超图问题的 Zeon 与 Idem-Clifford 表述
Zeon and Idem-Clifford Formulations of Hypergraph Problems
AI总结：
本文将 zeon 与 idem-Clifford 图论方法推广至超图，用于枚举路径、迹、独立集、团和匹配，并提出最小横截求解方法及开放问题的 zeon 表述。
摘要：
Zeon 代数已被证明可用于枚举图中的结构，例如路径、迹、圈、匹配、团和独立集。在普通图中，每条边恰好连接两个顶点；与此不同，在超图中，一条边（或称“超边”）可以连接任意数量的顶点。在博弈论中，超图被称为简单博弈。超图已用于生物学、化学、图像处理、无线网络等领域的问题。在当前工作中，zeon（“nil-Clifford”）和“idem-Clifford”图论方法被推广到超图。具体而言，zeon 和 idem-Clifford 方法被用于枚举超图中的路径、迹、独立集、团和匹配。文中还发展了一种寻找最小超图横截的方法，并给出了一些开放性超图问题的 zeon 表述。
英文摘要：
Zeon algebras have proven to be useful for enumerating structures in graphs, such as paths, trails, cycles, matchings, cliques, and independent sets. In contrast to an ordinary graph, in which each edge connects exactly two vertices, an edge (or, "hyperedge") can join any number of vertices in a hypergraph. In game theory, hypergraphs are called simple games. Hypergraphs have been used for problems in biology, chemistry, image processing, wireless networks, and more. In the current work, zeon ("nil-Clifford") and "idem-Clifford" graph-theoretic methods are generalized to hypergraphs. In particular, zeon and idem-Clifford methods are used to enumerate paths, trails, independent sets, cliques, and matchings in hypergraphs. An approach for finding minimum hypergraph transversals is developed, and zeon formulations of some open hypergraph problems are presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
