Tilings induced by a class of cubic Rauzy fractals

Sobre o artigo

co-autores Benoît Loridant
Ali Messaoudi
Jörg M. Thuswaldner
idioma inglês
publicado no Theoretical Computer Science 477 (2013)
páginas 6 to 31
DOI 10.1016/j.tcs.2012.12.019
suportado por FAPESP, processo 2009/07744-0
título em português Azulejamentos induzidos por uma classe de fractais de Rauzy cúbicos

Resumo

Nós estudamos azulejamentos periódicos e aperiódicos induzidos pelos Fractais de Rauzy e seus subazulejos associados com as beta-substituições relacionadas ao polinômio x3 - ax2 - bx -1 em que a ≥ b ≥ 1. Em particular, nós determinamos os grafos de fronteira que descrevem as vizinhanças dos azulejos dentro do azulejamento. Estes grafos são ferramentas valiosas para estudar propriedades topológicas dos Fractais de Rauzy. Como exemplo nós mostramos que os Fractais de Rauzy não são homomórfico a um disco quando a ≤ 2b - 4. Os métodos desenvolvidos neste artigo podem ser usados para obter resultados semelhantes para outras clesses de Fractais de Rauzy.

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Theoretical Computer Science
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