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Orientador(es)
Resumo(s)
We 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.
Descrição
Palavras-chave
Combinatorial game theory Lattices Modularity Representation theorems
Contexto Educativo
Citação
CARVALHO, 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. 37-49
Editora
Elsevier Science BV