Positivity for cluster algebras from surfaces |
| |
| Authors: | Gregg Musiker Ralf Schiffler Lauren Williams |
| |
| Institution: | aSchool of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States;bDepartment of Mathematics, University of Connecticut, Storrs, CT 06269-3009, United States;cDepartment of Mathematics, UC Berkeley, Berkeley, CA 94720, United States |
| |
| Abstract: | We give combinatorial formulas for the Laurent expansion of any cluster variable in any cluster algebra coming from a triangulated surface (with or without punctures), with respect to an arbitrary seed. Moreover, we work in the generality of principal coefficients. An immediate corollary of our formulas is a proof of the positivity conjecture of Fomin and Zelevinsky for cluster algebras from surfaces, in geometric type. |
| |
| Keywords: | MSC: 16S99 05C70 05E15 |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
