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

Symmetry Integrability and Geometry-Methods and Applications

article

Emily Gunawan¹  Gregg Musiker¹ 

[1] School of Mathematics, University of Minnesota

关键词: cluster algebra;    triangulated surface;    atomic basis;   

DOI  :  10.3842/SIGMA.2015.060

来源: National Academy of Science of Ukraine

【 摘 要 】

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 $D$.

【 授权许可】

Unknown