Positivity for cluster algebras from surfaces

Details Positivity for cluster algebras from surfaces Positivity for cluster algebras from surfaces

2009-06-03

arxiv.org/abs/0906.0748v1

Mathematics

Combinatorics

67 pages, 45 figures, comments welcome

Scientific paper

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.

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