ON A PARTITION PROBLEM OF FINITE ABELIAN GROUPS
2015 ◽
Vol 92
(1)
◽
pp. 24-31
Keyword(s):
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$r_{A_{1}}=r_{A_{2}}=\cdots =r_{A_{t}}$.
2011 ◽
Vol 12
(01n02)
◽
pp. 125-135
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2019 ◽
Vol 150
(4)
◽
pp. 1937-1964
◽
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2008 ◽
Vol 18
(02)
◽
pp. 243-255
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2007 ◽
Vol 17
(04)
◽
pp. 837-849
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