Generalized de Bruijn digraphs and the distribution of patterns in α-expansions Original Research Article

A generalization of de Bruijn digraphs is defined for Parryʹs 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 (Proceedings of the International Conference held in Graz, Austria, 1998, p. 103).