Generalized de Bruijn digraphs and the distribution of patterns in ?-expansions

A generalization of de Bruijn digraphs is defined for Parry’s α-expansions and it is shown that the characteristic polynomial of these graphs is in principle that of α. With the help of this result we prove that certain functionals of α-expansions, e.g. the number of specific digital patterns, satisfy a central limit theorem, which is an extension of a result due to Drmota [3].