منابع مشابه
Beta-expansions with Negative Bases
This paper investigates representations of real numbers with an arbitrary negative base −β < −1, which we call the (−β)-expansions. They arise from the orbits of the (−β)-transformation which is a natural modification of the β-transformation. We show some fundamental properties of (−β)-expansions, each of which corresponds to a well-known fact of ordinary β-expansions. In particular, we charact...
متن کاملUniversal Expansions in Negative and Complex Bases
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 ...
متن کاملProperties of Expansions in Complex Bases
Abstract. 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 exten...
متن کاملOn alpha-adic expansions in Pisot bases
We study α-adic expansions of numbers, that is to say, left infinite representations of numbers in the positional numeration system with the base α, where α is an algebraic conjugate of a Pisot number β. Based on a result of Bertrand and Schmidt, we prove that a number belongs to Q(α) if and only if it has an eventually periodic α-expansion. Then we consider α-adic expansions of elements of the...
متن کاملMinimal Weight Expansions in Some Pisot Bases
For numeration systems representing real numbers and integers, which are based on Pisot numbers, we study expansions with signed digits which are minimal with respect to the absolute sum of digits. It is proved that these expansions are recognizable by a finite automaton if the base β is the root of a polynomial whose (integer) coefficients satisfy a certain condition (D). When β is the Golden ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Publicationes Mathematicae Debrecen
سال: 2014
ISSN: 0033-3883
DOI: 10.5486/pmd.2014.5962