Related papers: Modified Erd\H{o}s-Ginzburg-Ziv constants for $\ma…

Let $G$ be a finite abelian group, and $r$ be a multiple of its exponent. The generalized Erd\H{o}s-Ginzburg-Ziv constant $s_r(G)$ is the smallest integer $s$ such that every sequence of length $s$ over $G$ has a zero-sum subsequence of…

For an abelian group $G$ and an integer $t > 0$, the modified Erd\H{o}s-Ginzburg-Ziv constant $s'_t(G)$ is the smallest integer $\ell$ such that any zero-sum sequence of length at least $\ell$ with elements in $G$ contains a zero-sum…

For an abelian group $G$ and an integer $t > 0$, the \emph{modified Erd\"os--Ginzburg--Ziv constant} $s_t'(G)$ is the smallest integer $\ell$ such that any zero-sum sequence of length at least $\ell$ with elements in $G$ contains a zero-sum…

Let $G$ be a finite abelian group. The Erd{\H o}s--Ginzburg--Ziv constant $\mathsf s (G)$ of $G$ is defined as the smallest integer $l \in \mathbb N$ such that every sequence \ $S$ \ over $G$ of length $|S| \ge l$ \ has a zero-sum…

Let $G$ be a finite abelian group. The Erd{\H{o}}s-Ginzburg-Ziv constant $\mathsf s(G)$ of $G$ is defined as the smallest integer $l\in \mathbb{N}$ such that every sequence $S$ over $G$ of length $|S|\geq l$ has a zero-sum subsequence $T$…

Let $G$ be a finite abelian group, and $r$ be a multiple of its exponent. The generalized Erd\H{o}s-Ginzburg-Ziv constant $s_r(G)$ is the smallest integer $s$ such that every sequence of length $s$ over $G$ has a zero-sum subsequence of…

Let $G$ be a multiplicatively written finite group of order $n$. The Erd\H{o}s-Ginzburg-Ziv Theorem constant of the group $G$, denoted $\mathsf E(G)$, is defined as the smallest positive integer $\ell$ with the following property: for any…

For a finite abelian group $G$, the Erd\H{o}s-Ginzburg-Ziv constant $\mathfrak{s}(G)$ is the smallest $s$ such that every sequence of $s$ (not necessarily distinct) elements of $G$ has a zero-sum subsequence of length…

The Erd\H{o}s-Ginzburg-Ziv constant of an abelian group $G$, denoted $\mathfrak{s}(G)$, is the smallest $k\in\mathbb{N}$ such that any sequence of elements of $G$ of length $k$ contains a zero-sum subsequence of length $\exp(G)$. In this…

Let $G$ be an additive finite abelian group with exponent $\exp(G)=m$. For any positive integer $k$, the $k$-th generalized Erd\H{o}s-Ginzburg-Ziv constant $\mathsf s_{km}(G)$ is defined as the smallest positive integer $t$ such that every…

Let $\mathcal{S}$ be a finite commutative semigroup written additively, and let $\exp(\mathcal{S})$ be its exponent which is defined as the least common multiple of all periods of the elements in $\mathcal{S}$. For every sequence $T$ of…

For a finite abelian group $G$, the generalized Erd\H{o}s--Ginzburg--Ziv constant $\mathsf s_{k}(G)$ is the smallest $m$ such that a sequence of $m$ elements in $G$ always contains a $k$-element subsequence which sums to zero. If $n =…

For a finite abelian group $G$ and a positive integer $d$, let $\mathsf s_{d \mathbb N} (G)$ denote the smallest integer $\ell \in \mathbb N_0$ such that every sequence $S$ over $G$ of length $|S| \ge \ell$ has a nonempty zero-sum…

If $G$ is a finite Abelian group, define $s_{k}(G)$ to be the minimal $m$ such that a sequence of $m$ elements in $G$ always contains a $k$-element subsequence which sums to zero. Recently Bitz et al. proved that if $n = exp(G)$, then…

The classical Erd\H{o}s-Ginzburg-Ziv constant of a group $G$ denotes the smallest positive integer $\ell$ such that any sequence $S$ of length at least $\ell$ contains a zero-sum subsequence of length $\exp(G)$. In a recent paper, Caro and…

Let $G$ be a multiplicatively written finite group. We denote by $\mathsf E(G)$ the smallest integer $t$ such that every sequence of $t$ elements in $G$ contains a product-one subsequence of length $|G|$. In 1961, Erd\H{o}s, Ginzburg and…

Let $G$ be a multiplicatively written finite group. We denote by $\mathsf E(G)$ the smallest integer $t$ such that every sequence of $t$ elements in $G$ contains a product-one subsequence of length $|G|$. In 1961, Erd\H{o}s, Ginzburg and…

Let $G$ be a finite abelian group, and let $m>0$ with $\exp(G)\mid m$. Let $s_{m}(G)$ be the generalized Erd\H{o}s-Ginzburg-Ziv invariant which denotes the smallest positive integer $d$ such that any sequence of elements in $G$ of length…

Let $G$ be an additive finite abelian group and let $k\in [\exp(G),\mathsf{D}(G)-1]$ be a positive integer. Denote by $\mathsf{s}_{\leq k}(G)$ the smallest positive integer $l\in \mathbb{N}\cup \{+\infty\}$ such that each sequence of length…

Let $G$ be a finite abelian group of exponent $n$, written additively, and let $A$ be a subset of $\mathbb{Z}$. The constant $s_A(G)$ is defined as the smallest integer $\ell$ such that any sequence over $G$ of length at least $\ell$ has an…