Duality between final-seed and initial-seed mutations in cluster algebras

DOI10.3842/SIGMA.2019.040zbMath1423.13123arXiv1808.02156MaRDI QIDQ2330809

Yasuaki Gyoda, Shogo Fujiwara

Publication date: 23 October 2019

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.02156

zbMATH Keywords

dualitymutationcluster algebra

Mathematics Subject Classification ID

Cluster algebras (13F60)

Related Items (7)

\(F\)-matrices of cluster algebras from triangulated surfaces ⋮ Combinatorial cluster expansion formulas from triangulated surfaces ⋮ Cluster duality between Calkin-Wilf tree and Stern-Brocot tree ⋮ The valuation pairing on an upper cluster algebra ⋮ Algebraic entropy of sign-stable mutation loops ⋮ Relation between \(f\)-vectors and \(d\)-vectors in cluster algebras of finite type or rank 2 ⋮ Synchronicity phenomenon in cluster patterns

Cites Work

• Cluster algebras and triangulated surfaces. I: Cluster complexes
• Initial-seed recursions and dualities for \(d\)-vectors
• Uniform column sign-coherence and the existence of maximal green sequences
• Tilting theory and cluster combinatorics.
• Cluster algebras I: Foundations
• Canonical bases for cluster algebras
• Cluster algebras IV: Coefficients
• Cluster ensembles, quantization and the dilogarithm
• On tropical dualities in cluster algebras

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