***************************************************************************** * 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: St000276 ----------------------------------------------------------------------------- Collection: Graphs ----------------------------------------------------------------------------- Description: The size of the preimage of the map 'to graph' from Ordered trees to Graphs. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: @cached_function def preimages(level): result = dict() for el in OrderedTrees(level): image = el.to_undirected_graph().canonical_label().copy(immutable=True) result[image] = result.get(image, 0) + 1 return result def statistic(x): return preimages(x.num_verts()).get(x.canonical_label().copy(immutable=True), 0) ----------------------------------------------------------------------------- Statistic values: ([],1) => 1 ([],2) => 0 ([(0,1)],2) => 1 ([],3) => 0 ([(1,2)],3) => 0 ([(0,2),(1,2)],3) => 2 ([(0,1),(0,2),(1,2)],3) => 0 ([],4) => 0 ([(2,3)],4) => 0 ([(1,3),(2,3)],4) => 0 ([(0,3),(1,3),(2,3)],4) => 2 ([(0,3),(1,2)],4) => 0 ([(0,3),(1,2),(2,3)],4) => 3 ([(1,2),(1,3),(2,3)],4) => 0 ([(0,3),(1,2),(1,3),(2,3)],4) => 0 ([(0,2),(0,3),(1,2),(1,3)],4) => 0 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0 ([],5) => 0 ([(3,4)],5) => 0 ([(2,4),(3,4)],5) => 0 ([(1,4),(2,4),(3,4)],5) => 0 ([(0,4),(1,4),(2,4),(3,4)],5) => 2 ([(1,4),(2,3)],5) => 0 ([(1,4),(2,3),(3,4)],5) => 0 ([(0,1),(2,4),(3,4)],5) => 0 ([(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,4),(2,3),(3,4)],5) => 8 ([(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(1,3),(1,4),(2,3),(2,4)],5) => 0 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 0 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 0 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,3),(2,3),(2,4)],5) => 4 ([(0,1),(2,3),(2,4),(3,4)],5) => 0 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 0 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 0 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 0 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 0 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 0 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 0 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 0 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([],6) => 0 ([(4,5)],6) => 0 ([(3,5),(4,5)],6) => 0 ([(2,5),(3,5),(4,5)],6) => 0 ([(1,5),(2,5),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2 ([(2,5),(3,4)],6) => 0 ([(2,5),(3,4),(4,5)],6) => 0 ([(1,2),(3,5),(4,5)],6) => 0 ([(3,4),(3,5),(4,5)],6) => 0 ([(1,5),(2,5),(3,4),(4,5)],6) => 0 ([(0,1),(2,5),(3,5),(4,5)],6) => 0 ([(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 10 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,5),(2,4),(3,4)],6) => 0 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 10 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 5 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,3)],6) => 0 ([(1,5),(2,4),(3,4),(3,5)],6) => 0 ([(0,1),(2,5),(3,4),(4,5)],6) => 0 ([(1,2),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 10 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 0 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 0 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 0 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 0 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 0 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 0 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 0 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 0 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 0 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 0 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => 0 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 0 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 0 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 0 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 0 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 0 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 0 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 0 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 0 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 0 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => 0 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 0 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ----------------------------------------------------------------------------- Created: Sep 10, 2015 at 14:57 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Sep 10, 2015 at 14:57 by Martin Rubey