We study multidimensional continued fraction algorithms throughout the field of formal power series. In this case, we establish a relation between the Jacobi-Perron algorithm and the version of it introduced by Dubois...
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We study multidimensional continued fraction algorithms throughout the field of formal power series. In this case, we establish a relation between the Jacobi-Perron algorithm and the version of it introduced by Dubois. Regarding the periodicity of the Jacobi-Perron algorithm, we define periodic vectors whose coordinates belong to certain finite degree extension fields. We prove also that the convergence of brun algorithm in the case of multidimensional continued fractions over the Field of Formal Power Series is not exponential.
Dual maps have been introduced as a generalization to higher dimensions of word substitutions and free group morphisms. In this paper, we study the action of these dual maps on particular discrete planes and surfaces,...
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Dual maps have been introduced as a generalization to higher dimensions of word substitutions and free group morphisms. In this paper, we study the action of these dual maps on particular discrete planes and surfaces, namely stepped planes and stepped surfaces. We show that dual maps can be seen as discretizations of toral automorphisms. We then provide a connection between stepped planes and the brun multi-dimensional continued fraction algorithm, based on a desubstitution process defined on local geometric configurations of stepped planes. By extending this connection to stepped surfaces, we obtain an effective characterization of stepped planes (more exactly, stepped quasi-planes) among stepped surfaces. (C) 2010 Elsevier B.V. All rights reserved.
This paper extends, in a multi-dimensional framework, pattern recognition techniques for generation or recognition of digital lines. More precisely, we show how the connection between chain codes of digital lines and ...
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This paper extends, in a multi-dimensional framework, pattern recognition techniques for generation or recognition of digital lines. More precisely, we show how the connection between chain codes of digital lines and continued fractions can be generalized by a connection between tilings and multi-dimensional continued fractions. This leads to a new approach for generating and recognizing digital hyperplanes. (c) 2008 Elsevier Ltd. All rights reserved.
This paper extends, in a multi-dimensional framework, pattern recognition techniques for generation or recognition of digital lines. More precisely, we show how the connection between chain codes of digital lines and ...
详细信息
ISBN:
(纸本)3540791256
This paper extends, in a multi-dimensional framework, pattern recognition techniques for generation or recognition of digital lines. More precisely, we show how the connection between chain codes of digital lines and continued fractions can be generalized by a connection between tilings and multi-dimensional continued fractions. This leads to a new approach for generating and recognizing digital hyperplanes. (c) 2008 Elsevier Ltd. All rights reserved.
We present a simple conversion algorithm which allows to rewrite the two-dimensional brun algorithm in terms of the Podsypanin algorithm. Further, we demonstrate how this conversion process can be used to transfer cer...
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We present a simple conversion algorithm which allows to rewrite the two-dimensional brun algorithm in terms of the Podsypanin algorithm. Further, we demonstrate how this conversion process can be used to transfer certain (statistical, approximation) properties from the original to the resulting algorithm. (C) 2007 Elsevier B.V. All rights reserved.
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