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Infinitely Often Dense Bases for the Integers with a Prescribed Representation Function
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Jaewoo Lee
Published/Copyright:
July 8, 2010
Abstract
Nathanson constructed asymptotic bases for the integers with prescribed representation functions, then asked how dense they can be. We can easily obtain an upper bound using a simple argument. In this paper, we will see this is indeed the best bound when we prescribe an arbitrary representation function.
Received: 2007-12-09
Accepted: 2010-02-16
Published Online: 2010-07-08
Published in Print: 2010-July
© de Gruyter 2010
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Articles in the same Issue
- Corrigendum and Statement on Priority for: Conjugacy Classes and Class Number
- The Euler Series Transformation and the Binomial Identities of Ljunggren, Munarini and Simons
- A Multitude of Expressions for the Stirling Numbers of the First Kind
- Infinitely Often Dense Bases for the Integers with a Prescribed Representation Function
- A Note on the Exact Expected Length of the kth Part of a Random Partition
- On Congruence Conditions for Primality
- The Divisibility of an – bn by Powers of n
- Long Arithmetic Progressions in Small Sumsets
- On the Least Common Multiple of Q-Binomial Coefficients
- Flat Cyclotomic Polynomials of Order Four and Higher
- On Vanishing Sums of Distinct Roots of Unity
