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) |
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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:The authors would like to thank Pasha Pylyavskyy, Vic Reiner, and Peter Webb for looking over an early version of this paper, Hugh Thomas for helpful discussions, and the referees for many useful comments. The authors were supported by NSF Grants DMS-1067183 and DMS-1148634. This paper is an abridged version of [GM14].
Funding Information:
†Email: egunawan@umn.edu. Supported by NSF Grants DMS-1067183 and DMS-1148634. ‡Email: musiker@umn.edu. 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