论文标题
在长度exp（g）的零和子序列上
On zero-sum subsequences of length exp(G)
论文作者
论文摘要
让$ g $为有限的阿贝尔集团。令$ g（g）$为最小的正整数$ t $，使得组的每个子集$ t $ g $都包含一个基因为零的基数$ \ mathrm {exp} $的基数。在本文中，我们表明，如果x是$ \ mathbb {z}^2_ {2_ {2n} $的子集，则具有基数$ 4N+1 $和$ 2N $或$ 2N $或$ 2N-1 $的元素的$ x $具有相同的第一个坐标，则$ x $包含一个零组件。作为我们结果的应用，我们证明$ g（\ mathbb {z}^2_6）= 13。
Let $G$ be a finite abelian group. Let $g(G)$ be the smallest positive integer $t$ such that every subset of cardinality $t$ of the group $G$ contains a subset of cardinality $\mathrm{exp}(G)$ whose sum is zero. In this paper, we show that if X is a subset of $\mathbb{Z}^2_{2n}$ with cardinality $4n+1$ and $2n$ or $2n-1$ elements of $X$ have the same first coordintes, then $X$ contains a zero sum subset. As an application of our results we prove that $g(\mathbb{Z}^2_6) = 13.$ This settles Gao-Thangaduri's conjecture for the case $n=6.$ We also prove some results towards the general even $n$ cases of the conjecture.
