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ON A PARTITION PROBLEM OF FINITE ABELIAN GROUPS

Part of: Sequences and sets Abelian groups

Published online by Cambridge University Press:  29 April 2015

ZHENHUA QU
ZHENHUA QU*
Affiliation:
Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, PR China email zhqu@math.ecnu.edu.cn
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Abstract

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Let $G$ be a finite abelian group and $A\subseteq G$. For $n\in G$, denote by $r_{A}(n)$ the number of ordered pairs $(a_{1},a_{2})\in A^{2}$ such that $a_{1}+a_{2}=n$. Among other things, we prove that for any odd number $t\geq 3$, it is not possible to partition $G$ into $t$ disjoint sets $A_{1},A_{2},\dots ,A_{t}$ with $r_{A_{1}}=r_{A_{2}}=\cdots =r_{A_{t}}$.

Keywords

representation functionpartitionfinite abelian group

MSC classification

Primary: 11B34: Representation functions
Secondary: 20K01: Finite abelian groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 1 , August 2015 , pp. 24 - 31
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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