We derive an explicit formula for the Abelian complexity of infinite words associated with quadratic Parry numbers. © 2011 Elsevier B.V. All rights reserved.

Expansions in noninteger positive bases have been intensively investigated since the pioneering works of Rényi (1957) and Parry (1960). The discovery of surprising unique expansions in certain noninteger bases by Erdős, Horváth and Joó (1991) was followed by many studies aiming to clarify the topological and combinatorial nature of the sets of these bases. In the present work we extend some of ...

We generalize several theorems of Rényi, Parry, Daróczy and Kátai by characterizing the greedy and quasi-greedy expansions in non-integer bases.

The (−β)-integers are natural generalisations of the β-integers, and thus of the integers, for negative real bases. When β is the analogue of a Parry number, we describe the structure of the set of (−β)-integers by a fixed point of an anti-morphism.

Parry O, Peel E, Douglas M, et al. Patients in waiting: a qualitative study of type 2 diabetes patients’ perceptions of diagnosis. Fam Pract 2004;21:131–6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....