Geodesic
Counting invertible Schrödinger operators over finite fields for trees, cycles and complete graphs
Roland Bacher1
1University Grenoble Alpes, Institut Fourier
The electronic journal of combinatorics, Tome 22 (2015) no. 4
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We count invertible Schrödinger operators (perturbations by diagonal matrices of the adjacency matrix) over finite fields for trees, cycles and complete graphs. This is achieved for trees through the definition and use of local invariants (algebraic constructions of perhaps independent interest). Cycles and complete graphs are treated by ad hoc methods.
DOI : 10.37236/5183
Classification : 05E18, 05C30, 05C50, 05C76
Mots-clés : enumerative combinatorics, invariants, Schrödinger operator

Roland Bacher  1

1 University Grenoble Alpes, Institut Fourier 
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     author = {Roland Bacher},
     title = {Counting invertible {Schr\"odinger} operators over finite fields for trees, cycles and complete graphs},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {4},
     doi = {10.37236/5183},
     zbl = {1329.05155},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/5183/}
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Roland Bacher. Counting invertible Schrödinger operators over finite fields for trees, cycles and complete graphs. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/5183

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