Abstract
Let β > 1 be a cubic Pisot unit. We study forms of Thurston tilings arising from the classical β-numeration system and from the (−β)-numeration system for both the Ito-Sadahiro and balanced definition of the (−β)-transformation.
Highlights
Representations of real numbers in a positional numeration system with an arbitrary base β > 1, so-called β-expansions, were introduced by Renyi [10]
This paper considers tilings generated by β-expansions in the case when β is a Pisot unit
A general method for constructing the tiling of a Euclidean space by a Pisot unit was proposed by Thurston [11], an example of such a tiling had already appeared in the work of Rauzy [9]
Summary
Representations of real numbers in a positional numeration system with an arbitrary base β > 1, so-called β-expansions, were introduced by Renyi [10]. A general method for constructing the tiling of a Euclidean space by a Pisot unit was proposed by Thurston [11], an example of such a tiling had already appeared in the work of Rauzy [9]. Fundamental properties of these tilings were later studied by Praggastis [8] and Akiyama [1, 2]. In 2009, Ito and Sadahiro introduced a new numeration system [6], using a non-integer negative base −β < −1 Their approach is very similar to the approach by Renyi. The paper is intended as an entry point into a study of the properties of these tilings
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
