About the article

language English
published in Mathematica Pannonica, 18, No. 2 (2007)
pages 265 to 297
supported by FWF, project P17557-N12
FWF, project S9610 (NFN S9600)

Abstract

For rRd define the function τr: ZdZd in the following way:
τr: ZdZd, a=(a1,…,ad)→(a2,…,ad,−⌊ra⌋).
τr is called a Shift Radix System (SRS) if ∀aZd ∃kN: τrk(a) = 0. In this paper we deal with new results concerning the characterisation of the set D0d:={rRdr is an SRS}, especially for d=2. For this purpose we adapt and generalise several results and methods presented in earlier papers.

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Mathematica® Notebook-File (Version 5.1) with an implementation of the algorithm Ak.
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Mathematica® Notebook-File (Version 5.1) with a list of all known nonempty periods. Because it consists of a lot of periods (more than 1000) this list is suitable for computational use only.
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Links

Mathematica Pannonica
Austrian Science Foundation (FWF)
National Research Network (NFN) S9600