Number systems, tilings and seminumerical algorithms

Paul Surer

Research output: ThesisDoctoral Thesis

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Abstract

The thesis deals with so-called shift radix systems and their relation to canonical number systems and beta-expansions. In the first part the finiteness property is treated (i.e., under which conditions all elements of a set can be represented in a finite way). It turns out that such an analysis is rather difficult. In the second part SRS-tiles are introduced, i.e., tiles that are induced by shift radix systems in a canonical way. It is shown that there is a linear connection between SRS-tiles and tiles associated to expanding polynomials (tiles associated to Pisot numbers, respectively). Finally variations of shift radix systems (so-called epsilon-shift radix systems) are presented and investigated. Surprisingly the finiteness property seems to be much easier to characterise here.
Translated title of the contributionZiffernsysteme, Tilings und seminumerische Algorithmen
Original languageEnglish
QualificationDr.mont.
Supervisors/Advisors
  • Pethő, Attila, Assessor B (external), External person
  • Thuswaldner, Jörg, Assessor A (internal)
Publication statusPublished - 2008

Bibliographical note

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Keywords

  • number systems
  • shift radix systems
  • canonical number systems
  • beta-expansions
  • tilings

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