Work

Cluster expansions: T-walks, labeled posets and matrix calculations

Year: 2025

Type: article

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.

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2025.01.024

Authors: Ezgi Kantarcı Oğuz, Emine Yıldırım

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310

Funders: Royal Society, Türkiye Bilimsel ve Teknolojik Araştırma Kurumu

Awards: G2377283187, G4595783300, G5651773380