***************************************************************************** * 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: St001520 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of strict 3-descents. A '''strict 3-descent''' of a permutation $\pi$ of $\{1,2, \dots ,n \}$ is a pair $(i,i+3)$ with $ i+3 \leq n$ and $\pi(i) > \pi(i+3)$. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(pi): return sum(1 for i in range(len(pi)-3) if pi[i] > pi[i+3]) ----------------------------------------------------------------------------- Statistic values: [1,2] => 0 [2,1] => 0 [1,2,3] => 0 [1,3,2] => 0 [2,1,3] => 0 [2,3,1] => 0 [3,1,2] => 0 [3,2,1] => 0 [1,2,3,4] => 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] => 1 [2,4,1,3] => 0 [2,4,3,1] => 1 [3,1,2,4] => 0 [3,1,4,2] => 1 [3,2,1,4] => 0 [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] => 0 [1,2,3,5,4] => 0 [1,2,4,3,5] => 0 [1,2,4,5,3] => 0 [1,2,5,3,4] => 0 [1,2,5,4,3] => 0 [1,3,2,4,5] => 0 [1,3,2,5,4] => 0 [1,3,4,2,5] => 0 [1,3,4,5,2] => 1 [1,3,5,2,4] => 0 [1,3,5,4,2] => 1 [1,4,2,3,5] => 0 [1,4,2,5,3] => 1 [1,4,3,2,5] => 0 [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] => 0 [2,1,3,5,4] => 0 [2,1,4,3,5] => 0 [2,1,4,5,3] => 0 [2,1,5,3,4] => 0 [2,1,5,4,3] => 0 [2,3,1,4,5] => 0 [2,3,1,5,4] => 0 [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] => 0 [2,4,1,5,3] => 1 [2,4,3,1,5] => 1 [2,4,3,5,1] => 1 [2,4,5,1,3] => 2 [2,4,5,3,1] => 1 [2,5,1,3,4] => 1 [2,5,1,4,3] => 1 [2,5,3,1,4] => 2 [2,5,3,4,1] => 1 [2,5,4,1,3] => 2 [2,5,4,3,1] => 1 [3,1,2,4,5] => 0 [3,1,2,5,4] => 0 [3,1,4,2,5] => 1 [3,1,4,5,2] => 0 [3,1,5,2,4] => 1 [3,1,5,4,2] => 0 [3,2,1,4,5] => 0 [3,2,1,5,4] => 0 [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] => 2 [3,4,5,2,1] => 2 [3,5,1,2,4] => 2 [3,5,1,4,2] => 1 [3,5,2,1,4] => 2 [3,5,2,4,1] => 1 [3,5,4,1,2] => 2 [3,5,4,2,1] => 2 [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] => 1 [4,1,5,3,2] => 1 [4,2,1,3,5] => 1 [4,2,1,5,3] => 0 [4,2,3,1,5] => 1 [4,2,3,5,1] => 1 [4,2,5,1,3] => 1 [4,2,5,3,1] => 2 [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] => 2 [4,3,5,2,1] => 2 [4,5,1,2,3] => 2 [4,5,1,3,2] => 2 [4,5,2,1,3] => 2 [4,5,2,3,1] => 2 [4,5,3,1,2] => 2 [4,5,3,2,1] => 2 [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] => 2 [5,2,4,1,3] => 1 [5,2,4,3,1] => 2 [5,3,1,2,4] => 1 [5,3,1,4,2] => 2 [5,3,2,1,4] => 1 [5,3,2,4,1] => 2 [5,3,4,1,2] => 2 [5,3,4,2,1] => 2 [5,4,1,2,3] => 2 [5,4,1,3,2] => 2 [5,4,2,1,3] => 2 [5,4,2,3,1] => 2 [5,4,3,1,2] => 2 [5,4,3,2,1] => 2 ----------------------------------------------------------------------------- Created: Feb 20, 2020 at 16:09 by Kathrin Meier ----------------------------------------------------------------------------- Last Updated: Feb 09, 2021 at 17:46 by Martin Rubey