Modified Erdös--Ginzburg--Ziv Constants for $\mathbb{Z}/n\mathbb{Z}$ and $(\mathbb{Z}/n\mathbb{Z}{)}^2$

Abstract

For an abelian group $G$ and an integer $t>0$, the \emph{modified Erdös--Ginzburg--Ziv constant} $s_t^{\prime }(G)$ is the smallest integer $\ell$ such that any zero-sum sequence of length at least $\ell$ with elements in $G$ contains a zero-sum subsequence (not necessarily consecutive) of length $t$. We compute $s_t^{\prime }(G)$ for $G=\mathbb{Z}/n\mathbb{Z}$ and for $t=n$, $G=(\mathbb{Z}/n\mathbb{Z}{)}^2$.