Counting Non-Standard Binary Representations
نویسنده
چکیده
Let A be a finite subset of N including 0 and let fA(n) be the number of ways to write n = ∑∞i=0 ǫi2 , where ǫi ∈ A. We consider asymptotics of the summatory function sA(r,m) of fA(n) from m2 r to m2 − 1, and show that sA(r,m) ∼ c(A,m) ∣A∣ r for some nonzero c(A,m) ∈ Q.
منابع مشابه
Using both Binary and Residue Representations for Achieving Fast Converters in RNS
In this paper, a new method is introduced for improving the efficiency of the Residue Number System, which uses both binary and residue representations in order to represent a number. A residue number system uses the remainder of the division in several different modules. Conversion of a number to smaller ones and carrying out parallel calculations on these numbers greatly increase the speed of...
متن کاملUsing both Binary and Residue Representations for Achieving Fast Converters in RNS
In this paper, a new method is introduced for improving the efficiency of the Residue Number System, which uses both binary and residue representations in order to represent a number. A residue number system uses the remainder of the division in several different modules. Conversion of a number to smaller ones and carrying out parallel calculations on these numbers greatly increase the speed of...
متن کاملSearch, Binary Representations and Counting Optima
Choosing a good representation is a vital component of solving any search problem. However, choosing a good representation for a problem is as diicult as choosing a good search algorithm for a problem. Wolpert and Macready's No Free Lunch theorem proves that no search algorithm is better than any other over all possible discrete functions. We elaborate on the No Free Lunch theorem by proving th...
متن کاملCounting Optimal Joint Digit Expansions
This paper deals with pairs of integers, written in base two expansions using digits 0,±1. Representations with minimal Hamming weight (number of non-zero pairs of digits) are of special importance because of applications in Cryptography. The interest here is to count the number of such optimal representations.
متن کاملAnalysis of Alternative Digit Sets for Nonadjacent Representations
It is known that every positive integer n can be represented as a finite sum of the form ∑ i ai2 , where ai ∈ {0, 1,−1} and no two consecutive ai’s are non-zero (“nonadjacent form”, NAF). Recently, Muir and Stinson [12, 13] investigated other digit sets of the form {0, 1, x}, such that each integer has a nonadjacent representation (such a number x is called admissible). The present paper contin...
متن کاملذخیره 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 2016