***************************************************************************** * 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: St000104 ----------------------------------------------------------------------------- Collection: Posets ----------------------------------------------------------------------------- Description: The number of facets in the order polytope of this poset. ----------------------------------------------------------------------------- References: [1] Stanley, R. P. Two poset polytopes [[MathSciNet:0824105]] ----------------------------------------------------------------------------- Code: def statistic(P): return P.order_polytope().n_facets() ----------------------------------------------------------------------------- Statistic values: ([],1) => 2 ([],2) => 4 ([(0,1)],2) => 3 ([],3) => 6 ([(1,2)],3) => 5 ([(0,1),(0,2)],3) => 5 ([(0,2),(2,1)],3) => 4 ([(0,2),(1,2)],3) => 5 ([],4) => 8 ([(2,3)],4) => 7 ([(1,2),(1,3)],4) => 7 ([(0,1),(0,2),(0,3)],4) => 7 ([(0,2),(0,3),(3,1)],4) => 6 ([(0,1),(0,2),(1,3),(2,3)],4) => 6 ([(1,2),(2,3)],4) => 6 ([(0,3),(3,1),(3,2)],4) => 6 ([(1,3),(2,3)],4) => 7 ([(0,3),(1,3),(3,2)],4) => 6 ([(0,3),(1,3),(2,3)],4) => 7 ([(0,3),(1,2)],4) => 6 ([(0,3),(1,2),(1,3)],4) => 7 ([(0,2),(0,3),(1,2),(1,3)],4) => 8 ([(0,3),(2,1),(3,2)],4) => 5 ([(0,3),(1,2),(2,3)],4) => 6 ([],5) => 10 ([(3,4)],5) => 9 ([(2,3),(2,4)],5) => 9 ([(1,2),(1,3),(1,4)],5) => 9 ([(0,1),(0,2),(0,3),(0,4)],5) => 9 ([(0,2),(0,3),(0,4),(4,1)],5) => 8 ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 8 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 8 ([(1,3),(1,4),(4,2)],5) => 8 ([(0,3),(0,4),(4,1),(4,2)],5) => 8 ([(1,2),(1,3),(2,4),(3,4)],5) => 8 ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 7 ([(0,3),(0,4),(3,2),(4,1)],5) => 7 ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8 ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 9 ([(2,3),(3,4)],5) => 8 ([(1,4),(4,2),(4,3)],5) => 8 ([(0,4),(4,1),(4,2),(4,3)],5) => 8 ([(2,4),(3,4)],5) => 9 ([(1,4),(2,4),(4,3)],5) => 8 ([(0,4),(1,4),(4,2),(4,3)],5) => 8 ([(1,4),(2,4),(3,4)],5) => 9 ([(0,4),(1,4),(2,4),(4,3)],5) => 8 ([(0,4),(1,4),(2,4),(3,4)],5) => 9 ([(0,4),(1,4),(2,3)],5) => 8 ([(0,4),(1,3),(2,3),(2,4)],5) => 9 ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 10 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 11 ([(0,4),(1,4),(2,3),(4,2)],5) => 7 ([(0,4),(1,3),(2,3),(3,4)],5) => 8 ([(0,4),(1,4),(2,3),(2,4)],5) => 9 ([(0,4),(1,4),(2,3),(3,4)],5) => 8 ([(1,4),(2,3)],5) => 8 ([(1,4),(2,3),(2,4)],5) => 9 ([(0,4),(1,2),(1,4),(2,3)],5) => 8 ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 8 ([(1,3),(1,4),(2,3),(2,4)],5) => 10 ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 9 ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 9 ([(0,4),(1,2),(1,4),(4,3)],5) => 8 ([(0,4),(1,2),(1,3)],5) => 8 ([(0,4),(1,2),(1,3),(1,4)],5) => 9 ([(0,2),(0,4),(3,1),(4,3)],5) => 7 ([(0,4),(1,2),(1,3),(3,4)],5) => 8 ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 7 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 8 ([(0,3),(0,4),(1,2),(1,4)],5) => 9 ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 10 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 11 ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 9 ([(0,3),(1,2),(1,4),(3,4)],5) => 8 ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 9 ([(1,4),(3,2),(4,3)],5) => 7 ([(0,3),(3,4),(4,1),(4,2)],5) => 7 ([(1,4),(2,3),(3,4)],5) => 8 ([(0,4),(1,2),(2,4),(4,3)],5) => 7 ([(0,3),(1,4),(4,2)],5) => 7 ([(0,4),(3,2),(4,1),(4,3)],5) => 7 ([(0,4),(1,2),(2,3),(2,4)],5) => 8 ([(0,4),(2,3),(3,1),(4,2)],5) => 6 ([(0,3),(1,2),(2,4),(3,4)],5) => 7 ([(0,4),(1,2),(2,3),(3,4)],5) => 7 ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 7 ([],6) => 12 ([(4,5)],6) => 11 ([(3,4),(3,5)],6) => 11 ([(2,3),(2,4),(2,5)],6) => 11 ([(1,2),(1,3),(1,4),(1,5)],6) => 11 ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 11 ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 10 ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 10 ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 10 ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 10 ([(1,3),(1,4),(1,5),(5,2)],6) => 10 ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 10 ([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 10 ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 10 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 9 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6) => 9 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6) => 10 ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 11 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => 10 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 9 ([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => 9 ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 9 ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => 10 ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => 11 ([(2,3),(2,4),(4,5)],6) => 10 ([(1,4),(1,5),(5,2),(5,3)],6) => 10 ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 10 ([(2,3),(2,4),(3,5),(4,5)],6) => 10 ([(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 9 ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => 9 ([(1,4),(1,5),(4,3),(5,2)],6) => 9 ([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 10 ([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 11 ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => 10 ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 10 ([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => 9 ([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => 9 ([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => 10 ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10 ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => 11 ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 12 ([(3,4),(4,5)],6) => 10 ([(2,3),(3,4),(3,5)],6) => 10 ([(1,5),(5,2),(5,3),(5,4)],6) => 10 ([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 10 ([(2,3),(3,5),(5,4)],6) => 9 ([(1,4),(4,5),(5,2),(5,3)],6) => 9 ([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 9 ([(3,5),(4,5)],6) => 11 ([(2,5),(3,5),(5,4)],6) => 10 ([(1,5),(2,5),(5,3),(5,4)],6) => 10 ([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => 10 ([(2,5),(3,5),(4,5)],6) => 11 ([(1,5),(2,5),(3,5),(5,4)],6) => 10 ([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => 10 ([(1,5),(2,5),(3,5),(4,5)],6) => 11 ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 10 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 11 ([(0,5),(1,5),(2,5),(3,4)],6) => 10 ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 9 ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 10 ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 11 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 10 ([(1,5),(2,5),(3,4)],6) => 10 ([(1,5),(2,4),(3,4),(3,5)],6) => 11 ([(0,5),(1,4),(2,4),(2,5),(5,3)],6) => 10 ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 10 ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12 ([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6) => 11 ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 11 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 13 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 12 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 12 ([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 11 ([(1,5),(2,5),(3,4),(5,3)],6) => 9 ([(1,5),(2,4),(3,4),(4,5)],6) => 10 ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 9 ([(0,5),(1,5),(2,3),(5,4)],6) => 9 ([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => 9 ([(0,5),(1,5),(2,4),(5,3),(5,4)],6) => 10 ([(1,5),(2,5),(3,4),(3,5)],6) => 11 ([(0,5),(1,5),(2,3),(2,5),(5,4)],6) => 10 ([(0,5),(1,5),(2,3),(2,5),(3,4)],6) => 10 ([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 10 ([(0,5),(1,5),(2,3),(2,4)],6) => 10 ([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => 9 ([(0,4),(1,4),(2,3),(2,5),(4,5)],6) => 10 ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 11 ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 11 ([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => 9 ([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => 9 ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 8 ([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 10 ([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 9 ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 9 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 10 ([(1,5),(2,5),(3,4),(4,5)],6) => 10 ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 9 ([(0,5),(1,5),(2,3),(3,4)],6) => 9 ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 8 ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 9 ([(0,5),(1,4),(3,5),(4,2),(4,3)],6) => 9 ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 9 ([(0,5),(1,5),(2,3),(3,4),(3,5)],6) => 10 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 9 ([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 9 ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 9 ([(0,5),(1,5),(2,4),(3,4)],6) => 10 ([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 11 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 12 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 13 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 14 ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 9 ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 9 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 10 ([(2,5),(3,4)],6) => 10 ([(2,5),(3,4),(3,5)],6) => 11 ([(1,5),(2,3),(2,5),(3,4)],6) => 10 ([(0,5),(1,4),(1,5),(4,2),(4,3)],6) => 10 ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => 10 ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => 11 ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 10 ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => 9 ([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => 9 ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => 10 ([(2,4),(2,5),(3,4),(3,5)],6) => 12 ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 11 ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => 11 ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 11 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => 10 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => 11 ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => 12 ([(0,4),(0,5),(1,4),(1,5),(2,3)],6) => 11 ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => 10 ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => 10 ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => 10 ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 11 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 11 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 12 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 12 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 13 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 12 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) => 11 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 12 ([(1,5),(2,3),(2,5),(5,4)],6) => 10 ([(0,5),(1,2),(1,5),(5,3),(5,4)],6) => 10 ([(1,5),(2,3),(2,4)],6) => 10 ([(1,5),(2,3),(2,4),(2,5)],6) => 11 ([(0,5),(1,3),(1,4),(1,5),(4,2)],6) => 10 ([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 10 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 10 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 10 ([(0,5),(1,2),(1,3),(1,5),(5,4)],6) => 10 ([(0,5),(1,2),(1,3),(1,4)],6) => 10 ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 11 ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 9 ([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 10 ([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) => 9 ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 10 ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 9 ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 10 ([(0,4),(1,2),(1,3),(1,5),(4,5)],6) => 10 ([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6) => 11 ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 12 ([(1,3),(1,5),(4,2),(5,4)],6) => 9 ([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 9 ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8 ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9 ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9 ([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => 9 ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => 10 ([(1,5),(2,3),(2,4),(4,5)],6) => 10 ([(0,5),(1,2),(1,3),(3,5),(5,4)],6) => 9 ([(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 9 ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 8 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 10 ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 9 ([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => 9 ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 10 ([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 11 ([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => 9 ([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => 9 ([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 10 ([(0,4),(1,3),(1,5),(5,2)],6) => 9 ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 9 ([(0,5),(1,3),(1,4),(4,2),(4,5)],6) => 10 ([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => 9 ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 8 ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => 9 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 9 ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 8 ([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 9 ([(1,4),(1,5),(2,3),(2,5)],6) => 11 ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 12 ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 11 ([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6) => 11 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 13 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 12 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => 12 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 12 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6) => 11 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 11 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 11 ([(0,4),(0,5),(1,3),(1,5),(5,2)],6) => 10 ([(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 11 ([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => 10 ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => 10 ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => 10 ([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => 10 ([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => 10 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6) => 11 ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 11 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6) => 10 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6) => 10 ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => 10 ([(0,4),(0,5),(1,2),(1,3)],6) => 10 ([(0,4),(0,5),(1,2),(1,3),(1,5)],6) => 11 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 12 ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 11 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 11 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => 12 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 13 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 14 ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 12 ([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6) => 11 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 12 ([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => 10 ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 11 ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => 10 ([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => 9 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6) => 10 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 10 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 11 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 12 ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) => 10 ([(1,4),(2,3),(2,5),(4,5)],6) => 10 ([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => 9 ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 11 ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => 10 ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 10 ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => 9 ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => 9 ([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => 10 ([(0,5),(1,3),(1,4),(5,2)],6) => 9 ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8 ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 9 ([(0,4),(1,3),(1,5),(4,2),(4,5)],6) => 10 ([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6) => 11 ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => 10 ([(2,5),(3,4),(4,5)],6) => 10 ([(1,5),(2,3),(3,5),(5,4)],6) => 9 ([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => 9 ([(1,3),(2,4),(4,5)],6) => 9 ([(1,5),(4,3),(5,2),(5,4)],6) => 9 ([(1,5),(2,3),(3,4),(3,5)],6) => 10 ([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => 9 ([(0,4),(1,5),(5,2),(5,3)],6) => 9 ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 9 ([(0,5),(1,4),(4,2),(4,3),(4,5)],6) => 10 ([(1,5),(3,4),(4,2),(5,3)],6) => 8 ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 8 ([(1,4),(2,3),(3,5),(4,5)],6) => 9 ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 8 ([(0,5),(1,4),(4,2),(5,3)],6) => 8 ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 8 ([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => 9 ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => 10 ([(1,5),(2,3),(3,4),(4,5)],6) => 9 ([(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 9 ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 8 ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 8 ([(0,5),(1,4),(2,3)],6) => 9 ([(0,5),(1,3),(2,4),(2,5)],6) => 10 ([(0,5),(1,4),(2,3),(2,4),(2,5)],6) => 11 ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => 9 ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 9 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 10 ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => 9 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 10 ([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => 9 ([(0,5),(1,4),(2,3),(2,4),(4,5)],6) => 10 ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 11 ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 12 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 13 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6) => 12 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) => 13 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 14 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 15 ([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6) => 11 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 12 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 11 ([(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 11 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 11 ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 10 ([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 11 ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => 9 ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => 10 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => 10 ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => 9 ([(0,5),(1,4),(2,3),(2,5),(4,5)],6) => 10 ([(0,5),(1,3),(4,2),(5,4)],6) => 8 ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 8 ([(0,5),(1,4),(3,2),(4,3),(4,5)],6) => 9 ([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => 9 ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 8 ([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => 9 ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7 ([(0,5),(1,3),(2,4),(4,5)],6) => 9 ([(0,5),(1,4),(2,3),(3,4),(3,5)],6) => 10 ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 8 ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 9 ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 8 ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 8 ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 8 ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 8 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 9 ----------------------------------------------------------------------------- Created: Jun 14, 2013 at 04:03 by Jessica Striker ----------------------------------------------------------------------------- Last Updated: May 29, 2015 at 16:43 by Martin Rubey