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We give explicit atomic bases of arbitrary coefficient-free cluster algebras of types $A$ and $\widetilde A$.
Tame algebras and integral quadratic forms
Claus Michael Ringel · 1984
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Cluster algebras I: Foundations
Sergey Fomin and Andrei Zelevinsky · 2002
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Sergey Fomin and Andrei Zelevinsky · 2003
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Positivity and canonical bases in rank 2 cluster algebras of finite and affine types
Paul Sherman and Andrei Zelevinsky · 2004
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Aslak Buan, Robert Marsh, Markus Reineke, Idun Reiten, and Gordana Todorov · 2006
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Philippe Caldero and Frédéric Chapoton · 2006
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From triangulated categories to cluster algebras II
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Elements of the Representation Theory of Associative Algebras, Volume 2: Tubes and Concealed Algebras of Euclidean type
Daniel Simson and Andrzej Skowroński · 2007
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From triangulated categories to cluster algebras
Philippe Caldero and Bernhard Keller · 2008
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Generic variables in acyclic cluster algebras and bases in affine cluster algebras
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Quivers with potentials and their representations. I. Mutations
Harm Derksen, Jerzy Weyman, and Andrei Zelevinsky · 2008
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Cluster algebras and triangulated surfaces. I. Cluster complexes
Sergey Fomin, Michael Shapiro, and Dylan Thurston · 2008
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Cluster characters for 2-Calabi-Yau triangulated categories
Yann Palu · 2008
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A cluster expansion formula ( A n A_{n} case)
Ralf Schiffler · 2008
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Quivers with potentials associated to triangulated surfaces
Daniel Labardini-Fragoso · 2009
Transverse quiver Grassmannians and bases in affine cluster algebras
Grégoire Dupont · 2010
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Quivers with potentials and their representations II: Applications to cluster algebras
Harm Derksen, Jerzy Weyman, and Andrei Zelevinsky · 2010
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Generic bases for cluster algebras and the Chamber Ansatz
Christof Geiss, Bernard Leclerc, and J. Schröer · 2010
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Quiver varieties and cluster algebras
Hiraku Nakajima · 2010
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On the cluster category of a marked surface
Thomas Brüstle and Jie Zhang · 2011
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Cluster algebras of type A 2 ( 1 ) A_{2}^{(1)}
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Positivity for cluster algebras from surfaces
Gregg Musiker, Ralf Schiffler, and Lauren Williams · 2009
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On cluster algebras arising from unpunctured surfaces
Ralf Schiffler and Hugh Thomas · 2009
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Gentle algebras arising from surface triangulations
Ibrahim Assem, Thomas Brüstle, Gabrielle Charbonneau-Jodoin, and Pierre-Guy Plamondon · 2010
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Quantized Chebyshev polynomials and cluster characters with coefficients
Grégoire Dupont · 2010
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Giovanni Cerulli Irelli · 2011
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Positivity in skew-symmetric cluster algebras of finite type
Giovanni Cerulli Irelli · 2011
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Generic variables in acyclic cluster algebras
Grégoire Dupont · 2011
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Quantum cluster algebras of type A and the dual canonical basis
Philipp Lampe · 2011
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Cluster characters II: A multiplication formula
Yann Palu · 2011
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