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Combinatorial identities from the spectral theory of quantum graphs
The electronic journal of combinatorics, The Fraenkel Festschrift volume, Tome 8 (2001) no. 2
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The purpose of this paper is to present a newly discovered link between three seemingly unrelated subjects—quantum graphs, the theory of random matrix ensembles and combinatorics. We discuss the nature of this connection, and demonstrate it in a special case pertaining to simple graphs, and to the random ensemble of ${2\times 2}$ unitary matrices. The corresponding combinatorial problem results in a few identities, which, to the best of our knowledge, were not proven previously.
DOI : 10.37236/1615
Classification : 05A19, 05C38, 90B10, 05C50 
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     author = {Holger Schanz and Uzy Smilansky},
     title = {Combinatorial identities from the spectral theory of quantum graphs},
     journal = {The electronic journal of combinatorics},
     year = {2001},
     volume = {8},
     number = {2},
     doi = {10.37236/1615},
     zbl = {0981.05012},
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}
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Holger Schanz; Uzy Smilansky. Combinatorial identities from the spectral theory of quantum graphs. The electronic journal of combinatorics, The Fraenkel Festschrift volume, Tome 8 (2001) no. 2. doi: 10.37236/1615

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