Rewriting rules for arithmetics in alternate base systems
For alternate Cantor real base numeration systems we generalize the result of Frougny and Solomyak on arithmetics on the set of numbers with finite expansion. We provide a class of alternate bases which satisfy the so-called finiteness property. The proof uses rewriting rules on the language of expansions in the corresponding numeration system. The proof is constructive and provides a method for performing addition of expansions in Cantor real bases.
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