Carvalho, AldaSantos, Carlos Pereira dosDias, CatiaCoelho, FranciscoNeto, João PedroNowakowski, RichardVinagre, Sandra2015-08-252015-08-252014-03CARVALHO, Alda Cristina Jesus V. Nunes de, [et al] – On lattices from combinatorial game theory modularity and a representation theorem: Finite case. Theroretical Computer Science. ISSN: 0304-3975. Vol. 527 (2014), pp. 37-490304-39751879-2294http://hdl.handle.net/10400.21/5012We show that a self-generated set of combinatorial games, S. may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question "Is there a set which will give a non-distributive but modular lattice?" appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented. (C) 2014 Elsevier B.V. All rights reserved.engCombinatorial game theoryLatticesModularityRepresentation theoremsjournal article10.1016/j.tcs.2014.01.025