3 [1,3,4,2,6,5] => 1 [1,3,4,5,2,6] => 2 [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] => 2 [1,3,5,2,6,4] => 1 [1,3,5,4,2,6] => 2 [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] => 3 [1,4,2,3,6,5] => 1 [1,4,2,5,3,6] => 2 [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] => 3 [1,4,3,2,6,5] => 1 [1,4,3,5,2,6] => 2 [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] => 2 [1,4,5,2,6,3] => 1 [1,4,5,3,2,6] => 2 [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] => 2 [1,5,2,3,6,4] => 1 [1,5,2,4,3,6] => 2 [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] => 2 [1,5,3,2,6,4] => 1 [1,5,3,4,2,6] => 2 [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] => 2 [1,5,4,2,6,3] => 1 [1,5,4,3,2,6] => 2 [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] => 4 [2,1,3,4,6,5] => 2 [2,1,3,5,4,6] => 2 [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] => 2 [2,1,4,3,6,5] => 0 [2,1,4,5,3,6] => 1 [2,1,4,5,6,3] => 0 [2,1,4,6,3,5] => 0 [2,1,4,6,5,3] => 0 [2,1,5,3,4,6] => 1 [2,1,5,3,6,4] => 0 [2,1,5,4,3,6] => 1 [2,1,5,4,6,3] => 0 [2,1,5,6,3,4] => 0 [2,1,5,6,4,3] => 0 [2,1,6,3,4,5] => 0 [2,1,6,3,5,4] => 0 [2,1,6,4,3,5] => 0 [2,1,6,4,5,3] => 0 [2,1,6,5,3,4] => 0 [2,1,6,5,4,3] => 0 [2,3,1,4,5,6] => 3 [2,3,1,4,6,5] => 1 [2,3,1,5,4,6] => 1 [2,3,1,5,6,4] => 0 [2,3,1,6,4,5] => 0 [2,3,1,6,5,4] => 0 [2,3,4,1,5,6] => 2 [2,3,4,1,6,5] => 0 [2,3,4,5,1,6] => 1 [2,3,4,5,6,1] => 0 [2,3,4,6,1,5] => 0 [2,3,4,6,5,1] => 0 [2,3,5,1,4,6] => 1 [2,3,5,1,6,4] => 0 [2,3,5,4,1,6] => 1 [2,3,5,4,6,1] => 0 [2,3,5,6,1,4] => 0 [2,3,5,6,4,1] => 0 [2,3,6,1,4,5] => 0 [2,3,6,1,5,4] => 0 [2,3,6,4,1,5] => 0 [2,3,6,4,5,1] => 0 [2,3,6,5,1,4] => 0 [2,3,6,5,4,1] => 0 [2,4,1,3,5,6] => 2 [2,4,1,3,6,5] => 0 [2,4,1,5,3,6] => 1 [2,4,1,5,6,3] => 0 [2,4,1,6,3,5] => 0 [2,4,1,6,5,3] => 0 [2,4,3,1,5,6] => 2 [2,4,3,1,6,5] => 0 [2,4,3,5,1,6] => 1 [2,4,3,5,6,1] => 0 [2,4,3,6,1,5] => 0 [2,4,3,6,5,1] => 0 [2,4,5,1,3,6] => 1 [2,4,5,1,6,3] => 0 [2,4,5,3,1,6] => 1 [2,4,5,3,6,1] => 0 [2,4,5,6,1,3] => 0 [2,4,5,6,3,1] => 0 [2,4,6,1,3,5] => 0 [2,4,6,1,5,3] => 0 [2,4,6,3,1,5] => 0 [2,4,6,3,5,1] => 0 [2,4,6,5,1,3] => 0 [2,4,6,5,3,1] => 0 [2,5,1,3,4,6] => 1 [2,5,1,3,6,4] => 0 [2,5,1,4,3,6] => 1 [2,5,1,4,6,3] => 0 [2,5,1,6,3,4] => 0 [2,5,1,6,4,3] => 0 [2,5,3,1,4,6] => 1 [2,5,3,1,6,4] => 0 [2,5,3,4,1,6] => 1 [2,5,3,4,6,1] => 0 [2,5,3,6,1,4] => 0 [2,5,3,6,4,1] => 0 [2,5,4,1,3,6] => 1 [2,5,4,1,6,3] => 0 [2,5,4,3,1,6] => 1 [2,5,4,3,6,1] => 0 [2,5,4,6,1,3] => 0 [2,5,4,6,3,1] => 0 [2,5,6,1,3,4] => 0 [2,5,6,1,4,3] => 0 [2,5,6,3,1,4] => 0 [2,5,6,3,4,1] => 0 [2,5,6,4,1,3] => 0 [2,5,6,4,3,1] => 0 [2,6,1,3,4,5] => 0 [2,6,1,3,5,4] => 0 [2,6,1,4,3,5] => 0 [2,6,1,4,5,3] => 0 [2,6,1,5,3,4] => 0 [2,6,1,5,4,3] => 0 [2,6,3,1,4,5] => 0 [2,6,3,1,5,4] => 0 [2,6,3,4,1,5] => 0 [2,6,3,4,5,1] => 0 [2,6,3,5,1,4] => 0 [2,6,3,5,4,1] => 0 [2,6,4,1,3,5] => 0 [2,6,4,1,5,3] => 0 [2,6,4,3,1,5] => 0 [2,6,4,3,5,1] => 0 [2,6,4,5,1,3] => 0 [2,6,4,5,3,1] => 0 [2,6,5,1,3,4] => 0 [2,6,5,1,4,3] => 0 [2,6,5,3,1,4] => 0 [2,6,5,3,4,1] => 0 [2,6,5,4,1,3] => 0 [2,6,5,4,3,1] => 0 [3,1,2,4,5,6] => 3 [3,1,2,4,6,5] => 1 [3,1,2,5,4,6] => 1 [3,1,2,5,6,4] => 0 [3,1,2,6,4,5] => 0 [3,1,2,6,5,4] => 0 [3,1,4,2,5,6] => 2 [3,1,4,2,6,5] => 0 [3,1,4,5,2,6] => 1 [3,1,4,5,6,2] => 0 [3,1,4,6,2,5] => 0 [3,1,4,6,5,2] => 0 [3,1,5,2,4,6] => 1 [3,1,5,2,6,4] => 0 [3,1,5,4,2,6] => 1 [3,1,5,4,6,2] => 0 [3,1,5,6,2,4] => 0 [3,1,5,6,4,2] => 0 [3,1,6,2,4,5] => 0 [3,1,6,2,5,4] => 0 [3,1,6,4,2,5] => 0 [3,1,6,4,5,2] => 0 [3,1,6,5,2,4] => 0 [3,1,6,5,4,2] => 0 [3,2,1,4,5,6] => 3 [3,2,1,4,6,5] => 1 [3,2,1,5,4,6] => 1 [3,2,1,5,6,4] => 0 [3,2,1,6,4,5] => 0 [3,2,1,6,5,4] => 0 [3,2,4,1,5,6] => 2 [3,2,4,1,6,5] => 0 [3,2,4,5,1,6] => 1 [3,2,4,5,6,1] => 0 [3,2,4,6,1,5] => 0 [3,2,4,6,5,1] => 0 [3,2,5,1,4,6] => 1 [3,2,5,1,6,4] => 0 [3,2,5,4,1,6] => 1 [3,2,5,4,6,1] => 0 [3,2,5,6,1,4] => 0 [3,2,5,6,4,1] => 0 [3,2,6,1,4,5] => 0 [3,2,6,1,5,4] => 0 [3,2,6,4,1,5] => 0 [3,2,6,4,5,1] => 0 [3,2,6,5,1,4] => 0 [3,2,6,5,4,1] => 0 [3,4,1,2,5,6] => 2 [3,4,1,2,6,5] => 0 [3,4,1,5,2,6] => 1 [3,4,1,5,6,2] => 0 [3,4,1,6,2,5] => 0 [3,4,1,6,5,2] => 0 [3,4,2,1,5,6] => 2 [3,4,2,1,6,5] => 0 [3,4,2,5,1,6] => 