Cluster expansion formulas and perfect matchings
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Publication:610448
DOI10.1007/s10801-009-0210-3zbMath1246.13035arXiv0810.3638OpenAlexW2592163020MaRDI QIDQ610448
Publication date: 8 December 2010
Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0810.3638
Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Representations of quivers and partially ordered sets (16G20) Cluster algebras (13F60)
Related Items (41)
New combinatorial formulas for cluster monomials of type \(A\) quivers ⋮ Solutions to the T-systems with principal coefficients ⋮ Brane brick models, toric Calabi-Yau 4-folds and 2d \((0,2)\) quivers ⋮ Twists of Plücker coordinates as dimer partition functions ⋮ Double dimer covers on snake graphs from super cluster expansions ⋮ Friezes ⋮ 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 ⋮ Knot theory and cluster algebras ⋮ \(q\)-rationals and finite Schubert varieties ⋮ Mixed dimer configuration model in type D cluster algebras ⋮ Combinatorial cluster expansion formulas from triangulated surfaces ⋮ Matrix formulae for decorated super Teichmüller spaces ⋮ Positive basis for surface skein algebras ⋮ Cluster algebras and continued fractions ⋮ Cluster algebras of type \(D\): pseudotriangulations approach ⋮ Noncommutative marked surfaces ⋮ Snake graph calculus and cluster algebras from surfaces ⋮ Snake graphs from triangulated orbifolds ⋮ Cluster expansion formulas in type \(A\) ⋮ Snake graph calculus and cluster algebras from surfaces. II: Self-crossing snake graphs ⋮ Snake graphs and 70 ⋮ Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths ⋮ Bases for cluster algebras from surfaces ⋮ Extensions in Jacobian algebras and cluster categories of marked surfaces ⋮ On cluster algebras arising from unpunctured surfaces. II ⋮ Positivity for cluster algebras from surfaces ⋮ Rooted clusters for graph LP algebras ⋮ Lattice bijections for string modules, snake graphs and the weak Bruhat order ⋮ On cluster algebras from unpunctured surfaces with one marked point ⋮ Towards a uniform subword complex description of acyclic finite type cluster algebras ⋮ Cluster variables, ancestral triangles and Alexander polynomials ⋮ An expansion formula for type \(A\) and Kronecker quantum cluster algebras ⋮ An expansion formula for quantum cluster algebras from unpunctured triangulated surfaces ⋮ Infinite rank surface cluster algebras ⋮ Cluster Algebras from Surfaces ⋮ Cluster algebraic interpretation of infinite friezes ⋮ Cluster algebras and Jones polynomials ⋮ On the ordering of the Markov numbers ⋮ Rooted clusters for graph LP algebras ⋮ Positivity for quantum cluster algebras from unpunctured orbifolds
Cites Work
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- Positivity for cluster algebras from surfaces
- A graph theoretic expansion formula for cluster algebras of classical type
- Cluster categories for algebras of global dimension 2 and quivers with potential.
- Quivers with relations and cluster tilted algebras.
- Combinatorial interpretations for rank-two cluster algebras of affine type.
- Semicanonical basis generators of the cluster algebra of type \(A_1^{(1)}\).
- Cluster characters for 2-Calabi-Yau triangulated categories.
- On cluster algebras arising from unpunctured surfaces. II
- Gentle algebras arising from surface triangulations.
- Cluster algebras and triangulated surfaces. I: Cluster complexes
- A cluster expansion formula (\(A_{n}\) case)
- Alternating-sign matrices and domino tilings. I
- Cluster algebras and Weil-Petersson forms
- From triangulated categories to cluster algebras
- Cluster algebras as Hall algebras of quiver representations.
- Moduli spaces of local systems and higher Teichmüller theory
- Tilting theory and cluster combinatorics.
- Cluster algebras I: Foundations
- On Cluster Algebras Arising from Unpunctured Surfaces
- Cluster algebras IV: Coefficients
- From triangulated categories to cluster algebras II
- Quivers with potentials associated to triangulated surfaces
- Denominators of cluster variables
- Cluster ensembles, quantization and the dilogarithm
- Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths
- On cluster algebras with coefficients and 2-Calabi-Yau categories
- Quivers with relations arising from clusters (𝐴_{𝑛} case)
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