T-Path Formula and Atomic Bases for Cluster Algebras of Type D

Abstract

We extend a T-path expansion formula for arcs on an unpunctured surface to the case of arcs on a once-punctured polygon and use this formula to give a combinatorial proof that cluster monomials form the atomic basis of a cluster algebra of type D.

References in corpus (4)

• Quivers with potentials associated to triangulated surfaces, Part III: tagged triangulations and cluster monomials
• Positivity in skew-symmetric cluster algebras of finite type
• Atomic bases in cluster algebras of types A and $\tilde{A}$
• On cluster algebras arising from unpunctured surfaces II

Cited by in corpus (7)

• Bases for cluster algebras from orbifolds
• Cluster algebraic interpretation of infinite friezes
• Cluster algebras of type D: pseudotriangulations approach
• Quiver Grassmannians of type extended Dynkin type D - Part 1: Schubert systems and decompositions into affine spaces
• Snake Graphs from Triangulated Orbifolds
• Friezes, weak friezes, and T-paths
• Rooted Clusters for Graph LP Algebras