Abstract
Abstract The factor complexity of the infinite word u β canonically associated with a non-simple Parry number β is studied. Our approach is based on the notion of special factors introduced by Berstel and Cassaigne. At first, we give a handy method for determining infinite left special branches; this method is applicable to a broad class of infinite words which are fixed points of a primitive substitution. In the second part of the article, we focus on infinite words u β only. To complete the description of their special factors, we define and study (a, b)-maximal left special factors. This enables us to characterize non-simple Parry numbers β for which the word u β has affine complexity.
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