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ON A PARTITION PROBLEM OF FINITE ABELIAN GROUPS

Published online by Cambridge University Press:  29 April 2015

ZHENHUA QU*
Affiliation:
Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, PR China email [email protected]
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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 $r_{A_{1}}=r_{A_{2}}=\cdots =r_{A_{t}}$.

Type
Research Article
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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