***************************************************************************** * 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: St000180 ----------------------------------------------------------------------------- Collection: Posets ----------------------------------------------------------------------------- Description: The number of chains of a poset. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(P): return len(list(P.chains())) ----------------------------------------------------------------------------- Statistic values: ([],1) => 2 ([],2) => 3 ([(0,1)],2) => 4 ([],3) => 4 ([(1,2)],3) => 5 ([(0,1),(0,2)],3) => 6 ([(0,2),(2,1)],3) => 8 ([(0,2),(1,2)],3) => 6 ([],4) => 5 ([(2,3)],4) => 6 ([(1,2),(1,3)],4) => 7 ([(0,1),(0,2),(0,3)],4) => 8 ([(0,2),(0,3),(3,1)],4) => 10 ([(0,1),(0,2),(1,3),(2,3)],4) => 12 ([(1,2),(2,3)],4) => 9 ([(0,3),(3,1),(3,2)],4) => 12 ([(1,3),(2,3)],4) => 7 ([(0,3),(1,3),(3,2)],4) => 12 ([(0,3),(1,3),(2,3)],4) => 8 ([(0,3),(1,2)],4) => 7 ([(0,3),(1,2),(1,3)],4) => 8 ([(0,2),(0,3),(1,2),(1,3)],4) => 9 ([(0,3),(2,1),(3,2)],4) => 16 ([(0,3),(1,2),(2,3)],4) => 10 ([],5) => 6 ([(3,4)],5) => 7 ([(2,3),(2,4)],5) => 8 ([(1,2),(1,3),(1,4)],5) => 9 ([(0,1),(0,2),(0,3),(0,4)],5) => 10 ([(0,2),(0,3),(0,4),(4,1)],5) => 12 ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 14 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 16 ([(1,3),(1,4),(4,2)],5) => 11 ([(0,3),(0,4),(4,1),(4,2)],5) => 14 ([(1,2),(1,3),(2,4),(3,4)],5) => 13 ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 24 ([(0,3),(0,4),(3,2),(4,1)],5) => 14 ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 16 ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 18 ([(2,3),(3,4)],5) => 10 ([(1,4),(4,2),(4,3)],5) => 13 ([(0,4),(4,1),(4,2),(4,3)],5) => 16 ([(2,4),(3,4)],5) => 8 ([(1,4),(2,4),(4,3)],5) => 13 ([(0,4),(1,4),(4,2),(4,3)],5) => 18 ([(1,4),(2,4),(3,4)],5) => 9 ([(0,4),(1,4),(2,4),(4,3)],5) => 16 ([(0,4),(1,4),(2,4),(3,4)],5) => 10 ([(0,4),(1,4),(2,3)],5) => 9 ([(0,4),(1,3),(2,3),(2,4)],5) => 10 ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 11 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 12 ([(0,4),(1,4),(2,3),(4,2)],5) => 24 ([(0,4),(1,3),(2,3),(3,4)],5) => 14 ([(0,4),(1,4),(2,3),(2,4)],5) => 10 ([(0,4),(1,4),(2,3),(3,4)],5) => 12 ([(1,4),(2,3)],5) => 8 ([(1,4),(2,3),(2,4)],5) => 9 ([(0,4),(1,2),(1,4),(2,3)],5) => 12 ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 16 ([(1,3),(1,4),(2,3),(2,4)],5) => 10 ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 15 ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 18 ([(0,4),(1,2),(1,4),(4,3)],5) => 14 ([(0,4),(1,2),(1,3)],5) => 9 ([(0,4),(1,2),(1,3),(1,4)],5) => 10 ([(0,2),(0,4),(3,1),(4,3)],5) => 18 ([(0,4),(1,2),(1,3),(3,4)],5) => 12 ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 20 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 14 ([(0,3),(0,4),(1,2),(1,4)],5) => 10 ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 11 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 12 ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 13 ([(0,3),(1,2),(1,4),(3,4)],5) => 12 ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 15 ([(1,4),(3,2),(4,3)],5) => 17 ([(0,3),(3,4),(4,1),(4,2)],5) => 24 ([(1,4),(2,3),(3,4)],5) => 11 ([(0,4),(1,2),(2,4),(4,3)],5) => 20 ([(0,3),(1,4),(4,2)],5) => 11 ([(0,4),(3,2),(4,1),(4,3)],5) => 20 ([(0,4),(1,2),(2,3),(2,4)],5) => 14 ([(0,4),(2,3),(3,1),(4,2)],5) => 32 ([(0,3),(1,2),(2,4),(3,4)],5) => 14 ([(0,4),(1,2),(2,3),(3,4)],5) => 18 ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 24 ([],6) => 7 ([(4,5)],6) => 8 ([(3,4),(3,5)],6) => 9 ([(2,3),(2,4),(2,5)],6) => 10 ([(1,2),(1,3),(1,4),(1,5)],6) => 11 ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 12 ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 14 ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 16 ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 18 ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 20 ([(1,3),(1,4),(1,5),(5,2)],6) => 13 ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 16 ([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 15 ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 17 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 32 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 24 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 28 ([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => 26 ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 16 ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => 20 ([(2,3),(2,4),(4,5)],6) => 12 ([(1,4),(1,5),(5,2),(5,3)],6) => 15 ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 18 ([(2,3),(2,4),(3,5),(4,5)],6) => 14 ([(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 25 ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => 36 ([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 19 ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => 30 ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 36 ([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => 28 ([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => 18 ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 24 ([(3,4),(4,5)],6) => 11 ([(2,3),(3,4),(3,5)],6) => 14 ([(1,5),(5,2),(5,3),(5,4)],6) => 17 ([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 20 ([(2,3),(3,5),(5,4)],6) => 18 ([(1,4),(4,5),(5,2),(5,3)],6) => 25 ([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 32 ([(3,5),(4,5)],6) => 9 ([(2,5),(3,5),(5,4)],6) => 14 ([(1,5),(2,5),(5,3),(5,4)],6) => 19 ([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => 24 ([(2,5),(3,5),(4,5)],6) => 10 ([(1,5),(2,5),(3,5),(5,4)],6) => 17 ([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => 24 ([(1,5),(2,5),(3,5),(4,5)],6) => 11 ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 20 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 12 ([(0,5),(1,5),(2,5),(3,4)],6) => 11 ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 32 ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 18 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 14 ([(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) => 16 ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 20 ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12 ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 22 ([(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) => 20 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 24 ([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 19 ([(1,5),(2,5),(3,4),(5,3)],6) => 25 ([(1,5),(2,4),(3,4),(4,5)],6) => 15 ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 28 ([(0,5),(1,5),(2,3),(5,4)],6) => 15 ([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => 30 ([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => 36 ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 21 ([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => 26 ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 28 ([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 22 ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 28 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 16 ([(1,5),(2,5),(3,4),(4,5)],6) => 13 ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 24 ([(0,5),(1,5),(2,3),(3,4)],6) => 13 ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 48 ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 18 ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 28 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 20 ([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 26 ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 32 ([(0,5),(1,5),(2,4),(3,4)],6) => 11 ([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 12 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 13 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 14 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 15 ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 26 ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 36 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 16 ([(2,5),(3,4)],6) => 9 ([(2,5),(3,4),(3,5)],6) => 10 ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => 20 ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => 24 ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 17 ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => 32 ([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => 18 ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => 22 ([(2,4),(2,5),(3,4),(3,5)],6) => 11 ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 16 ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => 21 ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 19 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => 21 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => 24 ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => 27 ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => 27 ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => 36 ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => 30 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 20 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) => 15 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 18 ([(1,5),(2,3),(2,5),(5,4)],6) => 15 ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 20 ([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) => 22 ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 24 ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 18 ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 20 ([(1,3),(1,5),(4,2),(5,4)],6) => 19 ([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 26 ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 22 ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 24 ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 32 ([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => 24 ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => 26 ([(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 21 ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 40 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 15 ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 28 ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 22 ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 36 ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 48 ([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 26 ([(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) => 18 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => 21 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 24 ([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => 19 ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => 23 ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => 26 ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 21 ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => 21 ([(0,4),(0,5),(1,2),(1,3)],6) => 11 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => 13 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 15 ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => 30 ([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => 28 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 21 ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) => 17 ([(1,4),(2,3),(2,5),(4,5)],6) => 13 ([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => 22 ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 16 ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => 25 ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 30 ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => 16 ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => 24 ([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => 19 ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 34 ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 28 ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => 23 ([(2,5),(3,4),(4,5)],6) => 12 ([(1,5),(2,3),(3,5),(5,4)],6) => 21 ([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => 30 ([(1,3),(2,4),(4,5)],6) => 12 ([(1,5),(4,3),(5,2),(5,4)],6) => 21 ([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => 24 ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 24 ([(1,5),(3,4),(4,2),(5,3)],6) => 33 ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 48 ([(1,4),(2,3),(3,5),(4,5)],6) => 15 ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 28 ([(0,5),(1,4),(4,2),(5,3)],6) => 15 ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 36 ([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => 18 ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => 21 ([(1,5),(2,3),(3,4),(4,5)],6) => 19 ([(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 25 ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 48 ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 36 ([(0,5),(1,4),(2,3)],6) => 10 ([(0,5),(1,3),(2,4),(2,5)],6) => 11 ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => 20 ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 24 ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => 28 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 18 ([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => 26 ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 12 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 16 ([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6) => 17 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 13 ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 14 ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => 20 ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => 27 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => 36 ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => 32 ([(0,5),(1,3),(4,2),(5,4)],6) => 19 ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 28 ([(0,5),(1,4),(3,2),(4,3),(4,5)],6) => 22 ([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => 28 ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 40 ([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => 26 ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 64 ([(0,5),(1,3),(2,4),(4,5)],6) => 