1 [3,4,2,5,6,1] => 0 [3,4,2,6,1,5] => 0 [3,4,2,6,5,1] => 0 [3,4,5,1,2,6] => 1 [3,4,5,1,6,2] => 0 [3,4,5,2,1,6] => 1 [3,4,5,2,6,1] => 0 [3,4,5,6,1,2] => 0 [3,4,5,6,2,1] => 0 [3,4,6,1,2,5] => 0 [3,4,6,1,5,2] => 0 [3,4,6,2,1,5] => 0 [3,4,6,2,5,1] => 0 [3,4,6,5,1,2] => 0 [3,4,6,5,2,1] => 0 [3,5,1,2,4,6] => 1 [3,5,1,2,6,4] => 0 [3,5,1,4,2,6] => 1 [3,5,1,4,6,2] => 0 [3,5,1,6,2,4] => 0 [3,5,1,6,4,2] => 0 [3,5,2,1,4,6] => 1 [3,5,2,1,6,4] => 0 [3,5,2,4,1,6] => 1 [3,5,2,4,6,1] => 0 [3,5,2,6,1,4] => 0 [3,5,2,6,4,1] => 0 [3,5,4,1,2,6] => 1 [3,5,4,1,6,2] => 0 [3,5,4,2,1,6] => 1 [3,5,4,2,6,1] => 0 [3,5,4,6,1,2] => 0 [3,5,4,6,2,1] => 0 [3,5,6,1,2,4] => 0 [3,5,6,1,4,2] => 0 [3,5,6,2,1,4] => 0 [3,5,6,2,4,1] => 0 [3,5,6,4,1,2] => 0 [3,5,6,4,2,1] => 0 [3,6,1,2,4,5] => 0 [3,6,1,2,5,4] => 0 [3,6,1,4,2,5] => 0 [3,6,1,4,5,2] => 0 [3,6,1,5,2,4] => 0 [3,6,1,5,4,2] => 0 [3,6,2,1,4,5] => 0 [3,6,2,1,5,4] => 0 [3,6,2,4,1,5] => 0 [3,6,2,4,5,1] => 0 [3,6,2,5,1,4] => 0 [3,6,2,5,4,1] => 0 [3,6,4,1,2,5] => 0 [3,6,4,1,5,2] => 0 [3,6,4,2,1,5] => 0 [3,6,4,2,5,1] => 0 [3,6,4,5,1,2] => 0 [3,6,4,5,2,1] => 0 [3,6,5,1,2,4] => 0 [3,6,5,1,4,2] => 0 [3,6,5,2,1,4] => 0 [3,6,5,2,4,1] => 0 [3,6,5,4,1,2] => 0 [3,6,5,4,2,1] => 0 [4,1,2,3,5,6] => 2 [4,1,2,3,6,5] => 0 [4,1,2,5,3,6] => 1 [4,1,2,5,6,3] => 0 [4,1,2,6,3,5] => 0 [4,1,2,6,5,3] => 0 [4,1,3,2,5,6] => 2 [4,1,3,2,6,5] => 0 [4,1,3,5,2,6] => 1 [4,1,3,5,6,2] => 0 [4,1,3,6,2,5] => 0 [4,1,3,6,5,2] => 0 [4,1,5,2,3,6] => 1 [4,1,5,2,6,3] => 0 [4,1,5,3,2,6] => 1 [4,1,5,3,6,2] => 0 [4,1,5,6,2,3] => 0 [4,1,5,6,3,2] => 0 [4,1,6,2,3,5] => 0 [4,1,6,2,5,3] => 0 [4,1,6,3,2,5] => 0 [4,1,6,3,5,2] => 0 [4,1,6,5,2,3] => 0 [4,1,6,5,3,2] => 0 [4,2,1,3,5,6] => 2 [4,2,1,3,6,5] => 0 [4,2,1,5,3,6] => 1 [4,2,1,5,6,3] => 0 [4,2,1,6,3,5] => 0 [4,2,1,6,5,3] => 0 [4,2,3,1,5,6] => 2 [4,2,3,1,6,5] => 0 [4,2,3,5,1,6] => 1 [4,2,3,5,6,1] => 0 [4,2,3,6,1,5] => 0 [4,2,3,6,5,1] => 0 [4,2,5,1,3,6] => 1 [4,2,5,1,6,3] => 0 [4,2,5,3,1,6] => 1 [4,2,5,3,6,1] => 0 [4,2,5,6,1,3] => 0 [4,2,5,6,3,1] => 0 [4,2,6,1,3,5] => 0 [4,2,6,1,5,3] => 0 [4,2,6,3,1,5] => 0 [4,2,6,3,5,1] => 0 [4,2,6,5,1,3] => 0 [4,2,6,5,3,1] => 0 [4,3,1,2,5,6] => 2 [4,3,1,2,6,5] => 0 [4,3,1,5,2,6] => 1 [4,3,1,5,6,2] => 0 [4,3,1,6,2,5] => 0 [4,3,1,6,5,2] => 0 [4,3,2,1,5,6] => 2 [4,3,2,1,6,5] => 0 [4,3,2,5,1,6] => 1 [4,3,2,5,6,1] => 0 [4,3,2,6,1,5] => 0 [4,3,2,6,5,1] => 0 [4,3,5,1,2,6] => 1 [4,3,5,1,6,2] => 0 [4,3,5,2,1,6] => 1 [4,3,5,2,6,1] => 0 [4,3,5,6,1,2] => 0 [4,3,5,6,2,1] => 0 [4,3,6,1,2,5] => 0 [4,3,6,1,5,2] => 0 [4,3,6,2,1,5] => 0 [4,3,6,2,5,1] => 0 [4,3,6,5,1,2] => 0 [4,3,6,5,2,1] => 0 [4,5,1,2,3,6] => 1 [4,5,1,2,6,3] => 0 [4,5,1,3,2,6] => 1 [4,5,1,3,6,2] => 0 [4,5,1,6,2,3] => 0 [4,5,1,6,3,2] => 0 [4,5,2,1,3,6] => 1 [4,5,2,1,6,3] => 0 [4,5,2,3,1,6] => 1 [4,5,2,3,6,1] => 0 [4,5,2,6,1,3] => 0 [4,5,2,6,3,1] => 0 [4,5,3,1,2,6] => 1 [4,5,3,1,6,2] => 0 [4,5,3,2,1,6] => 1 [4,5,3,2,6,1] => 0 [4,5,3,6,1,2] => 0 [4,5,3,6,2,1] => 0 [4,5,6,1,2,3] => 0 [4,5,6,1,3,2] => 0 [4,5,6,2,1,3] => 0 [4,5,6,2,3,1] => 0 [4,5,6,3,1,2] => 0 [4,5,6,3,2,1] => 0 [4,6,1,2,3,5] => 0 [4,6,1,2,5,3] => 0 [4,6,1,3,2,5] => 0 [4,6,1,3,5,2] => 0 [4,6,1,5,2,3] => 0 [4,6,1,5,3,2] => 0 [4,6,2,1,3,5] => 0 [4,6,2,1,5,3] => 0 [4,6,2,3,1,5] => 0 [4,6,2,3,5,1] => 0 [4,6,2,5,1,3] => 0 [4,6,2,5,3,1] => 0 [4,6,3,1,2,5] => 0 [4,6,3,1,5,2] => 0 [4,6,3,2,1,5] => 0 [4,6,3,2,5,1] => 0 [4,6,3,5,1,2] => 0 [4,6,3,5,2,1] => 0 [4,6,5,1,2,3] => 0 [4,6,5,1,3,2] => 0 [4,6,5,2,1,3] => 0 [4,6,5,2,3,1] => 0 [4,6,5,3,1,2] => 0 [4,6,5,3,2,1] => 0 [5,1,2,3,4,6] => 1 [5,1,2,3,6,4] => 0 [5,1,2,4,3,6] => 1 [5,1,2,4,6,3] => 0 [5,1,2,6,3,4] => 0 [5,1,2,6,4,3] => 0 [5,1,3,2,4,6] => 1 [5,1,3,2,6,4] => 0 [5,1,3,4,2,6] => 1 [5,1,3,4,6,2] => 0 [5,1,3,6,2,4] => 0 [5,1,3,6,4,2] => 0 [5,1,4,2,3,6] => 1 [5,1,4,2,6,3] => 0 [5,1,4,3,2,6] => 1 [5,1,4,3,6,2] => 0 [5,1,4,6,2,3] => 0 [5,1,4,6,3,2] => 0 [5,1,6,2,3,4] => 0 [5,1,6,2,4,3] => 0 [5,1,6,3,2,4] => 0 [5,1,6,3,4,2] => 0 [5,1,6,4,2,3] => 0 [5,1,6,4,3,2] => 0 [5,2,1,3,4,6] => 1 [5,2,1,3,6,4] => 0 [5,2,1,4,3,6] => 1 [5,2,1,4,6,3] => 0 [5,2,1,6,3,4] => 0 [5,2,1,6,4,3] => 0 [5,2,3,1,4,6] => 1 [5,2,3,1,6,4] => 0 [5,2,3,4,1,6] => 1 [5,2,3,4,6,1] => 