The Zeta Function of a Hypergraph

We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto's factorization results for biregular bipartite graphs apply, leading to exact factorizations. For $(d,r)$-regular hypergraphs, we show that a modified Riemann hypothesis is true if and only if the hypergraph is Ramanujan in the sense of Winnie Li and Patrick Sol\'e. Finally, we give an example to show how the generalized zeta function can be applied to graphs to distinguish non-isomorphic graphs with the same Ihara-Selberg zeta function.Comment: 24 pages, 6 figure

Comment: Desegregation -- The Times They Are A-Changin\u27

Courts are currently concerned over the extent of their powers to integrate racially separate housing and schools within metropolitan areas containing black inner cities and white suburbs. This Comment reviews the jurisprudence addressing when it is a proper exercise of a court\u27s equity jurisdiction to fashion a metropolitan or interdistrict remedial order in which the city and its surrounding suburbs are treated as one system. The Comment focuses on the recent Supreme Court decision in Milliken v. Bradley, in which the Court reversed a decision of the Sixth Circuit Court of Appeals which upheld the district court\u27s power to order enforcement of a plan that would have integrated the schools of up to fifty-four school districts in Detroit. The Court held that an interdistrict remedy is dependent on finding an interdistrict constitutional violation, which it found was not present in the Milliken case. The Comment observes that Milliken was the first time since Brown I that the Court had reversed a lower court order which sought to promote the integration of the races after finding unconstitutional segregation. It thus concludes that the history of the Supreme Court as an instrument of reversing the separation of the races has entered a new phase

A Sword Cuts Two Ways: Cold War Policymaking in the OAS

Latin American Studie