论文标题
一致性涵盖系统的计算和观察
Computations and observations on congruence covering systems
论文作者
论文摘要
$ \ textit {covering system} $是整数一致性的集合，因此每个整数都可以满足该集合中至少一个一致性。如果其所有模量都不同，则覆盖系统称为$ \ textit {不同的} $。自ERDS引入以来，已经开发了涵盖系统的广泛文献。在这里，我们提供了最多十个模量的不同覆盖系统的完整分类，我们根据两种形式的等价形式将其分组在一起。结果，我们确定了一个超过$ 2 $的不同覆盖系统的最低基数，即$ 11 $。
A $\textit{covering system}$ is a collection of integer congruences such that every integer satisfies at least one congruence in the collection. A covering system is called $\textit{distinct}$ if all of its moduli are distinct. An expansive literature has developed on covering systems since their introduction by Erdős. Here we provide a full classification of distinct covering systems with at most ten moduli, which we group together based on two forms of equivalence. As a consequence, we determine the minimum cardinality of a distinct covering system with all moduli exceeding $2$, which is $11$.
