T-Path Formula and Atomic Bases for Cluster Algebras of Type D - Gunawan, E.; Musiker, G. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
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.