***************************************************************************** * 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: St001964 ----------------------------------------------------------------------------- Collection: Posets ----------------------------------------------------------------------------- Description: The interval resolution global dimension of a poset. This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra. ----------------------------------------------------------------------------- References: [1] Aoki, T., Escolar, E. G., Tada, S. Summand-injectivity of interval covers and monotonicity of interval resolution global dimensions [[arXiv:2308.14979]] [2] [[https://github.com/xHoukakun/Interval-Resolution-Global-Dimension/tree/main]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: ([],1) => 0 ([],2) => 0 ([(0,1)],2) => 0 ([],3) => 0 ([(0,1),(0,2)],3) => 0 ([(0,2),(2,1)],3) => 0 ([(0,2),(1,2)],3) => 0 ([],4) => 0 ([(0,1),(0,2),(0,3)],4) => 1 ([(0,2),(0,3),(3,1)],4) => 0 ([(0,1),(0,2),(1,3),(2,3)],4) => 0 ([(1,2),(2,3)],4) => 0 ([(0,3),(3,1),(3,2)],4) => 1 ([(1,3),(2,3)],4) => 0 ([(0,3),(1,3),(3,2)],4) => 1 ([(0,3),(1,3),(2,3)],4) => 1 ([(0,3),(1,2),(1,3)],4) => 0 ([(0,2),(0,3),(1,2),(1,3)],4) => 2 ([(0,3),(2,1),(3,2)],4) => 0 ([(0,3),(1,2),(2,3)],4) => 0 ([],5) => 0 ([(0,1),(0,2),(0,3),(0,4)],5) => 2 ([(0,2),(0,3),(0,4),(4,1)],5) => 1 ([(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) => 1 ([(0,3),(0,4),(4,1),(4,2)],5) => 1 ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1 ([(0,3),(0,4),(3,2),(4,1)],5) => 0 ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1 ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 2 ([(2,3),(3,4)],5) => 0 ([(0,4),(4,1),(4,2),(4,3)],5) => 2 ([(2,4),(3,4)],5) => 0 ([(1,4),(2,4),(4,3)],5) => 1 ([(0,4),(1,4),(4,2),(4,3)],5) => 2 ([(0,4),(1,4),(2,4),(4,3)],5) => 2 ([(0,4),(1,4),(2,4),(3,4)],5) => 2 ([(0,4),(1,4),(2,3)],5) => 0 ([(0,4),(1,3),(2,3),(2,4)],5) => 0 ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 2 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3 ([(0,4),(1,4),(2,3),(4,2)],5) => 1 ([(0,4),(1,3),(2,3),(3,4)],5) => 1 ([(0,4),(1,4),(2,3),(2,4)],5) => 1 ([(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) => 2 ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 2 ([(0,4),(1,2),(1,4),(4,3)],5) => 1 ([(0,4),(1,2),(1,3),(1,4)],5) => 1 ([(0,2),(0,4),(3,1),(4,3)],5) => 0 ([(0,4),(1,2),(1,3),(3,4)],5) => 0 ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 0 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 1 ([(0,3),(0,4),(1,2),(1,4)],5) => 0 ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 3 ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2 ([(0,3),(1,2),(1,4),(3,4)],5) => 0 ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 2 ([(1,4),(3,2),(4,3)],5) => 0 ([(0,3),(3,4),(4,1),(4,2)],5) => 1 ([(1,4),(2,3),(3,4)],5) => 0 ([(0,4),(1,2),(2,4),(4,3)],5) => 1 ([(0,3),(1,4),(4,2)],5) => 0 ([(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) => 0 ([(0,3),(1,2),(2,4),(3,4)],5) => 0 ([(0,4),(1,2),(2,3),(3,4)],5) => 0 ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1 ([],6) => 0 ([(3,4),(4,5)],6) => 0 ([(2,3),(3,5),(5,4)],6) => 0 ([(3,5),(4,5)],6) => 0 ([(2,5),(3,5),(5,4)],6) => 1 ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 3 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 3 ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 2 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2 ([(1,5),(2,5),(3,4)],6) => 0 ([(1,5),(2,4),(3,4),(3,5)],6) => 0 ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 2 ([(1,5),(2,5),(3,4),(5,3)],6) => 1 ([(1,5),(2,4),(3,4),(4,5)],6) => 1 ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 2 ([(0,5),(1,5),(2,3),(5,4)],6) => 1 ([(1,5),(2,5),(3,4),(4,5)],6) => 1 ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 2 ([(0,5),(1,5),(2,3),(3,4)],6) => 0 ([(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),(1,5),(2,3),(3,4),(4,5)],6) => 1 ([(0,5),(1,5),(2,4),(3,4)],6) => 0 ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 1 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2 ([(2,5),(3,4),(4,5)],6) => 0 ([(1,5),(2,3),(3,5),(5,4)],6) => 1 ([(1,3),(2,4),(4,5)],6) => 0 ([(1,5),(3,4),(4,2),(5,3)],6) => 0 ([(1,4),(2,3),(3,5),(4,5)],6) => 0 ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 1 ([(0,5),(1,4),(4,2),(5,3)],6) => 0 ([(1,5),(2,3),(3,4),(4,5)],6) => 0 ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 1 ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0 ([(0,5),(1,3),(4,2),(5,4)],6) => 0 ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0 ([(0,5),(1,3),(2,4),(4,5)],6) => 0 ([(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) => 0 ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1 ----------------------------------------------------------------------------- Created: Mar 07, 2025 at 13:26 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Mar 07, 2025 at 15:43 by Jannek Müller