***************************************************************************** * 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: St001630 ----------------------------------------------------------------------------- Collection: Lattices ----------------------------------------------------------------------------- Description: The global dimension of the incidence algebra of the lattice over the rational numbers. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: ([(0,2),(2,1)],3) => 1 ([(0,1),(0,2),(1,3),(2,3)],4) => 2 ([(0,3),(2,1),(3,2)],4) => 2 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2 ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 2 ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2 ([(0,4),(2,3),(3,1),(4,2)],5) => 1 ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2 ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 2 ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 2 ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 2 ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 2 ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 2 ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2 ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 2 ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 2 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 2 ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 2 ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 2 ([(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) => 1 ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 2 ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2 ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 2 ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 2 ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 2 ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 2 ([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7) => 2 ([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7) => 2 ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => 2 ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7) => 2 ([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7) => 2 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 2 ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2 ([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => 2 ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2 ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7) => 2 ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => 2 ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 2 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2 ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7) => 2 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 2 ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => 2 ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => 2 ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7) => 2 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => 2 ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7) => 2 ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => 2 ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => 2 ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => 2 ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 2 ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 2 ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 2 ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => 2 ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => 2 ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7) => 2 ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => 2 ([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7) => 2 ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => 2 ([(0,3),(0,4),(1,6),(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 ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => 2 ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7) => 2 ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => 2 ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 2 ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => 2 ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 2 ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1 ([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => 2 ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => 2 ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2 ----------------------------------------------------------------------------- Created: Oct 02, 2020 at 18:03 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Oct 03, 2020 at 17:12 by Rene Marczinzik