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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Tilings induced by a class of cubic Rauzy fractals

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Author(s):
Loridant, B. [1] ; Messaoudi, A. [2] ; Surer, P. [2] ; Thuswaldner, J. M. [1]
Total Authors: 4
Affiliation:
[1] Univ Leoben, Lehrstuhl Math & Stat, A-8700 Leoben - Austria
[2] IBILCE UNESP, Dept Matemat, Sao Jose Do Rio Preto - Brazil
Total Affiliations: 2
Document type: Journal article
Source: THEORETICAL COMPUTER SCIENCE; v. 477, p. 6-31, MAR 18 2013.
Web of Science Citations: 10
Abstract

We study aperiodic and periodic tilings induced by the Rauzy fractal and its subtiles associated with beta-substitutions related to the polynomial x(3) - ax(2) - bx - 1 for a >= b >= 1. In particular, we compute the corresponding boundary graphs, describing the adjacencies in the tilings. These graphs are a valuable tool for more advanced studies of the topological properties of the Rauzy fractals. As an example, we show that the Rauzy fractals are not homeomorphic to a closed disc as soon as a <= 2b - 4. The methods presented in this paper may be used to obtain similar results for other classes of substitutions. (c) 2013 Elsevier B.V. All rights reserved. (AU)

FAPESP's process: 09/07744-0 - Substitutions, Numeration Systems and Rauzy Fractals
Grantee:Paul Surer
Support Opportunities: Scholarships in Brazil - Post-Doctoral