Graph coverings and twisted operators
Résumé
Given a graph and a representation of its fundamental group, there is a naturally associated twisted adjacency operator. The main result of this article is the fact that these operators behave in a controlled way under graph covering maps. When such an operator can be used to enumerate objects, or compute a partition function, this has concrete implications on the corresponding enumeration problem, or statistical mechanics model. For example, we show that if $\widetilde{\Gamma}$ is a finite connected covering graph of a graph $\Gamma$ endowed with edge-weights $x=\{x_e\}_e$, then the spanning tree partition function of $\Gamma$ divides the one of $\widetilde{\Gamma}$ in the ring $\mathbb{Z}[x]$. Several other consequences are obtained, some known, others new.
Domaines
Mathématiques [math]
Fichier principal
graph-coverings.pdf (526.4 Ko)
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Gmn.pdf (3.72 Ko)
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gamma.pdf (5.91 Ko)
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graph-coverings.bbl (5.51 Ko)
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| Origine | Fichiers produits par l'(les) auteur(s) |
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| Origine | Fichiers produits par l'(les) auteur(s) |
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