Linear numeration systems of order two

AbstractA numeration system is a sequence of integers such that any integer can be represented by means of the sequence using integers of bounded size. We study numeration systems defined by linear recurrences of order two. We give a necessary and sufficient condition on the system such that every integer has a canonical representation. We show that this canonical representation can be computed from any representation by a rational function. This rational function is the composition of two subsequential functions that are simply obtained from the system. The addition of two integers represented in the system can be performed by a subsequential machine