Positivity for cluster algebras from surfaces
Combinatorics
2009-06-04 v1 Representation Theory
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.
Cite
@article{arxiv.0906.0748,
title = {Positivity for cluster algebras from surfaces},
author = {Gregg Musiker and Ralf Schiffler and Lauren Williams},
journal= {arXiv preprint arXiv:0906.0748},
year = {2009}
}
Comments
67 pages, 45 figures, comments welcome