Disk-like Tiles Derived from Complex Bases |
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Authors: | Email author" target="_blank">Jun?LuoEmail author Zuo?Ling?Zhou |
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Institution: | (1) School of Mathematics and Computing Science, Zhongshan University, Guangzhou 510275, P. R. China;(2) Lingnan College, Zhongshan University, Guangzhou 510275, P. R. China |
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Abstract: | For each positive integer k, the radix representation of the complex numbers in the base –k+i gives rise to a lattice self-affine tile T
k
in the plane, which consists of all the complex numbers that can be expressed in the form ∑
j≥1
d
j
(–k+i)–j
, where d
j
∈{0, 1, 2, ...,k
2}. We prove that T
k
is homeomorphic to the closed unit disk {z∈C:∣z∣ ≤ 1} if and only if k ≠ 2.
The first author is supported by Youth Project of Tianyuan Foundation (10226031) and Zhongshan University Promotion Foundation
for Young Teachers (34100-1131206); the second author is supported by National Science Foundation (10041005) and Guangdong
Province Science Foundation (011221) |
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Keywords: | Representation Lattice self-affine tile Disk-like |
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