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Book Editors IOS Press, 2003

Summary: Book Title
Book Editors
IOS Press, 2003
Pisot number system and its dual tiling
Shigeki Akiyama 1
Niigata Univ. JAPAN
Abstract. Number systems in Pisot number base are discussed in relation to arith-
metic construction of quasi-crystal model. One of the most important ideas is to
introduce a `dual tiling' of this system. This provides us a geometric way to under-
stand the `algebraic structure' of the above model as well as dynamical understand-
ing of arithmetics algorithms.
Keywords. Pisot Number, Number System, Symbolic Dynamical System, Tiling
1. Beta expansion and Pisot number system
For this section, the reader finds a nice survey by Frougny [41]. However we give a brief
review and concise proofs of fundamental results to make this note more self-contained.
Let us fix > 1 and A = [0, ) Z. Denote by A
the set of finite words over A and
by AN
the set of right infinite words over A. By concatenation :


Source: Akiyama, Shigeki - Department of Mathematics, Niigata University


Collections: Mathematics