A combinatorial formula for rank 2 cluster variables

DOI10.1007/s10801-012-0359-zzbMath1266.13017arXiv1106.0952OpenAlexW2071996763MaRDI QIDQ1938795

Kyungyong Lee, Ralf Schiffler

Publication date: 25 February 2013

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.0952

zbMATH Keywords

Laurent polynomialscluster algebras

Mathematics Subject Classification ID

Representations of quivers and partially ordered sets (16G20) Cluster algebras (13F60)

Related Items

New combinatorial formulas for cluster monomials of type \(A\) quivers ⋮ Brane brick models, toric Calabi-Yau 4-folds and 2d \((0,2)\) quivers ⋮ CLUSTER AUTOMORPHISMS AND COMPATIBILITY OF CLUSTER VARIABLES ⋮ Positivity for cluster algebras of rank 3 ⋮ Initial-seed recursions and dualities for \(d\)-vectors ⋮ Toric mutations in the \(\mathrm{dp}_2\) quiver and subgraphs of the \(\mathrm{dp}_2\) brane tiling ⋮ Greedy elements in rank 2 cluster algebras ⋮ Newton polytopes of rank 3 cluster variables ⋮ Positivity and tameness in rank 2 cluster algebras ⋮ Cluster expansion formulas in type \(A\) ⋮ Relation between \(f\)-vectors and \(d\)-vectors in cluster algebras of finite type or rank 2 ⋮ The greedy basis equals the theta basis: A rank two haiku ⋮ Positivity for cluster algebras

Uses Software

• Macaulay2

Cites Work

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