***************************************************************************** * 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: St001632 ----------------------------------------------------------------------------- Collection: Posets ----------------------------------------------------------------------------- Description: The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: gap('LoadPackage("QPA");') def incidence_algebra_gap(P): P = P.relabel() return gap("PosetAlgebra(GF(3), Poset(%s, %s))" % (list(P), P.cover_relations())) def statistic(P): A = incidence_algebra_gap(P) RegA = A.IndecProjectiveModules().DirectSumOfQPAModules() injectives = A.IndecInjectiveModules() return sum(1 for M in injectives if M.ExtOverAlgebra(RegA)[2].Size().sage() == 1) ----------------------------------------------------------------------------- Statistic values: ([(0,1)],2) => 1 ([(0,1),(0,2)],3) => 2 ([(0,2),(2,1)],3) => 1 ([(0,2),(1,2)],3) => 1 ([(0,1),(0,2),(0,3)],4) => 0 ([(0,2),(0,3),(3,1)],4) => 2 ([(0,1),(0,2),(1,3),(2,3)],4) => 2 ([(0,3),(3,1),(3,2)],4) => 1 ([(0,3),(1,3),(3,2)],4) => 1 ([(0,3),(1,3),(2,3)],4) => 0 ([(0,3),(1,2),(1,3)],4) => 0 ([(0,2),(0,3),(1,2),(1,3)],4) => 0 ([(0,3),(2,1),(3,2)],4) => 1 ([(0,3),(1,2),(2,3)],4) => 1 ([(0,1),(0,2),(0,3),(0,4)],5) => 0 ([(0,2),(0,3),(0,4),(4,1)],5) => 0 ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 0 ([(0,3),(0,4),(4,1),(4,2)],5) => 1 ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2 ([(0,3),(0,4),(3,2),(4,1)],5) => 2 ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 2 ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 2 ([(0,4),(4,1),(4,2),(4,3)],5) => 1 ([(0,4),(1,4),(4,2),(4,3)],5) => 0 ([(0,4),(1,4),(2,4),(4,3)],5) => 0 ([(0,4),(1,4),(2,4),(3,4)],5) => 0 ([(0,4),(1,3),(2,3),(2,4)],5) => 0 ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 0 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 0 ([(0,4),(1,4),(2,3),(4,2)],5) => 1 ([(0,4),(1,3),(2,3),(3,4)],5) => 0 ([(0,4),(1,4),(2,3),(2,4)],5) => 0 ([(0,4),(1,4),(2,3),(3,4)],5) => 1 ([(0,4),(1,2),(1,4),(2,3)],5) => 0 ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 1 ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 0 ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 2 ([(0,4),(1,2),(1,4),(4,3)],5) => 0 ([(0,4),(1,2),(1,3),(1,4)],5) => 0 ([(0,2),(0,4),(3,1),(4,3)],5) => 2 ([(0,4),(1,2),(1,3),(3,4)],5) => 1 ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 2 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2 ([(0,3),(0,4),(1,2),(1,4)],5) => 0 ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 0 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 0 ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 0 ([(0,3),(1,2),(1,4),(3,4)],5) => 1 ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 1 ([(0,3),(3,4),(4,1),(4,2)],5) => 1 ([(0,4),(1,2),(2,4),(4,3)],5) => 1 ([(0,4),(3,2),(4,1),(4,3)],5) => 1 ([(0,4),(1,2),(2,3),(2,4)],5) => 1 ([(0,4),(2,3),(3,1),(4,2)],5) => 1 ([(0,3),(1,2),(2,4),(3,4)],5) => 2 ([(0,4),(1,2),(2,3),(3,4)],5) => 1 ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2 ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 0 ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 0 ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 0 ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 1 ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 0 ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 0 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 0 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6) => 1 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6) => 2 ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => 0 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 1 ([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => 1 ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 0 ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => 0 ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 1 ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => 2 ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => 2 ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2 ([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => 2 ([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => 1 ([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => 1 ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 2 ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => 2 ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2 ([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 1 ([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 1 ([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => 0 ([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => 0 ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 0 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 0 ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 0 ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1 ([(0,5),(1,4),(2,4),(2,5),(5,3)],6) => 0 ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6) => 0 ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 0 ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 0 ([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => 0 ([(0,5),(1,5),(2,4),(5,3),(5,4)],6) => 0 ([(0,5),(1,5),(2,3),(2,5),(5,4)],6) => 0 ([(0,5),(1,5),(2,3),(2,5),(3,4)],6) => 0 ([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 0 ([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => 0 ([(0,4),(1,4),(2,3),(2,5),(4,5)],6) => 0 ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 0 ([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => 1 ([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => 2 ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 2 ([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 1 ([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 2 ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 1 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 1 ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 1 ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(3,5),(4,2),(4,3)],6) => 1 ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 2 ([(0,5),(1,5),(2,3),(3,4),(3,5)],6) => 1 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1 ([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 2 ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 5 ([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 0 ([(0,5),(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 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 0 ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 1 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0 ([(0,5),(1,4),(1,5),(4,2),(4,3)],6) => 0 ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => 0 ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => 0 ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => 1 ([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => 0 ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => 2 ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) => 1 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 1 ([(0,5),(1,2),(1,5),(5,3),(5,4)],6) => 0 ([(0,5),(1,3),(1,4),(1,5),(4,2)],6) => 0 ([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 0 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 0 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 1 ([(0,5),(1,2),(1,3),(1,5),(5,4)],6) => 0 ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 0 ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 0 ([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 0 ([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) => 1 ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 0 ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 0 ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 0 ([(0,4),(1,2),(1,3),(1,5),(4,5)],6) => 1 ([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6) => 1 ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 1 ([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 1 ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 2 ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 2 ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2 ([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => 2 ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => 2 ([(0,5),(1,2),(1,3),(3,5),(5,4)],6) => 