6 citations · 7 across the 3 of their papers we have counts for
6 papers
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…
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…
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…