46 citations · 91 across the 16 of their papers we have counts for
6 papers · 1 filter
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…
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…
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.
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,…
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…