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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 721-732 |
| Number of pages | 12 |
| Journal | Discrete Mathematics and Theoretical Computer Science |
| State | Published - 2015 |
| Event | 27th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2015 - Daejeon, Korea, Republic of Duration: Jul 6 2015 → Jul 10 2015 |
Bibliographical note
Funding Information:†Email: [email protected]. Supported by NSF Grants DMS-1067183 and DMS-1148634. ‡Email: [email protected]. Supported by NSF Grants DMS-1067183 and DMS-1148634.
Publisher Copyright:
© 2015 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France
Keywords
- Atomic basis
- Cluster algebra
- Triangulated surface