相关论文: The Weighted Davenport Constant of a group and a r…

Let $G$ be a finite abelian group of exponent $n$ and let $A$ be a non-empty subset of $[1,n-1]$. The Davenport constant of $G$ with weight $A$, denoted by $D_A(G)$, is defined to be the least positive integer $\ell$ such that any sequence…

For a finite abelian group $G,$ the Davenport Constant, denoted by $D(G)$, is defined to be the least positive integer $k$ such that every sequence of length at least $k$ has a non-trivial zero-sum subsequence. A long-standing conjecture is…

For a finite abelian group $G$ with $\exp(G)=n$ and an integer $k\ge 2$, Balachandran and Mazumdar \cite{BM} introduced the extremal function $\fD_G(k)$ which is defined to be $\min\{|A|: \emptyset \neq A\subseteq[1,n-1]\textrm{\ with\…

For a finite group $G,$ $\mathsf{D}(G)$ is defined as the least positive integer $k$ such that for every sequence $S=g_1\bdot g_2\bdot \dotsc \bdot g_k$ of length $k$ over $G$, there exist $1 \le i_1 < i_2 <\cdots < i_m \le k $ such that…

For the cyclic group $G=\mathbb{Z}/n\mathbb{Z}$ and any non-empty $A\in\mathbb{Z}$. We define the Davenport constant of $G$ with weight $A$, denoted by $D_A(n)$, to be the least natural number $k$ such that for any sequence $(x_1, ...,…

For $(G,+)$ a finite abelian group the plus-minus weighted Davenport constant, denoted $\mathsf{D}_{\pm}(G)$, is the smallest $\ell$ such that each sequence $g_1 ... g_{\ell}$ over $G$ has a weighted zero-subsum with weights +1 and -1,…

A generalization of the Davenport constant is investigated. For a finite abelian group $G$ and a positive integer $k$, let $D_k(G)$ denote the smallest $\ell$ such that each sequence over $G$ of length at least $\ell$ has $k$ disjoint…

Let $G$ be a finite additive abelian group with exponent $d^kn, d,n>1,$ and $k$ a positive integer. For $S$ a sequence over $G$ and $A=\{1,2,\ldots,d^kn-1\}\setminus\{d^kn/d^i:i\in[1,k]\}, $ we investigate the lower bound of the number…

For a finite abelian group $G$ and a positive integer $k$, let $\mathsf{D}_k(G)$ denote the smallest integer $\ell$ such that each sequence over $G$ of length at least $\ell$ has $k$ disjoint nontrivial zero-sum subsequences. It is known…

Let $G = C_{n_1} \oplus \cdots \oplus C_{n_r}$ with $1 < n_1 | \cdots | n_r$ be a finite abelian group. The Davenport constant $\mathsf D(G)$ is the smallest integer $t$ such that every sequence $S$ over $G$ of length $|S|\ge t$ has a…

Let $G$ be a finite abelian group and let $\varnothing \neq A \subset \mathbb Z$. The $A$-weighted Davenport constant of $G$ is the smallest positive integer ${\sf D}_A(G)$ such that every sequence $x_1 \boldsymbol{\cdot} {\dots}…

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…

Let p be a prime number. Let G be a finite abelian p-group of exponent n (written additively) and A be a non-empty subset of $]n[:= \{1,2,..., n\}$ such that elements of A are incongruent modulo p and non-zero modulo p. Let $k \geq…

The Davenport constant for a finite abelian group $G$ is the minimal length $\ell$ such that any sequence of $\ell$ terms from $G$ must contain a nontrivial zero-sum sequence. For the group $G=(\mathbb Z/n\mathbb Z)^2$, its value is $2n-1$,…

We consider two families of weighted zero-sum constants for finite abelian groups. For a finite abelian group $( G , + )$, a set of weights $W \subset \mathbb{Z}$, and an integral parameter $m$, the $m$-wise Davenport constant with weights…

Let $G$ be a finite (not necessarily abelian) group and let $p=p(G)$ be the smallest prime number dividing $|G|$. We prove that $d(G)\leq \frac{|G|}{p}+9p^2-10p$, where $d(G)$ denotes the small Davenport constant of $G$ which is defined as…

$G$ be an additive finite abelian group. The Davenport constant $\mathsf D(G)$ is the smallest integer $t$ such that every sequence (multiset) $S$ over $G$ of length $|S|\ge t$ has a non-empty zero-sum subsequence. Recently, B. Girard…

Let $G$ be a group and $A\subseteq [1,\exp(G)-1]$. We define the constant ${\sf C}_A(G),$ which is the least positive integer $\ell$ such that every sequence over $G$ of length at least $\ell$ has an $A$-weighted consecutive product-one…

We investigate a certain well-established generalization of the Davenport constant. For $j$ a positive integer (the case $j=1$, is the classical one) and a finite Abelian group $(G,+,0)$, the invariant $\Dav_j(G)$ is defined as the smallest…

Let $G$ be a finite group written multiplicatively. By a sequence over $G$, we mean a finite sequence of terms from $G$ which is unordered, repetition of terms allowed, and we say that it is a product-one sequence if its terms can be…