72 research outputs found
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 -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
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Combinatorics
Combinatorics is a fundamental mathematical discipline which focuses on the study of discrete objects and their properties. The current workshop brought together researchers from diverse fields such as Extremal and Probabilistic Combinatorics, Discrete Geometry, Graph theory, Combinatorial Optimization and Algebraic Combinatorics for a fruitful interaction. New results, methods and developments and future challenges were discussed. This is a report on the meeting containing abstracts of the presentations and a summary of the problem session
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