Direct and inverse theorems on signed sumsets of integers

JOURNAL OF NUMBER THEORY

卷:196

Article

Bhanja, Jagannath¹  Pandey, Ram Krishna¹ 

[1] Indian Inst Technol, Dept Math, Roorkee 247667, Uttarakhand, India

关键词: Sumset;    Signed sumset;    Direct and inverse problems;   

DOI  :  10.1016/j.jnt.2018.09.005

来源: Elsevier

【 摘 要 】

Let G be an additive abelian group and h be a positive integer. For a nonempty finite subset A = {a(0), a(1), ... , a(k-1)} of G, we let h +/- A := {Sigma(k-1)(i=0) lambda(i)a(i) : (lambda(0), ... , lambda(k-1)) is an element of Z(k), Sigma(k-1)(i=0) vertical bar lambda(i)vertical bar = h}, be the h-fold signed sumset of A. The direct problem for the signed sumset h +/- A is to find a nontrivial lower bound for vertical bar h +/- A vertical bar in terms of vertical bar A vertical bar. The inverse problem for h +/- A is to determine the structure of the finite set A for which vertical bar h +/- A vertical bar is minimal. In this article, we solve both the direct and inverse problems for vertical bar h +/- A vertical bar, when A is a finite set of integers. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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