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Published online by Cambridge University Press: 15 December 2002
Two linear numeration systems, withcharacteristic polynomial equal to theminimal polynomial of two Pisot numbers β and γ respectively,such thatβ and γ are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other oneis computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodicpoints of a sofic dynamical system associated with some Parry number.