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math.QAAug 7, 2015
36
citations (OpenAlex)
authors
  • Man Wai Cheung
  • Mark Gross
  • Greg Muller
  • Gregg Musiker
  • Dylan Rupel
  • Salvatore Stella
  • Harold Williams
institutions
  • Sapienza University of Rome
  • The University of Texas at Austin
  • University of California San Diego
  • University of Cambridge
  • University of Michigan
  • University of Minnesota
  • University of Notre Dame
arXiv abstractPDF
paper

The greedy basis equals the theta basis

arXiv:1508.01404 · doi:10.1016/j.jcta.2016.08.004

Abstract

We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee-Li-Zelevinsky and the theta basis of Gross-Hacking-Keel-Kontsevich.

17 pages

References in corpus (2)

  • Mirror symmetry for P^2 and tropical geometry
  • A tropical view on Landau-Ginzburg models

Cited by in corpus (14)

  • Bases for cluster algebras from orbifolds
  • Scattering fans
  • A combinatorial approach to scattering diagrams
  • Strong positivity for quantum theta bases of quantum cluster algebras
  • Explicit equations for mirror families to log Calabi-Yau surfaces
  • τ-Cluster Morphism Categories and Picture Groups
  • Theta functions and quiver Grassmannians
  • Cluster Algebras and Scattering Diagrams, Part II. Cluster Patterns and Scattering Diagrams
  • On Generalized Minors and Quiver Representations
  • From frieze patterns to cluster categories
  • Dominance phenomena: mutation, scattering and cluster algebras
  • Affine cluster monomials are generalized minors
  • Theta bases are atomic
  • Cluster algebras and their bases
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