Taiwanese Journal of Mathematics

A REMARK ON WEIGHTED REPRESENTATION FUNCTIONS

Zhenhua Qu

Full-text: Open access

Abstract

Let $G$ be a finite abelian group, and $k_1,k_2$ be two integers. For any subset $A\subset G$, let $r_{k_1,k_2}(A,n)$ denote the number of solutions of $n=k_1a_1+k_2a_2$ with $a_1,a_2\in A$. In this paper, we generalize a result of Q.-H. Yang and Y.-G. Chen to finite abelian groups. More precisely, we characterize all subsets $A\subset G$ such that $r_{k_1,k_2}(A,n)=r_{k_1,k_2}(G\backslash A,n)$ for all $n\in G$.

Article information

Source
Taiwanese J. Math., Volume 18, Number 6 (2014), 1713-1719.

Dates
First available in Project Euclid: 21 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500667492

Digital Object Identifier
doi:10.11650/tjm.18.2014.4334

Mathematical Reviews number (MathSciNet)
MR3284027

Zentralblatt MATH identifier
1357.11015

Subjects
Primary: 11B34: Representation functions 20K01: Finite abelian groups [For sumsets, see 11B13 and 11P70]

Keywords
representation function partition Sárközy problem

Citation

Qu, Zhenhua. A REMARK ON WEIGHTED REPRESENTATION FUNCTIONS. Taiwanese J. Math. 18 (2014), no. 6, 1713--1719. doi:10.11650/tjm.18.2014.4334. https://projecteuclid.org/euclid.twjm/1500667492


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