  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.
