论文标题
某些加权零和定理的概括和相关的极端序列
Generalization of some weighted zero-sum theorems and related Extremal sequence
论文作者
论文摘要
令$ g $为有限的Abelian offonent $ n $，让$ a $为$ [1，n-1] $的非空子集。 $ g $的davenport常数$ a $，用$ d_a（g）$表示，定义为最低的正整数$ \ ell $，使得超过$ g $ length $ \ ell $的任何序列都具有非空的$ a $加权的零 - 零 - 零余量。同样，组合不变的$ e_ {a}（g）$被定义为最低的正整数$ \ ell $，以使得任何$ g $ length $ \ ell $的序列具有$ a $ a $ a $ weper的零sum长度$ | g | $。在本文中，我们确定$ d_a（\ mathbb {z} _n）$的确切值，对于$ n $的某些特定值，其中$ a $是$ \ mathbb {z} _n^*$中的所有立方体的集合。在这种情况下，我们还确定了相关的极端序列的结构。
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 over $G$ of length $\ell$ has a non-empty $A$-weighted zero-sum subsequence. Similarly, the combinatorial invariant $E_{A}(G)$ is defined to be the least positive integer $\ell$ such that any sequence over $G$ of length $\ell$ has an $A$-weighted zero-sum subsequence of length $|G|$. In this article, we determine the exact value of $D_A(\mathbb{Z}_n)$, for some particular values of $n$, where $A$ is the set of all cubes in $\mathbb{Z}_n^*$. We also determine the structure of the related extremal sequence in this case.
