***************************************************************************** * 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: St000327 ----------------------------------------------------------------------------- Collection: Posets ----------------------------------------------------------------------------- Description: The number of cover relations in a poset. Equivalently, this is also the number of edges in the Hasse diagram [1]. ----------------------------------------------------------------------------- References: [1] [[wikipedia:Hasse_diagram]] ----------------------------------------------------------------------------- Code: def statistic(P): return len(P.cover_relations()) ----------------------------------------------------------------------------- Statistic values: ([],2) => 0 ([(0,1)],2) => 1 ([],3) => 0 ([(1,2)],3) => 1 ([(0,1),(0,2)],3) => 2 ([(0,2),(2,1)],3) => 2 ([(0,2),(1,2)],3) => 2 ([],4) => 0 ([(2,3)],4) => 1 ([(1,2),(1,3)],4) => 2 ([(0,1),(0,2),(0,3)],4) => 3 ([(0,2),(0,3),(3,1)],4) => 3 ([(0,1),(0,2),(1,3),(2,3)],4) => 4 ([(1,2),(2,3)],4) => 2 ([(0,3),(3,1),(3,2)],4) => 3 ([(1,3),(2,3)],4) => 2 ([(0,3),(1,3),(3,2)],4) => 3 ([(0,3),(1,3),(2,3)],4) => 3 ([(0,3),(1,2)],4) => 2 ([(0,3),(1,2),(1,3)],4) => 3 ([(0,2),(0,3),(1,2),(1,3)],4) => 4 ([(0,3),(2,1),(3,2)],4) => 3 ([(0,3),(1,2),(2,3)],4) => 3 ([],5) => 0 ([(3,4)],5) => 1 ([(2,3),(2,4)],5) => 2 ([(1,2),(1,3),(1,4)],5) => 3 ([(0,1),(0,2),(0,3),(0,4)],5) => 4 ([(0,2),(0,3),(0,4),(4,1)],5) => 4 ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 5 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 6 ([(1,3),(1,4),(4,2)],5) => 3 ([(0,3),(0,4),(4,1),(4,2)],5) => 4 ([(1,2),(1,3),(2,4),(3,4)],5) => 4 ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 5 ([(0,3),(0,4),(3,2),(4,1)],5) => 4 ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 5 ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 6 ([(2,3),(3,4)],5) => 2 ([(1,4),(4,2),(4,3)],5) => 3 ([(0,4),(4,1),(4,2),(4,3)],5) => 4 ([(2,4),(3,4)],5) => 2 ([(1,4),(2,4),(4,3)],5) => 3 ([(0,4),(1,4),(4,2),(4,3)],5) => 4 ([(1,4),(2,4),(3,4)],5) => 3 ([(0,4),(1,4),(2,4),(4,3)],5) => 4 ([(0,4),(1,4),(2,4),(3,4)],5) => 4 ([(0,4),(1,4),(2,3)],5) => 3 ([(0,4),(1,3),(2,3),(2,4)],5) => 4 ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 5 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 6 ([(0,4),(1,4),(2,3),(4,2)],5) => 4 ([(0,4),(1,3),(2,3),(3,4)],5) => 4 ([(0,4),(1,4),(2,3),(2,4)],5) => 4 ([(0,4),(1,4),(2,3),(3,4)],5) => 4 ([(1,4),(2,3)],5) => 2 ([(1,4),(2,3),(2,4)],5) => 3 ([(0,4),(1,2),(1,4),(2,3)],5) => 4 ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 5 ([(1,3),(1,4),(2,3),(2,4)],5) => 4 ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 5 ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 6 ([(0,4),(1,2),(1,4),(4,3)],5) => 4 ([(0,4),(1,2),(1,3)],5) => 3 ([(0,4),(1,2),(1,3),(1,4)],5) => 4 ([(0,2),(0,4),(3,1),(4,3)],5) => 4 ([(0,4),(1,2),(1,3),(3,4)],5) => 4 ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 5 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 5 ([(0,3),(0,4),(1,2),(1,4)],5) => 4 ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 5 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 6 ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 5 ([(0,3),(1,2),(1,4),(3,4)],5) => 4 ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 5 ([(1,4),(3,2),(4,3)],5) => 3 ([(0,3),(3,4),(4,1),(4,2)],5) => 4 ([(1,4),(2,3),(3,4)],5) => 3 ([(0,4),(1,2),(2,4),(4,3)],5) => 4 ([(0,3),(1,4),(4,2)],5) => 3 ([(0,4),(3,2),(4,1),(4,3)],5) => 4 ([(0,4),(1,2),(2,3),(2,4)],5) => 4 ([(0,4),(2,3),(3,1),(4,2)],5) => 4 ([(0,3),(1,2),(2,4),(3,4)],5) => 4 ([(0,4),(1,2),(2,3),(3,4)],5) => 4 ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 5 ----------------------------------------------------------------------------- Created: Dec 13, 2015 at 01:36 by Daniel Shira ----------------------------------------------------------------------------- Last Updated: Dec 13, 2015 at 07:44 by Christian Stump