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

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2015
• Hauptverfasser: Gunawan, E., Musiker, G.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2015
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/147131
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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.