***************************************************************************** * 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: St001909 ----------------------------------------------------------------------------- Collection: Posets ----------------------------------------------------------------------------- Description: The number of interval-closed sets of a poset. For a poset $P$ and a subset $I$ of $P$, we say that $I$ is an ''interval-closed'' set if for all $x, y \in I$ such that $x \leq y$, then $z \in I$ if $x \leq z \leq y$. There is a bijection between interval-closed sets of a poset $P$ and pairs of disjoint antichains $(A, B)$ of $P$ such that any element in $B$ is in the order ideal $\Delta(A)$ generated by $A$. (Proposition 2.5 of [1]). ----------------------------------------------------------------------------- References: [1] Elder, J., Lafrenière, N., McNicholas, E., Striker, J., Welch, A. Toggling, rowmotion, and homomesy on interval-closed sets [[arXiv:2307.08520]] ----------------------------------------------------------------------------- Code: def statistic(x): ICS_count = 0 for A in x.antichains_iterator(): I = x.order_ideal(A) Q = x.subposet(set(I).difference(A)) ICS_count += Q.antichains().cardinality() return ICS_count ----------------------------------------------------------------------------- Statistic values: ([],1) => 2 ([],2) => 4 ([(0,1)],2) => 4 ([],3) => 8 ([(1,2)],3) => 8 ([(0,1),(0,2)],3) => 8 ([(0,2),(2,1)],3) => 7 ([(0,2),(1,2)],3) => 8 ([],4) => 16 ([(2,3)],4) => 16 ([(1,2),(1,3)],4) => 16 ([(0,1),(0,2),(0,3)],4) => 16 ([(0,2),(0,3),(3,1)],4) => 14 ([(0,1),(0,2),(1,3),(2,3)],4) => 13 ([(1,2),(2,3)],4) => 14 ([(0,3),(3,1),(3,2)],4) => 13 ([(1,3),(2,3)],4) => 16 ([(0,3),(1,3),(3,2)],4) => 13 ([(0,3),(1,3),(2,3)],4) => 16 ([(0,3),(1,2)],4) => 16 ([(0,3),(1,2),(1,3)],4) => 16 ([(0,2),(0,3),(1,2),(1,3)],4) => 16 ([(0,3),(2,1),(3,2)],4) => 11 ([(0,3),(1,2),(2,3)],4) => 14 ([],5) => 32 ([(3,4)],5) => 32 ([(2,3),(2,4)],5) => 32 ([(1,2),(1,3),(1,4)],5) => 32 ([(0,1),(0,2),(0,3),(0,4)],5) => 32 ([(0,2),(0,3),(0,4),(4,1)],5) => 28 ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 26 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 25 ([(1,3),(1,4),(4,2)],5) => 28 ([(0,3),(0,4),(4,1),(4,2)],5) => 26 ([(1,2),(1,3),(2,4),(3,4)],5) => 26 ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 19 ([(0,3),(0,4),(3,2),(4,1)],5) => 25 ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 24 ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 23 ([(2,3),(3,4)],5) => 28 ([(1,4),(4,2),(4,3)],5) => 26 ([(0,4),(4,1),(4,2),(4,3)],5) => 25 ([(2,4),(3,4)],5) => 32 ([(1,4),(2,4),(4,3)],5) => 26 ([(0,4),(1,4),(4,2),(4,3)],5) => 23 ([(1,4),(2,4),(3,4)],5) => 32 ([(0,4),(1,4),(2,4),(4,3)],5) => 25 ([(0,4),(1,4),(2,4),(3,4)],5) => 32 ([(0,4),(1,4),(2,3)],5) => 32 ([(0,4),(1,3),(2,3),(2,4)],5) => 32 ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 32 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 32 ([(0,4),(1,4),(2,3),(4,2)],5) => 19 ([(0,4),(1,3),(2,3),(3,4)],5) => 26 ([(0,4),(1,4),(2,3),(2,4)],5) => 32 ([(0,4),(1,4),(2,3),(3,4)],5) => 28 ([(1,4),(2,3)],5) => 32 ([(1,4),(2,3),(2,4)],5) => 32 ([(0,4),(1,2),(1,4),(2,3)],5) => 28 ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 24 ([(1,3),(1,4),(2,3),(2,4)],5) => 32 ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 26 ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 23 ([(0,4),(1,2),(1,4),(4,3)],5) => 26 ([(0,4),(1,2),(1,3)],5) => 32 ([(0,4),(1,2),(1,3),(1,4)],5) => 32 ([(0,2),(0,4),(3,1),(4,3)],5) => 22 ([(0,4),(1,2),(1,3),(3,4)],5) => 28 ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 21 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 26 ([(0,3),(0,4),(1,2),(1,4)],5) => 32 ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 32 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 32 ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 28 ([(0,3),(1,2),(1,4),(3,4)],5) => 28 ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 26 ([(1,4),(3,2),(4,3)],5) => 22 ([(0,3),(3,4),(4,1),(4,2)],5) => 19 ([(1,4),(2,3),(3,4)],5) => 28 ([(0,4),(1,2),(2,4),(4,3)],5) => 21 ([(0,3),(1,4),(4,2)],5) => 28 ([(0,4),(3,2),(4,1),(4,3)],5) => 21 ([(0,4),(1,2),(2,3),(2,4)],5) => 26 ([(0,4),(2,3),(3,1),(4,2)],5) => 16 ([(0,3),(1,2),(2,4),(3,4)],5) => 25 ([(0,4),(1,2),(2,3),(3,4)],5) => 22 ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 19 ([],6) => 64 ([(4,5)],6) => 64 ([(3,4),(3,5)],6) => 64 ([(2,3),(2,4),(2,5)],6) => 64 ([(1,2),(1,3),(1,4),(1,5)],6) => 64 ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 64 ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 56 ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 52 ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 50 ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 49 ([(1,3),(1,4),(1,5),(5,2)],6) => 56 ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 52 ([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 52 ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 50 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 35 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6) => 47 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6) => 45 ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 44 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 43 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => 46 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 37 ([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => 38 ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 50 ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => 48 ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => 46 ([(2,3),(2,4),(4,5)],6) => 56 ([(1,4),(1,5),(5,2),(5,3)],6) => 52 ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 50 ([(2,3),(2,4),(3,5),(4,5)],6) => 52 ([(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 38 ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => 31 ([(1,4),(1,5),(4,3),(5,2)],6) => 50 ([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 48 ([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 46 ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => 35 ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 31 ([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => 36 ([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => 47 ([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => 46 ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 45 ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => 44 ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 43 ([(3,4),(4,5)],6) => 56 ([(2,3),(3,4),(3,5)],6) => 52 ([(1,5),(5,2),(5,3),(5,4)],6) => 50 ([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 49 ([(2,3),(3,5),(5,4)],6) => 44 ([(1,4),(4,5),(5,2),(5,3)],6) => 38 ([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 35 ([(3,5),(4,5)],6) => 64 ([(2,5),(3,5),(5,4)],6) => 52 ([(1,5),(2,5),(5,3),(5,4)],6) => 46 ([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => 43 ([(2,5),(3,5),(4,5)],6) => 64 ([(1,5),(2,5),(3,5),(5,4)],6) => 50 ([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => 