Q-system Cluster Algebras, Paths and Total Positivity

We review the solution of the $A_r$ Q-systems in terms of the partition function of paths on a weighted graph, and show that it is possible to modify the graphs and transfer matrices so as to provide an explicit connection to the theory of planar networks introduced in the context of totally positiv...

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Bibliographic Details
Main Authors Di Francesco, P, Kedem, R
Format Journal Article
LanguageEnglish
Published 18.06.2009
Subjects
Computer Science - Social and Information Networks
Physics - Physics and Society
Quantitative Finance - Economics
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Summary:We review the solution of the $A_r$ Q-systems in terms of the partition function of paths on a weighted graph, and show that it is possible to modify the graphs and transfer matrices so as to provide an explicit connection to the theory of planar networks introduced in the context of totally positive matrices by Fomin and Zelevinsky.
Bibliography:t09-083
DOI:10.48550/arxiv.0906.3421