1 ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 2 ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 2 ([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => 1 ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 1 ([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => 1 ([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => 1 ([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 2 ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 1 ([(0,5),(1,3),(1,4),(4,2),(4,5)],6) => 1 ([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => 2 ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 2 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 3 ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2 ([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 2 ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 0 ([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6) => 2 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 0 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => 0 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6) => 0 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 0 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 4 ([(0,4),(0,5),(1,3),(1,5),(5,2)],6) => 0 ([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => 0 ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => 0 ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => 2 ([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => 0 ([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6) => 0 ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 0 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6) => 0 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(1,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 0 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 0 ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 0 ([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6) => 0 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 1 ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => 2 ([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => 2 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6) => 2 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) => 0 ([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => 1 ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => 1 ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2 ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => 1 ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => 1 ([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 2 ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 1 ([(0,4),(1,3),(1,5),(4,2),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6) => 1 ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => 1 ([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => 1 ([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => 1 ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 1 ([(0,5),(1,4),(4,2),(4,3),(4,5)],6) => 1 ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 1 ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 2 ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 1 ([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => 2 ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2 ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 1 ([(0,5),(1,4),(2,3),(2,4),(2,5)],6) => 0 ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => 0 ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0 ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => 1 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => 0 ([(0,5),(1,4),(2,3),(2,4),(4,5)],6) => 0 ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 0 ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 0 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6) => 0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) => 0 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 0 ([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 0 ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 1 ([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 1 ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => 1 ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => 1 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => 2 ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => 2 ([(0,5),(1,4),(2,3),(2,5),(4,5)],6) => 1 ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 1 ([(0,5),(1,4),(3,2),(4,3),(4,5)],6) => 1 ([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => 2 ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 1 ([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => 1 ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1 ([(0,5),(1,4),(2,3),(3,4),(3,5)],6) => 1 ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 1 ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1 ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 1 ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1 ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2 ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 3 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2 ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0 ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => 0 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 1 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => 1 ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 1 ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => 0 ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 0 ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => 2 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 2 ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => 2 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 3 ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 1 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2 ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 1 ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 6 ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 1 ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 0 ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => 0 ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7) => 1 ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => 0 ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7) => 1 ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7) => 0 ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7) => 0 ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7) => 1 ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => 0 ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2 ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => 2 ([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7) => 1 ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2 ([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => 2 ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 2 ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 2 ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 3 ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => 5 ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => 3 ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 2 ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 2 ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7) => 1 ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => 1 ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => 2 ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7) => 1 ([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7) => 5 ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 2 ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1 ([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7) => 6 ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => 1 ([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => 4 ([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7) => 5 ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2 ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => 1 ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => 4 ----------------------------------------------------------------------------- Created: Oct 03, 2020 at 21:04 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Nov 13, 2022 at 12:12 by Martin Rubey