Number systems, tilings and seminumerical algorithms

Paul Surer

Research output: ThesisDoctoral Thesis

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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
  • Pethő, Attila, Assessor B (external), External person
  • Thuswaldner, Jörg, Assessor A (internal)
Publication statusPublished - 2008

Bibliographical note

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

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