论文标题
发病率超图：盒子产品和laplacian
Incidence Hypergraphs: Box Products & the Laplacian
论文作者
论文摘要
盒子产品及其相关的框指数的特征是砂码（有向图），多编码，SET系统超图和发病率超图。结果表明，只能通过其自己的类别中的homs来表征盒子指数的箭袋案例。发生率超图盒产物中的不对称性通过双重锁定的概括来纠正，该概括分别将顶点和边缘视为复数的真实和虚构部分。这种新的超图盒产品被证明具有自然的解释，作为通过两部分表示函子作为图形的典型框产品，其相关的盒子指数完全表示为HOMS，完全是在入射率超法类别中的类别。通过通过发病率映射确定的发生率。表明对路径的盒子指数的评估与方向超高的无标志性拉普拉斯矩阵的半能力相对应。
The box product and its associated box exponential are characterized for the categories of quivers (directed graphs), multigraphs, set system hypergraphs, and incidence hypergraphs. It is shown that only the quiver case of the box exponential can be characterized via homs entirely within their own category. An asymmetry in the incidence hypergraphic box product is rectified via an incidence dual-closed generalization that effectively treats vertices and edges as real and imaginary parts of a complex number, respectively. This new hypergraphic box product is shown to have a natural interpretation as the canonical box product for graphs via the bipartite representation functor, and its associated box exponential is represented as homs entirely in the category of incidence hypergraphs; with incidences determined by incidence-prism mapping. The evaluation of the box exponential at paths is shown to correspond to the entries in half-powers of the oriented hypergraphic signless Laplacian matrix.
