# On the number of weighted subsequences with zero-sum in a finite abelian group

@article{Lemos2015OnTN, title={On the number of weighted subsequences with zero-sum in a finite abelian group}, author={Ab'ilio Lemos and Allan De Oliveira Moura}, journal={arXiv: Number Theory}, year={2015} }

Suppose G is a finite abelian group and S = g1 ···gl is a sequence of elements in G. For any element g of G and A ⊆ Z\{0}, let NA,g(S) denote the number of subsequences T = Q i∈I gi of S such that P i∈I aigi = g , where I ⊆ {1,...,l} and ai ∈ A. The purpose of this paper is to investigate the lower bound for NA,0(S). In particular, we prove that NA,0(S) ≥ 2 |S|=D A(G)+1 , where DA(G) is the smallest positive integer l such that every sequence over G of length at least l has a nonempty A-zero…

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