***************************************************************************** * 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: St001569 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The maximal modular displacement of a permutation. This is $\max_{1\leq i \leq n} \left(\min(\pi(i)-i\pmod n, i-\pi(i)\pmod n)\right)$ for a permutation $\pi$ of $\{1,\dots,n\}$. ----------------------------------------------------------------------------- References: [1] lemon314 Permutations with bounded displacement on a circle [[MathOverflow:366137]] ----------------------------------------------------------------------------- Code: def statistic(pi): n = len(pi) return max(min((e-1-i)%n,(i-e+1)%n) for i,e in enumerate(pi)) ----------------------------------------------------------------------------- Statistic values: [1,2] => 0 [2,1] => 1 [1,2,3] => 0 [1,3,2] => 1 [2,1,3] => 1 [2,3,1] => 1 [3,1,2] => 1 [3,2,1] => 1 [1,2,3,4] => 0 [1,2,4,3] => 1 [1,3,2,4] => 1 [1,3,4,2] => 2 [1,4,2,3] => 2 [1,4,3,2] => 2 [2,1,3,4] => 1 [2,1,4,3] => 1 [2,3,1,4] => 2 [2,3,4,1] => 1 [2,4,1,3] => 2 [2,4,3,1] => 2 [3,1,2,4] => 2 [3,1,4,2] => 2 [3,2,1,4] => 2 [3,2,4,1] => 2 [3,4,1,2] => 2 [3,4,2,1] => 2 [4,1,2,3] => 1 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 1 [4,3,1,2] => 2 [4,3,2,1] => 1 [1,2,3,4,5] => 0 [1,2,3,5,4] => 1 [1,2,4,3,5] => 1 [1,2,4,5,3] => 2 [1,2,5,3,4] => 2 [1,2,5,4,3] => 2 [1,3,2,4,5] => 1 [1,3,2,5,4] => 1 [1,3,4,2,5] => 2 [1,3,4,5,2] => 2 [1,3,5,2,4] => 2 [1,3,5,4,2] => 2 [1,4,2,3,5] => 2 [1,4,2,5,3] => 2 [1,4,3,2,5] => 2 [1,4,3,5,2] => 2 [1,4,5,2,3] => 2 [1,4,5,3,2] => 2 [1,5,2,3,4] => 2 [1,5,2,4,3] => 2 [1,5,3,2,4] => 2 [1,5,3,4,2] => 2 [1,5,4,2,3] => 2 [1,5,4,3,2] => 2 [2,1,3,4,5] => 1 [2,1,3,5,4] => 1 [2,1,4,3,5] => 1 [2,1,4,5,3] => 2 [2,1,5,3,4] => 2 [2,1,5,4,3] => 2 [2,3,1,4,5] => 2 [2,3,1,5,4] => 2 [2,3,4,1,5] => 2 [2,3,4,5,1] => 1 [2,3,5,1,4] => 2 [2,3,5,4,1] => 2 [2,4,1,3,5] => 2 [2,4,1,5,3] => 2 [2,4,3,1,5] => 2 [2,4,3,5,1] => 2 [2,4,5,1,3] => 2 [2,4,5,3,1] => 2 [2,5,1,3,4] => 2 [2,5,1,4,3] => 2 [2,5,3,1,4] => 2 [2,5,3,4,1] => 2 [2,5,4,1,3] => 2 [2,5,4,3,1] => 2 [3,1,2,4,5] => 2 [3,1,2,5,4] => 2 [3,1,4,2,5] => 2 [3,1,4,5,2] => 2 [3,1,5,2,4] => 2 [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] => 2 [3,4,1,2,5] => 2 [3,4,1,5,2] => 2 [3,4,2,1,5] => 2 [3,4,2,5,1] => 2 [3,4,5,1,2] => 2 [3,4,5,2,1] => 2 [3,5,1,2,4] => 2 [3,5,1,4,2] => 2 [3,5,2,1,4] => 2 [3,5,2,4,1] => 2 [3,5,4,1,2] => 2 [3,5,4,2,1] => 2 [4,1,2,3,5] => 2 [4,1,2,5,3] => 2 [4,1,3,2,5] => 2 [4,1,3,5,2] => 2 [4,1,5,2,3] => 2 [4,1,5,3,2] => 2 [4,2,1,3,5] => 2 [4,2,1,5,3] => 2 [4,2,3,1,5] => 2 [4,2,3,5,1] => 2 [4,2,5,1,3] => 2 [4,2,5,3,1] => 2 [4,3,1,2,5] => 2 [4,3,1,5,2] => 2 [4,3,2,1,5] => 2 [4,3,2,5,1] => 2 [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] => 2 [5,1,3,2,4] => 2 [5,1,3,4,2] => 2 [5,1,4,2,3] => 2 [5,1,4,3,2] => 2 [5,2,1,3,4] => 2 [5,2,1,4,3] => 2 [5,2,3,1,4] => 2 [5,2,3,4,1] => 1 [5,2,4,1,3] => 2 [5,2,4,3,1] => 1 [5,3,1,2,4] => 2 [5,3,1,4,2] => 2 [5,3,2,1,4] => 2 [5,3,2,4,1] => 1 [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: Jul 21, 2020 at 21:37 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jul 21, 2020 at 21:37 by Martin Rubey