Expansions in Non-integer Bases: Lower Order Revisited

نویسندگان

  • SIMON BAKER
  • NIKITA SIDOROV
چکیده

Let q ∈ (1, 2) and x ∈ [0, 1 q−1 ]. We say that a sequence (εi) ∞ i=1 ∈ {0, 1}N is an expansion of x in base q (or a q-expansion) if

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Greedy and Quasi-greedy Expansions in Non-integer Bases

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

متن کامل

Robot's finger and expansions in non-integer bases

We study a robot finger model in the framework of the theory of expansions in non-integer bases. We investigate the reachable set and its closure. A control policy to get approximate reachability is also proposed.

متن کامل

Expansions in Non-integer Bases: Lower, Middle and Top Order

Let q ∈ (1, 2); it is known that each x ∈ [0, 1/(q− 1)] has an expansion of the form x = ∑ ∞ n=1 anq −n with an ∈ {0, 1}. It was shown in [3] that if q < ( √ 5 + 1)/2, then each x ∈ (0, 1/(q − 1)) has a continuum of such expansions; however, if q > ( √ 5 + 1)/2, then there exist infinitely many x having a unique expansion [4]. In the present paper we begin the study of parameters q for which th...

متن کامل

Minimal weight expansions in Pisot bases

Abstract. For applications to cryptography, it is important to represent numbers with a small number of non-zero digits (Hamming weight) or with small absolute sum of digits. The problem of finding representations with minimal weight has been solved for integer bases, e.g. by the non-adjacent form in base 2. In this paper, we consider numeration systems with respect to real bases β which are Pi...

متن کامل

On the expansions of a real number to several integer bases

Only very little is known on the expansions of a real number to several integer bases. We establish various results showing that the expansions of a real number in two multiplicatively independent bases cannot both be simple, in a suitable sense. We also construct explicitly a real number ξ which is rich to all integer bases, that is, with the property that, for every integer b ≥ 2, every finit...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013