论文标题
解决零和理论中指数猜想的解决方案
Solution to the index conjecture in zero-sum theory
论文作者
论文摘要
零和理论中的一个问题是确定所有对$（k，n）$的所有最小零和长度序列的$ k $ modulo $ n $具有指数$ 1 $。尽管所有其他案件已经解决了十多年前，但$ k $等于$ 4 $而$ n $的案例均为$ 6 $保持开放。确切地说，该主题的索引猜想指出，如果$ n $占$ 6 $，那么每个最小的零和长度序列的$ 4 $ modulo $ n $具有指数$ 1 $。在本文中，我们证明了对于某些绝对常数$ n $的所有$ n> n $的猜想的同等版本。
A problem in zero-sum theory is to determine all pairs $(k,n)$ for which every minimal zero-sum sequence of length $k$ modulo $n$ has index $1$. While all other cases have been solved more than a decade ago, the case when $k$ equals $4$ and $n$ is coprime to $6$ remains open. Precisely, The Index Conjecture in this subject states that if $n$ is coprime to $6$ then every minimal zero-sum sequence of length $4$ modulo $n$ has index $1$. In this paper, we prove an equivalent version of this conjecture for all $n>N$ for some absolute constant $N$.
