Zero sums in restricted sequences

Article Type

Research Article

Publication Title

Discrete Mathematics


Suppose A⊂Zn∖{0}. A sequence x=(x1,…,xm) of elements of Zn is called an A-weighted Davenport Z-sequence if there exists a≔(a1,…,am)∈(A∪{0})m∖0m such that ∑iaixi=0, where 0m=(0,…,0)∈Znm. Similarly, the sequence x is called an A-weighted Erdős Z-sequence if there exists a=(a1,…,am)∈(A∪{0})m with |Supp(a)|=n, such that ∑iaixi=0, where Supp(a)≔{i:ai≠0}. A Zn-sequence x is called k-restricted if no element of Zn appears more than k times in x. In this paper, we study the problem of determining the least value of m for which a k-restricted Zn-sequence of length m is an A-weighted Davenport Z-sequence (resp. an A-weighted Erdős Z-sequence). We also consider the same problem for random Zn-sequences and some very natural choices of the set A.



Publication Date



Open Access, Green

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