T-Path Formula and Atomic Bases for Cluster Algebras of Type D

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2015
• Main Authors: Gunawan, E., Musiker, G.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147131
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: T-Path Formula and Atomic Bases for Cluster Algebras of Type D / E. Gunawan, G. Musiker // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 23 назв. — англ.

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.