43 ([(1,5),(2,5),(3,5),(4,5)],6) => 64 ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 49 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 64 ([(0,5),(1,5),(2,5),(3,4)],6) => 64 ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 35 ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 50 ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 64 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 56 ([(1,5),(2,5),(3,4)],6) => 64 ([(1,5),(2,4),(3,4),(3,5)],6) => 64 ([(0,5),(1,4),(2,4),(2,5),(5,3)],6) => 52 ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 45 ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 64 ([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6) => 52 ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 44 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 64 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 50 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 43 ([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 50 ([(1,5),(2,5),(3,4),(5,3)],6) => 38 ([(1,5),(2,4),(3,4),(4,5)],6) => 52 ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 37 ([(0,5),(1,5),(2,3),(5,4)],6) => 52 ([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => 35 ([(0,5),(1,5),(2,4),(5,3),(5,4)],6) => 46 ([(1,5),(2,5),(3,4),(3,5)],6) => 64 ([(0,5),(1,5),(2,3),(2,5),(5,4)],6) => 50 ([(0,5),(1,5),(2,3),(2,5),(3,4)],6) => 56 ([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 46 ([(0,5),(1,5),(2,3),(2,4)],6) => 64 ([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => 31 ([(0,4),(1,4),(2,3),(2,5),(4,5)],6) => 52 ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 46 ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 64 ([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => 44 ([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => 38 ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 35 ([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 56 ([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 42 ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 37 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 52 ([(1,5),(2,5),(3,4),(4,5)],6) => 56 ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 41 ([(0,5),(1,5),(2,3),(3,4)],6) => 56 ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 26 ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 47 ([(0,5),(1,4),(3,5),(4,2),(4,3)],6) => 42 ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 37 ([(0,5),(1,5),(2,3),(3,4),(3,5)],6) => 52 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 44 ([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 38 ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 35 ([(0,5),(1,5),(2,4),(3,4)],6) => 64 ([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 64 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 64 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 64 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 64 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 64 ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 38 ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 31 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 52 ([(2,5),(3,4)],6) => 64 ([(2,5),(3,4),(3,5)],6) => 64 ([(1,5),(2,3),(2,5),(3,4)],6) => 56 ([(0,5),(1,4),(1,5),(4,2),(4,3)],6) => 52 ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => 44 ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => 40 ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 48 ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => 33 ([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => 46 ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => 42 ([(2,4),(2,5),(3,4),(3,5)],6) => 64 ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 52 ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => 46 ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 46 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => 43 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => 40 ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => 37 ([(0,4),(0,5),(1,4),(1,5),(2,3)],6) => 64 ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => 38 ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => 31 ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => 35 ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 52 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 46 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 64 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 52 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 64 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 56 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) => 56 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 52 ([(1,5),(2,3),(2,5),(5,4)],6) => 52 ([(0,5),(1,2),(1,5),(5,3),(5,4)],6) => 46 ([(1,5),(2,3),(2,4)],6) => 64 ([(1,5),(2,3),(2,4),(2,5)],6) => 64 ([(0,5),(1,3),(1,4),(1,5),(4,2)],6) => 56 ([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 48 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 52 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 46 ([(0,5),(1,2),(1,3),(1,5),(5,4)],6) => 52 ([(0,5),(1,2),(1,3),(1,4)],6) => 64 ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 64 ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 44 ([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 56 ([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) => 42 ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 52 ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 41 ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 50 ([(0,4),(1,2),(1,3),(1,5),(4,5)],6) => 56 ([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6) => 52 ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 50 ([(1,3),(1,5),(4,2),(5,4)],6) => 44 ([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 38 ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 40 ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 39 ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 33 ([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => 39 ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => 38 ([(1,5),(2,3),(2,4),(4,5)],6) => 56 ([(0,5),(1,2),(1,3),(3,5),(5,4)],6) => 42 ([(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 42 ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 29 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 52 ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 37 ([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => 50 ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 48 ([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 46 ([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => 40 ([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => 40 ([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 48 ([(0,4),(1,3),(1,5),(5,2)],6) => 56 ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 42 ([(0,5),(1,3),(1,4),(4,2),(4,5)],6) => 52 ([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => 50 ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 31 ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => 52 