46 citations · 91 across the 16 of their papers we have counts for
19 papers
Super Caldero--Chapoton map for type
İlke Çanakçı, Francesca Fedele, Ana Garcia Elsener +1
One can explicitly compute the generators of a surface cluster algebra either combinatorially, through dimer covers of snake graphs, or homologically, through the CC-map applied to…
Cluster categories for completed infinity-gons I: Categorifying triangulations
İlke Çanakçı, Martin Kalck, Matthew Pressland
Paquette and Yıldırım recently introduced triangulated categories of arcs in completed infinity-gons, which are discs with an infinite closed set of marked points on their boundary…
Friezes for a pair of pants
Ilke Canakci, Anna Felikson, Ana Garcia Elsener +1
Frieze patterns are numerical arrangements that satisfy a local arithmetic rule. These arrangements are actively studied in connection to the theory of cluster algebras. In the set…
Perfect matching modules, dimer partition functions and cluster characters
İlke Çanakçı, Alastair King, Matthew Pressland
Cluster algebra structures for Grassmannians and their (open) positroid strata are controlled by a Postnikov diagram D or, equivalently, a dimer model on the disc, as encoded by ei…
Infinite friezes and triangulations of annuli
Karin Baur, Ilke Canakci, Karin M. Jacobsen +2
It is known that any infinite frieze comes from a triangulation of an annulus by Baur, Parsons and Tschabold. In this paper we show that each periodic infinite frieze determines a…
Friezes, weak friezes, and T-paths
Ilke Canakci, Peter Jorgensen
Frieze patterns form a nexus between algebra, combinatorics, and geometry. T-paths with respect to triangulations of surfaces have been used to obtain expansion formulae for cluste…
Addendum and Erratum: Mapping cones for morphisms involving a band complex in the bounded derived category of a gentle algebra
Ilke Canakci, David Pauksztello, Sibylle Schroll
In this note we correct two oversights in [Mapping cones in the bounded derived category of a gentle algebra, J. Algebra 530 (2019), 163--194, also arXiv:1609.09688] which only occ…
Lattice bijections for string modules, snake graphs and the weak Bruhat order
Ilke Canakci, Sibylle Schroll
In this paper we introduce abstract string modules and give an explicit bijection between the submodule lattice of an abstract string module and the perfect matching lattice of the…
An expansion formula for type A and Kronecker quantum cluster algebras
Ilke Canakci, Philipp Lampe
We introduce an expansion formula for elements in quantum cluster algebras associated to type A and Kronecker quivers with principal quantization. Our formula is parametrized by pe…
Bases for cluster algebras from orbifolds with one marked point
Ilke Canakci, Pavel Tumarkin
We generalize the construction of the bangle, band and the bracelet bases for cluster algebras from orbifolds to the case where there is only one marked point on the boundary.
On extensions for gentle algebras
Ilke Canakci, David Pauksztello, Sibylle Schroll
We give a complete description of a basis of the extension spaces between indecomposable string and quasi-simple band modules in the module category of a gentle algebra.
Infinite rank surface cluster algebras
Ilke Canakci, Anna Felikson
We generalise surface cluster algebras to the case of infinite surfaces where the surface contains finitely many accumulation points of boundary marked points. To connect different…
Cluster algebras and continued fractions
Ilke Canakci, Ralf Schiffler
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,…
Mapping cones in the bounded derived category of a gentle algebra
Ilke Canakci, David Pauksztello, Sibylle Schroll
In this article we describe the triangulated structure of the bounded derived category of a gentle algebra by describing the triangles induced by the morphisms between indecomposab…
Snake graph calculus and cluster algebras from surfaces III: Band graphs and snake rings
Ilke Canakci, Ralf Schiffler
We introduce several commutative rings, the snake rings, that have strong connections to cluster algebras. The elements of these rings are residue classes of unions of certain labe…
Extensions in Jacobian Algebras and Cluster Categories of Marked Surfaces
Ilke Canakci, Sibylle Schroll
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-under…
Snake graph calculus and cluster algebras from surfaces II: Self-crossing snake graphs
Ilke Canakci, Ralf Schiffler
Snake graphs appear naturally in the theory of cluster algebras. For cluster algebras from surfaces, each cluster variable is given by a formula which is parametrized by the perfec…
On cluster algebras from unpunctured surfaces with one marked point
Ilke Canakci, Kyungyong Lee, Ralf Schiffler
We extend the construction of canonical bases for cluster algebras from unpunctured surfaces to the case where the number of marked points is one, and we show that the cluster alge…
Snake graph calculus and cluster algebras from surfaces
Ilke Canakci, Ralf Schiffler
Snake graphs appear naturally in the theory of cluster algebras. For cluster algebras from surfaces, each cluster variable is given by a formula which is parametrized by the perfec…