论文标题
精确覆盖系统的定向图
Directed Graphs from Exact Covering Systems
论文作者
论文摘要
给定一个精确的覆盖系统$ s = \ {a_i $（mod $ d_i $）$：1 \ leq i \ leq r \} $，我们介绍了相应的精确覆盖系统digraph（ecsd）$ g_s = g（d_1n+a_1，a_1，\ a_1，\ ldots，d_rn+a_r+a_r）$。 $ g_s $的顶点是整数，每个$ n \ in \ mathbb {z} $的边缘为$（n，d_in+a_i）$，对于封面系统中的每个一致性。我们研究了这些有针对性图的结构，这些图形具有有限的许多组件，每个组件的一个周期以及indegree 1和每个顶点的超级$ r $。我们还探索具有整数的单个组件和非标准数字表示的ECSD之间的链接。
Given an exact covering system $S = \{a_i$ (mod $d_i$) $: 1 \leq i \leq r\}$, we introduce the corresponding exact covering system digraph (ECSD) $G_S = G(d_1n+a_1, \ldots, d_rn+a_r)$. The vertices of $G_S$ are the integers and the edges are $(n, d_in+a_i)$ for each $n \in \mathbb{Z}$ and for each congruence in the covering system. We study the structure of these directed graphs, which have finitely many components, one cycle per component, as well as indegree 1 and outdegree $r$ at each vertex. We also explore the link between ECSDs that have a single component and non-standard digital representations of integers.