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 47 ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 26 ([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 38 ([(1,4),(1,5),(2,3),(2,5)],6) => 64 ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 64 ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 52 ([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6) => 46 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 64 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 52 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => 46 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 43 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6) => 56 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 48 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 44 ([(0,4),(0,5),(1,3),(1,5),(5,2)],6) => 52 ([(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 56 ([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => 46 ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => 42 ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => 38 ([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => 56 ([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => 48 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6) => 52 ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 44 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6) => 50 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6) => 45 ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => 44 ([(0,4),(0,5),(1,2),(1,3)],6) => 64 ([(0,4),(0,5),(1,2),(1,3),(1,5)],6) => 64 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 64 ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 56 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 52 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => 64 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 64 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 64 ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 56 ([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6) => 56 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 52 ([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => 56 ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 52 ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => 35 ([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => 36 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6) => 52 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 50 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 48 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 46 ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) => 49 ([(1,4),(2,3),(2,5),(4,5)],6) => 56 ([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => 42 ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 52 ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => 40 ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 35 ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => 49 ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => 39 ([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => 46 ([(0,5),(1,3),(1,4),(5,2)],6) => 56 ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 32 ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 37 ([(0,4),(1,3),(1,5),(4,2),(4,5)],6) => 52 ([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6) => 50 ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => 42 ([(2,5),(3,4),(4,5)],6) => 56 ([(1,5),(2,3),(3,5),(5,4)],6) => 42 ([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => 35 ([(1,3),(2,4),(4,5)],6) => 56 ([(1,5),(4,3),(5,2),(5,4)],6) => 42 ([(1,5),(2,3),(3,4),(3,5)],6) => 52 ([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => 40 ([(0,4),(1,5),(5,2),(5,3)],6) => 52 ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 41 ([(0,5),(1,4),(4,2),(4,3),(4,5)],6) => 50 ([(1,5),(3,4),(4,2),(5,3)],6) => 32 ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 26 ([(1,4),(2,3),(3,5),(4,5)],6) => 50 ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 35 ([(0,5),(1,4),(4,2),(5,3)],6) => 49 ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 31 ([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => 46 ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => 43 ([(1,5),(2,3),(3,4),(4,5)],6) => 44 ([(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 38 ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 26 ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 31 ([(0,5),(1,4),(2,3)],6) => 64 ([(0,5),(1,3),(2,4),(2,5)],6) => 64 ([(0,5),(1,4),(2,3),(2,4),(2,5)],6) => 64 ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => 44 ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 39 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 56 ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => 36 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 48 ([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => 38 ([(0,5),(1,4),(2,3),(2,4),(4,5)],6) => 52 ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 64 ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 64 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 64 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6) => 64 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) => 64 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 64 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 64 ([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6) => 52 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 64 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 56 ([(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 64 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 56 ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 56 ([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 52 ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => 44 ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => 38 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => 31 ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => 33 ([(0,5),(1,4),(2,3),(2,5),(4,5)],6) => 56 ([(0,5),(1,3),(4,2),(5,4)],6) => 44 ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 35 ([(0,5),(1,4),(3,2),(4,3),(4,5)],6) => 42 ([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => 36 ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 29 ([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => 38 ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 22 ([(0,5),(1,3),(2,4),(4,5)],6) => 56 ([(0,5),(1,4),(2,3),(3,4),(3,5)],6) => 52 ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 29 ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 42 ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 32 ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 26 ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 40 ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 29 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 50 ----------------------------------------------------------------------------- Created: Jul 28, 2023 at 18:44 by Nadia Lafreniere ----------------------------------------------------------------------------- Last Updated: Jan 19, 2024 at 18:31 by Nadia Lafreniere