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Summary: Self affine tiling and Pisot numeration system
Shigeki Akiyama
1 Introduction
Let > 1 be a real number. Consider an expansion of positive real number
x:
x = aN N
+ aN-1N-1
+ aN-2N-2
+ · · · ,
with ai Z[0, ). A greedy expansion of x in base is such expansion with
|x -
N
M
aii
| < M
(1)
for any M. By using greedy algorithm, such an expansion always exists for
any x. This is a natural extension of decimal or binary expansion to a real
base. An expansion of x is admissible, if (1) holds for all M. Hereafter, we
use a notation
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