Add to ORKGAbstract. In a multi-base representation of an integer (in contrast to, for example, the binary or decimal representation) the base (or radix) is replaced by products of powers of single bases. The resulting numeral system is usually redundant, which means that each integer can have multiple different digit expansions. We provide a general asymptotic formula for the number of such multi-base representations of a positive integer n. Moreover, we prove central limit theorems for the sum of digits and the Hamming weight of a random representation. 1
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...
We study representations of integers n in binary expansions using the digits 0, ±1. We analyze the a...
We investigate the existence of simultaneous representations of real numbers x in bases 1 < q1< ⯠<...
We investigate the existence of simultaneous representations of real numbers x in bases 1 < q1< ⯠<...
Applications of signed digit representations of an integer include computer arith-metic, cryptograph...
This paper deals with pairs of integers, written in base two expansions using digits 0, ±1. Represen...
Abstract. Number systems with a rational number a/b> 1 as base have gained interest in recent yea...
summary:Binary signed digit representations (BSDR's) of integers have been studied since the 1950's....
summary:Binary signed digit representations (BSDR's) of integers have been studied since the 1950's....
summary:Binary signed digit representations (BSDR's) of integers have been studied since the 1950's....
This paper deals with pairs of integers, written in base two expansions using digits 0,±1. Represent...
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...
We study representations of integers n in binary expansions using the digits 0, ±1. We analyze the a...
We investigate the existence of simultaneous representations of real numbers x in bases 1 < q1< ⯠<...
We investigate the existence of simultaneous representations of real numbers x in bases 1 < q1< ⯠<...
Applications of signed digit representations of an integer include computer arith-metic, cryptograph...
This paper deals with pairs of integers, written in base two expansions using digits 0, ±1. Represen...
Abstract. Number systems with a rational number a/b> 1 as base have gained interest in recent yea...
summary:Binary signed digit representations (BSDR's) of integers have been studied since the 1950's....
summary:Binary signed digit representations (BSDR's) of integers have been studied since the 1950's....
summary:Binary signed digit representations (BSDR's) of integers have been studied since the 1950's....
This paper deals with pairs of integers, written in base two expansions using digits 0,±1. Represent...
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...