***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew <info@findstat.org> * * * * 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: St001876 ----------------------------------------------------------------------------- Collection: Lattices ----------------------------------------------------------------------------- Description: The number of 2-regular simple modules in the incidence algebra of the lattice. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: ([(0,2),(2,1)],3) => 0 ([(0,1),(0,2),(1,3),(2,3)],4) => 1 ([(0,3),(2,1),(3,2)],4) => 0 ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1 ([(0,4),(2,3),(3,1),(4,2)],5) => 0 ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1 ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 1 ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1 ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1 ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2 ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0 ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 1 ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2 ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 1 ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2 ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => 1 ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0 ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 1 ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => 2 ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8) => 2 ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8) => 1 ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => 2 ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 3 ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2 ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8) => 3 ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8) => 2 ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8) => 1 ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8) => 1 ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => 1 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0 ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2 ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 0 ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8) => 1 ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9) => 0 ([(0,4),(0,5),(2,8),(3,8),(4,7),(5,7),(6,2),(6,3),(7,6),(8,1)],9) => 2 ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => 2 ([(0,3),(0,4),(1,7),(2,7),(3,8),(4,8),(5,6),(6,1),(6,2),(8,5)],9) => 2 ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9) => 1 ([(0,2),(0,3),(2,8),(3,8),(4,6),(5,4),(6,1),(7,5),(8,7)],9) => 1 ([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9) => 2 ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9) => 3 ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9) => 3 ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 3 ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9) => 2 ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 3 ([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9) => 1 ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 4 ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(8,5)],9) => 2 ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9) => 2 ([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9) => 2 ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => 3 ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => 3 ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9) => 0 ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => 2 ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9) => 2 ([(0,6),(1,8),(2,8),(3,5),(4,3),(5,7),(6,4),(7,1),(7,2)],9) => 1 ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 0 ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9) => 1 ([(0,6),(1,8),(2,8),(4,5),(5,7),(6,4),(7,1),(7,2),(8,3)],9) => 1 ----------------------------------------------------------------------------- Created: Oct 03, 2020 at 18:31 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Oct 03, 2020 at 18:31 by Rene Marczinzik