Outputs (3)

Cluster algebras and continued fractions (2017)
Journal Article
Çanakçı, İ., & Schiffler, R. (2018). Cluster algebras and continued fractions. Compositio Mathematica, 154(03), 565-593. https://doi.org/10.1112/s0010437x17007631

We establish a combinatorial realization of continued fractions as quotients of cardinalities of sets. These sets are sets of perfect matchings of certain graphs, the snake graphs, that appear naturally in the theory of cluster algebras. To a continu... Read More about Cluster algebras and continued fractions.

Snake graph calculus and cluster algebras from surfaces III: Band graphs and snake rings (2017)
Journal Article
Canakci, I., & Schiffler, R. (2019). Snake graph calculus and cluster algebras from surfaces III: Band graphs and snake rings. International Mathematics Research Notices, 2019(4), 1145-1226. https://doi.org/10.1093/imrn/rnx157

We introduce several commutative rings, the snake rings, that have strong connections to cluster algebras and that are interesting on their own right as combinatorially defined rings. The elements of these rings are residue classes of unions of certa... Read More about Snake graph calculus and cluster algebras from surfaces III: Band graphs and snake rings.

Extensions in Jacobian algebras and cluster categories of marked surfaces (2017)
Journal Article
Canakci, I., & Schroll, S. (2017). Extensions in Jacobian algebras and cluster categories of marked surfaces. Advances in Mathematics, 313, 1-49. https://doi.org/10.1016/j.aim.2017.03.016

In the context of representation theory of finite dimensional algebras, string algebras have been extensively studied and most aspects of their representation theory are well-understood. One exception to this is the classification of extensions betwe... Read More about Extensions in Jacobian algebras and cluster categories of marked surfaces.