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A REMARK ON WEIGHTED REPRESENTATION FUNCTIONS
- Source :
- Taiwanese J. Math. 18, no. 6 (2014), 1713-1719
- Publication Year :
- 2014
- Publisher :
- The Mathematical Society of the Republic of China, 2014.
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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 $n\in G$.
Details
- ISSN :
- 10275487
- Volume :
- 18
- Database :
- OpenAIRE
- Journal :
- Taiwanese Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....b889c558d023272dd31534583f41b673