 
Summary: POSITIVE FINITENESS OF NUMBER
SYSTEMS
Shigeki Akiyama
Department of Mathematics, Faculty of Science, Niigata University
Ikarashi 28050, Niigata 9502181, Japan
akiyama@math.sc.niigatau.ac.jp
Abstract We characterize the set of 's that each polynomial in base with non
negative integer coefficients has a finite admissible expression in some
number systems.
Keywords: Beta expansion, Canonical number system, Pisot number
1. Introduction
In this note, we study a certain finiteness property of number systems
given by power series in some base , which are called betaexpansion
and canonical number system.
In relation to symbolic dynamics, an important problem is to deter
mine the set of 's that each polynomial in base with nonnegative
integer coefficients has a finite expression in the corresponding number
system. However this problem may be pretty difficult in general. We
narrow our scope on the set of such 's which does not have `global'
finiteness. Let us explain exactly the problem for betaexpansion (c.f.
