# Zero sums in restricted sequences

## Article Type

Research Article

## Publication Title

Discrete Mathematics

## Abstract

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.

## DOI

10.1016/j.disc.2021.112394

## Publication Date

7-1-2021

## Recommended Citation

Balachandran, Niranjan and Mazumdar, Eshita, "Zero sums in restricted sequences" (2021). *Journal Articles*. 1898.

https://digitalcommons.isical.ac.in/journal-articles/1898

## Comments

Open Access, Green