Summary: POSITIVE FINITENESS OF NUMBER
Department of Mathematics, Faculty of Science, Niigata University
Ikarashi 2-8050, Niigata 950-2181, Japan
Abstract We characterize the set of 's that each polynomial in base with non-
negative integer coefficients has a finite admissible expression in some
Keywords: Beta expansion, Canonical number system, Pisot number
In this note, we study a certain finiteness property of number systems
given by power series in some base , which are called beta-expansion
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 non-negative
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 beta-expansion (c.f.