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.
|Original language||English (US)|
|Journal||Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)|
|State||Published - Aug 12 2015|
- Atomic basis
- Cluster algebra
- Triangulated surface