Ramanujan Hypergraphs and Ramanujan Geometries

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Ramanujan hypergraphs or bigraphs (bipartite biregular graphs) are to the biregular tree what Ramanujan graphs are to the homogeneous tree. A survey of the known constructions is given. Of special interest is the case when the bidegree (k, l) is non-symmetric, i.e. kl. The case of r—partite graphs is sketched out and a connection with buildings and chamber systems is looked at. The concept of universal cover of a family of finite graphs by an infinite locally finite graph is emphasized.