Minimal expansions in redundant number systems: Fibonacci bases and Greedy algorithms
نویسنده
چکیده
We study digit expansions with arbitrary integer digits in base q (q integer) and the Fibonacci base such that the sum of the absolute values of the digits is minimal. For the Fibonacci case, we describe a unique minimal expansion and give a greedy algorithm to compute it. Additionally, transducers to calculate minimal expansions from other expansions are given. For the case of even integer bases q, similar results are given which complement those given in [6].
منابع مشابه
Redundancy of minimal weight expansions in Pisot bases
Motivated by multiplication algorithms based on redundant number representations, we study representations of an integer n as a sum n=∑kεkUk, where the digits εk are taken from a finite alphabet Σ and (Uk)k is a linear recurrent sequence of Pisot type with U0=1. The most prominent example of a base sequence (Uk)k is the sequence of Fibonacci numbers. We prove that the representations of minimal...
متن کاملAdditive Functions on the Greedy and Lazy Fibonacci Expansions
We find all complex-valued functions that are additive with respect to both the greedy and the lazy Fibonacci expansions. We take it a little further by considering the subsets of these functions that are also multiplicative. In the final section we extend these ideas to Tribonacci expansions.
متن کاملGreedy 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 کاملTo appear in J. Théor. Nombres Bordeaux MINIMAL REDUNDANT DIGIT EXPANSIONS IN THE GAUSSIAN INTEGERS
We consider minimal redundant digit expansions in canonical number systems in the Gaussian integers. In contrast to the case of rational integers, where the knowledge of the two least significant digits in the “standard” expansion suffices to calculate the least significant digit in a minimal redundant expansion, such a property does not hold in the Gaussian numbers: We prove that there exist p...
متن کاملThe Joint Distribution of Greedy and Lazy Fibonacci Expansions
with digits k ∈ {0, 1}. The maximal expansion with respect to the lexicographic order on (. . . , 4, 3, 2) is the Zeckendorf expansion or, more generally, the greedy expansion, which has been studied by Zeckendorf [7] and many others. (Lexicographic order means (. . . , 3, 2) < (. . . , 3, ′ 2) if k < ′ k for some k ≥ 2 and j ≤ j for all j ≥ k.) The minimal expansion with respect to this order ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Periodica Mathematica Hungarica
دوره 49 شماره
صفحات -
تاریخ انتشار 2004