Cluster Expansions: T-walks, Labeled Posets and Matrix Calculations
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ID: 283445
2022
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Abstract
We give two new combinatorial methods for computing cluster expansion
formulas for arcs coming from possibly punctured surfaces. The first is by
using $T$-walks, an extension of the $T$-path model for unpunctured surfaces to
general surfaces. We also introduce a new way of generating $T$-paths. The
second method is by using order ideals of labeled posets associated to arcs. We
also use the theory of oriented posets to give a quick way to calculate the
expressions using $2$ by $2$ matrices. The techniques introduced are applicable
to different settings in cluster algebras and beyond.
| Reference Key |
yıldırım2022cluster
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|---|---|
| Authors | Ezgi Kantarcı Oğuz; Emine Yıldırım |
| Journal | arXiv |
| Year | 2022 |
| DOI |
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