Geodesic
A new determinant expression of the zeta function for a hypergraph
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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Recently, Storm defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it by the Perron-Frobenius operator of a digraph and a deformation of the usual Laplacian of a graph. We present a new determinant expression for the Ihara-Selberg zeta function of a hypergraph, and give a linear algebraic proof of Storm's Theorem. Furthermore, we generalize these results to the Bartholdi zeta function of a hypergraph.
DOI : 10.37236/221
Classification : 05C65, 05C50, 11M99, 15A15
Mots-clés : Ihara-Selberg zeta function of a hypergraph, Bartholdi zeta function of a hypergraph 
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     author = {Iwao Sato},
     title = {A new determinant expression of the zeta function for a hypergraph},
     journal = {The electronic journal of combinatorics},
     year = {2009},
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     doi = {10.37236/221},
     zbl = {1230.05221},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/221/}
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Iwao Sato. A new determinant expression of the zeta function for a hypergraph. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/221

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