Elsevier

Discrete Mathematics

Volume 162, Issues 1–3, 25 December 1996, Pages 127-132
Discrete Mathematics

Regular paper
On weighted sums in abelian groups

https://doi.org/10.1016/0012-365X(95)00281-ZGet rights and content
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Abstract

Let G be an abelian group of order n and Davenport constant d and let k be a natural number. Let x0,x1, …,xm be a sequence of elements of G such that xo has the most repeated value in the sequence. Let {wi; 1 ⩽ ik} be a family of integers prime relative to n. We obtain the following two generalizations of the Erdös-Ginzburg-Ziv Theorem.

For mn + k − 1, we prove that there is a permutation α of [1,m] such that 1 ⩽ i ⩽ kwixα(i)=1 ⩽ i ⩽ kwix0.

For kn − 1 and mk + d − 1, we prove that there is a k-subset K ⊂ [1, m] such that i ∈ Kxi=kx0.

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