13 ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 40 ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 22 ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 34 ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 48 ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 22 ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 40 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 16 ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => 14 ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => 16 ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => 18 ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => 18 ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => 20 ([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => 20 ([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7) => 20 ([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7) => 22 ([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7) => 22 ([(0,5),(0,6),(5,3),(5,4),(6,1),(6,2)],7) => 22 ([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7) => 24 ([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7) => 40 ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 24 ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 14 ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 40 ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 22 ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 16 ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 28 ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 64 ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 36 ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 22 ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 36 ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 22 ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 34 ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 20 ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 28 ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 18 ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 36 ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 68 ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 40 ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 96 ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 26 ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 52 ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 32 ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => 22 ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 56 ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 30 ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 48 ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 26 ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 18 ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 50 ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 30 ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 20 ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 42 ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 24 ([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => 22 ([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7) => 28 ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7) => 24 ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7) => 24 ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7) => 36 ([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7) => 34 ([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7) => 30 ([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7) => 26 ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7) => 26 ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7) => 38 ([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7) => 44 ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7) => 26 ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7) => 30 ([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7) => 50 ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 38 ([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7) => 36 ([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7) => 32 ([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7) => 28 ([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7) => 64 ([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7) => 40 ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7) => 52 ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 44 ([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7) => 30 ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7) => 42 ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => 30 ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 66 ([(0,6),(4,3),(5,1),(5,2),(6,4),(6,5)],7) => 36 ([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7) => 56 ([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7) => 48 ([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7) => 96 ([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7) => 72 ([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7) => 68 ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 32 ([(0,6),(4,3),(5,2),(6,1),(6,4),(6,5)],7) => 32 ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7) => 56 ([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => 80 ([(0,6),(3,4),(4,1),(5,2),(6,3),(6,5)],7) => 44 ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 128 ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 80 ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 44 ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 26 ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 24 ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 38 ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 20 ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 56 ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 30 ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 72 ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 38 ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 66 ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 30 ([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8) => 81 ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8) => 45 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 45 ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8) => 33 ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 21 ([(0,6),(0,7),(1,6),(1,7),(6,2),(6,3),(6,4),(6,5),(7,2),(7,3),(7,4),(7,5)],8) => 45 ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => 25 ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,2),(6,3),(7,2),(7,3)],8) => 33 ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 17 ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8) => 21 ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => 17 ([(4,6),(4,7),(5,6),(5,7)],8) => 13 ([],8) => 9 ([(0,3),(1,2),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8) => 63 ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8) => 45 ([(0,3),(0,7),(1,2),(1,6),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8) => 51 ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(6,3),(7,2)],8) => 63 ([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8) => 31 ([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8) => 33 ([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8) => 37 ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8) => 45 ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4)],8) => 51 ([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8) => 41 ([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8) => 37 ([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8) => 49 ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(6,5),(7,4),(7,5)],8) => 63 ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8) => 39 ([(0,7),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8) => 31 ([(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8) => 29 ([(2,5),(3,4),(4,6),(4,7),(5,6),(5,7)],8) => 23 ([(0,7),(1,6),(2,5),(3,4),(4,6),(4,7),(5,6),(5,7)],8) => 25 ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(4,6),(4,7),(5,6),(5,7)],8) => 27 ([(0,5),(1,5),(2,4),(3,4),(4,6),(4,7),(5,6),(5,7)],8) => 33 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 39 ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 33 ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 19 ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => 15 ([(0,7),(1,7),(2,6),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => 17 ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(4,6),(5,7)],8) => 21 ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6),(4,7),(5,6)],8) => 23 ([(0,3),(0,5),(1,2),(1,4),(2,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 29 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 35 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => 39 ([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(6,4),(6,5),(7,4),(7,5)],8) => 31 ([(0,3),(0,5),(1,2),(1,4),(4,6),(4,7),(5,6),(5,7)],8) => 25 ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7)],8) => 19 ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6)],8) => 17 ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8) => 15 ([(4,7),(5,6)],8) => 11 ([(0,7),(1,6),(2,5),(3,4)],8) => 13 ([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8) => 15 ([(0,5),(0,7),(1,4),(1,6),(6,2),(7,3)],8) => 19 ([(0,3),(0,5),(0,7),(1,2),(1,4),(1,6),(4,7),(5,6)],8) => 21 ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(6,3),(7,2)],8) => 25 ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,3),(7,2)],8) => 27 ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(4,3),(5,3),(6,2),(7,2)],8) => 33 ([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(2,4),(3,5),(6,4),(7,5)],8) => 29 ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,7),(3,7),(4,6),(5,6)],8) => 25 ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,7),(5,7)],8) => 23 ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8) => 19 ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => 15 ([(2,7),(3,7),(4,6),(5,6)],8) => 13 ([(2,5),(3,4),(4,6),(5,7)],8) => 17 ([(0,6),(1,6),(2,7),(3,7),(6,5),(7,4)],8) => 23 ([(0,5),(0,7),(1,5),(1,7),(2,4),(2,6),(3,4),(3,6),(4,7),(5,6)],8) => 27 ([(0,5),(1,4),(2,4),(2,7),(3,5),(3,6),(4,6),(5,7)],8) => 25 ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,6),(5,7)],8) => 21 ([(2,5),(2,7),(3,4),(3,6),(4,7),(5,6)],8) => 19 ([(2,6),(2,7),(3,6),(3,7),(6,5),(7,4)],8) => 23 ([(0,7),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,7)],8) => 25 ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(6,4),(7,5)],8) => 29 ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6),(6,5),(7,4)],8) => 31 ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,5),(7,4)],8) => 35 ([(0,3),(1,2),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => 35 ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => 23 ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => 21 ([(0,7),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => 19 ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7)],8) => 15 ([(0,5),(1,4),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7)],8) => 17 ([(0,5),(0,7),(1,4),(1,6),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7)],8) => 19 ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7)],8) => 21 ([(0,5),(1,4),(4,2),(4,6),(4,7),(5,3),(5,6),(5,7)],8) => 29 ([(0,3),(0,7),(1,2),(1,6),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6)],8) => 31 ([(0,6),(0,7),(1,6),(1,7),(6,3),(6,4),(6,5),(7,2),(7,4),(7,5)],8) => 39 ([(0,6),(0,7),(1,6),(1,7),(6,4),(6,5),(7,2),(7,3)],8) => 33 ([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,6),(2,7),(3,4),(3,5)],8) => 27 ([(0,5),(0,7),(1,4),(1,6),(4,2),(4,7),(5,3),(5,6)],8) => 25 ([(0,7),(1,6),(6,2),(6,3),(7,4),(7,5)],8) => 23 ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7)],8) => 17 ([(2,6),(2,7),(3,4),(3,5)],8) => 13 ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(4,2),(5,3)],8) => 21 ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,5),(3,4)],8) => 23 ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7)],8) => 19 ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7)],8) => 17 ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4)],8) => 15 ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => 62 ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,8),(6,8),(8,7)],9) => 46 ([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9) => 38 ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => 126 ([(0,9),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,10),(8,9),(10,8)],11) => 94 ([(0,8),(1,9),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,10),(10,9)],11) => 78 ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => 70 ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,9),(8,9),(9,10)],11) => 54 ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,8),(7,9),(8,10),(9,10)],11) => 54 ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => 254 ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13) => 190 ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => 158 ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,11),(9,12),(11,9),(12,10)],13) => 142 ([(0,10),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,12),(8,11),(9,11),(11,12),(12,10)],13) => 110 ([(0,7),(1,7),(2,8),(3,8),(4,11),(5,10),(6,9),(7,10),(8,11),(10,12),(11,12),(12,9)],13) => 110 ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13) => 134 ([(0,10),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,12),(8,11),(9,11),(10,12),(11,10)],13) => 102 ([(0,10),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(7,12),(8,11),(9,10),(10,12),(12,11)],13) => 86 ([(0,7),(1,7),(2,8),(3,8),(4,9),(5,10),(6,11),(7,10),(8,11),(9,12),(10,12),(11,9)],13) => 86 ([(0,10),(1,8),(2,8),(3,7),(4,7),(5,9),(6,9),(7,11),(8,11),(9,10),(10,12),(11,12)],13) => 70 ----------------------------------------------------------------------------- Created: Apr 22, 2014 at 08:19 by Stephen Anderson ----------------------------------------------------------------------------- Last Updated: Jun 20, 2018 at 16:44 by Martin Rubey