0 [5,2,3,6,1,4] => 0 [5,2,3,6,4,1] => 0 [5,2,4,1,3,6] => 1 [5,2,4,1,6,3] => 0 [5,2,4,3,1,6] => 1 [5,2,4,3,6,1] => 0 [5,2,4,6,1,3] => 0 [5,2,4,6,3,1] => 0 [5,2,6,1,3,4] => 0 [5,2,6,1,4,3] => 0 [5,2,6,3,1,4] => 0 [5,2,6,3,4,1] => 0 [5,2,6,4,1,3] => 0 [5,2,6,4,3,1] => 0 [5,3,1,2,4,6] => 1 [5,3,1,2,6,4] => 0 [5,3,1,4,2,6] => 1 [5,3,1,4,6,2] => 0 [5,3,1,6,2,4] => 0 [5,3,1,6,4,2] => 0 [5,3,2,1,4,6] => 1 [5,3,2,1,6,4] => 0 [5,3,2,4,1,6] => 1 [5,3,2,4,6,1] => 0 [5,3,2,6,1,4] => 0 [5,3,2,6,4,1] => 0 [5,3,4,1,2,6] => 1 [5,3,4,1,6,2] => 0 [5,3,4,2,1,6] => 1 [5,3,4,2,6,1] => 0 [5,3,4,6,1,2] => 0 [5,3,4,6,2,1] => 0 [5,3,6,1,2,4] => 0 [5,3,6,1,4,2] => 0 [5,3,6,2,1,4] => 0 [5,3,6,2,4,1] => 0 [5,3,6,4,1,2] => 0 [5,3,6,4,2,1] => 0 [5,4,1,2,3,6] => 1 [5,4,1,2,6,3] => 0 [5,4,1,3,2,6] => 1 [5,4,1,3,6,2] => 0 [5,4,1,6,2,3] => 0 [5,4,1,6,3,2] => 0 [5,4,2,1,3,6] => 1 [5,4,2,1,6,3] => 0 [5,4,2,3,1,6] => 1 [5,4,2,3,6,1] => 0 [5,4,2,6,1,3] => 0 [5,4,2,6,3,1] => 0 [5,4,3,1,2,6] => 1 [5,4,3,1,6,2] => 0 [5,4,3,2,1,6] => 1 [5,4,3,2,6,1] => 0 [5,4,3,6,1,2] => 0 [5,4,3,6,2,1] => 0 [5,4,6,1,2,3] => 0 [5,4,6,1,3,2] => 0 [5,4,6,2,1,3] => 0 [5,4,6,2,3,1] => 0 [5,4,6,3,1,2] => 0 [5,4,6,3,2,1] => 0 [5,6,1,2,3,4] => 0 [5,6,1,2,4,3] => 0 [5,6,1,3,2,4] => 0 [5,6,1,3,4,2] => 0 [5,6,1,4,2,3] => 0 [5,6,1,4,3,2] => 0 [5,6,2,1,3,4] => 0 [5,6,2,1,4,3] => 0 [5,6,2,3,1,4] => 0 [5,6,2,3,4,1] => 0 [5,6,2,4,1,3] => 0 [5,6,2,4,3,1] => 0 [5,6,3,1,2,4] => 0 [5,6,3,1,4,2] => 0 [5,6,3,2,1,4] => 0 [5,6,3,2,4,1] => 0 [5,6,3,4,1,2] => 0 [5,6,3,4,2,1] => 0 [5,6,4,1,2,3] => 0 [5,6,4,1,3,2] => 0 [5,6,4,2,1,3] => 0 [5,6,4,2,3,1] => 0 [5,6,4,3,1,2] => 0 [5,6,4,3,2,1] => 0 [6,1,2,3,4,5] => 0 [6,1,2,3,5,4] => 0 [6,1,2,4,3,5] => 0 [6,1,2,4,5,3] => 0 [6,1,2,5,3,4] => 0 [6,1,2,5,4,3] => 0 [6,1,3,2,4,5] => 0 [6,1,3,2,5,4] => 0 [6,1,3,4,2,5] => 0 [6,1,3,4,5,2] => 0 [6,1,3,5,2,4] => 0 [6,1,3,5,4,2] => 0 [6,1,4,2,3,5] => 0 [6,1,4,2,5,3] => 0 [6,1,4,3,2,5] => 0 [6,1,4,3,5,2] => 0 [6,1,4,5,2,3] => 0 [6,1,4,5,3,2] => 0 [6,1,5,2,3,4] => 0 [6,1,5,2,4,3] => 0 [6,1,5,3,2,4] => 0 [6,1,5,3,4,2] => 0 [6,1,5,4,2,3] => 0 [6,1,5,4,3,2] => 0 [6,2,1,3,4,5] => 0 [6,2,1,3,5,4] => 0 [6,2,1,4,3,5] => 0 [6,2,1,4,5,3] => 0 [6,2,1,5,3,4] => 0 [6,2,1,5,4,3] => 0 [6,2,3,1,4,5] => 0 [6,2,3,1,5,4] => 0 [6,2,3,4,1,5] => 0 [6,2,3,4,5,1] => 0 [6,2,3,5,1,4] => 0 [6,2,3,5,4,1] => 0 [6,2,4,1,3,5] => 0 [6,2,4,1,5,3] => 0 [6,2,4,3,1,5] => 0 [6,2,4,3,5,1] => 0 [6,2,4,5,1,3] => 0 [6,2,4,5,3,1] => 0 [6,2,5,1,3,4] => 0 [6,2,5,1,4,3] => 0 [6,2,5,3,1,4] => 0 [6,2,5,3,4,1] => 0 [6,2,5,4,1,3] => 0 [6,2,5,4,3,1] => 0 [6,3,1,2,4,5] => 0 [6,3,1,2,5,4] => 0 [6,3,1,4,2,5] => 0 [6,3,1,4,5,2] => 0 [6,3,1,5,2,4] => 0 [6,3,1,5,4,2] => 0 [6,3,2,1,4,5] => 0 [6,3,2,1,5,4] => 0 [6,3,2,4,1,5] => 0 [6,3,2,4,5,1] => 0 [6,3,2,5,1,4] => 0 [6,3,2,5,4,1] => 0 [6,3,4,1,2,5] => 0 [6,3,4,1,5,2] => 0 [6,3,4,2,1,5] => 0 [6,3,4,2,5,1] => 0 [6,3,4,5,1,2] => 0 [6,3,4,5,2,1] => 0 [6,3,5,1,2,4] => 0 [6,3,5,1,4,2] => 0 [6,3,5,2,1,4] => 0 [6,3,5,2,4,1] => 0 [6,3,5,4,1,2] => 0 [6,3,5,4,2,1] => 0 [6,4,1,2,3,5] => 0 [6,4,1,2,5,3] => 0 [6,4,1,3,2,5] => 0 [6,4,1,3,5,2] => 0 [6,4,1,5,2,3] => 0 [6,4,1,5,3,2] => 0 [6,4,2,1,3,5] => 0 [6,4,2,1,5,3] => 0 [6,4,2,3,1,5] => 0 [6,4,2,3,5,1] => 0 [6,4,2,5,1,3] => 0 [6,4,2,5,3,1] => 0 [6,4,3,1,2,5] => 0 [6,4,3,1,5,2] => 0 [6,4,3,2,1,5] => 0 [6,4,3,2,5,1] => 0 [6,4,3,5,1,2] => 0 [6,4,3,5,2,1] => 0 [6,4,5,1,2,3] => 0 [6,4,5,1,3,2] => 0 [6,4,5,2,1,3] => 0 [6,4,5,2,3,1] => 0 [6,4,5,3,1,2] => 0 [6,4,5,3,2,1] => 0 [6,5,1,2,3,4] => 0 [6,5,1,2,4,3] => 0 [6,5,1,3,2,4] => 0 [6,5,1,3,4,2] => 0 [6,5,1,4,2,3] => 0 [6,5,1,4,3,2] => 0 [6,5,2,1,3,4] => 0 [6,5,2,1,4,3] => 0 [6,5,2,3,1,4] => 0 [6,5,2,3,4,1] => 0 [6,5,2,4,1,3] => 0 [6,5,2,4,3,1] => 0 [6,5,3,1,2,4] => 0 [6,5,3,1,4,2] => 0 [6,5,3,2,1,4] => 0 [6,5,3,2,4,1] => 0 [6,5,3,4,1,2] => 0 [6,5,3,4,2,1] => 0 [6,5,4,1,2,3] => 0 [6,5,4,1,3,2] => 0 [6,5,4,2,1,3] => 0 [6,5,4,2,3,1] => 0 [6,5,4,3,1,2] => 0 [6,5,4,3,2,1] => 0 ----------------------------------------------------------------------------- Created: Sep 22, 2014 at 16:58 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Oct 17, 2017 at 17:52 by Jang Soo Kim