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)|
|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 noteFunding Information:
†Email: email@example.com. Supported by NSF Grants DMS-1067183 and DMS-1148634. ‡Email: firstname.lastname@example.org. Supported by NSF Grants DMS-1067183 and DMS-1148634.
© 2015 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France
- Atomic basis
- Cluster algebra
- Triangulated surface