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

Wolfgang Steiner (1)

1 Institut für Geometrie

A generalization of de Bruijn digraphs is defined for Parry's $\alpha$-expansions and it is shown that the characteristic polynomial of these graphs is in principle that of $\alpha$. With the help of this result we prove that certain functionals of $\alpha$-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].

Mots clés: graphes de de Bruijn; polynôme caractéristique; systèmes de numération; théorème central limite

Domaines: Mathématique discrète [cs.DM]; Théorie des nombres [math.NT]

Wolfgang Steiner. Generalized de Bruijn digraphs and the distribution of patterns in alpha-expansions. Discrete Mathematics, 2003, 263, pp.247-268. ⟨hal-00023225⟩