Number systems, tilings and seminumerical algorithms
Publikationen: Thesis / Studienabschlussarbeiten und Habilitationsschriften › Dissertation
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2008. 105 S.
Publikationen: Thesis / Studienabschlussarbeiten und Habilitationsschriften › Dissertation
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TY - BOOK
T1 - Number systems, tilings and seminumerical algorithms
AU - Surer, Paul
N1 - no embargo
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
KW - Ziffernsysteme
KW - Kanonische Ziffernsysteme
KW - beta-Entwicklungen
KW - Shift Ziffern Systeme
KW - Tiles
KW - number systems
KW - shift radix systems
KW - canonical number systems
KW - beta-expansions
KW - tilings
M3 - Doctoral Thesis
ER -