242 citations · 546 across the 54 of their papers we have counts for
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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,…
Modules over cluster-tilted algebras that do not lie on local slices
Ibrahim Assem, Ralf Schiffler, Khrystyna Serhiyenko
We characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number…
Cluster-tilted and quasi-tilted algebras
Ibrahim Assem, Ralf Schiffler, Khrystyna Serhiyenko
In this paper, we prove that relation-extensions of quasi-tilted algebras are 2-Calabi-Yau tilted. With the objective of describing the module category of a cluster-tilted algebra…
Injective Presentations of Induced Modules over Cluster-Tilted Algebras
Ralf Schiffler, Khrystyna Serhiyenko
Every cluster-tilted algebra is the relation extension of a tilted algebra . A -module is called induced if it is of the form $M\otimes_C…
On syzygies over 2-Calabi-Yau tilted algebras
Ana Garcia Elsener, Ralf Schiffler
We characterize the syzygies and co-syzygies over 2-Calabi-Yau tilted algebras in terms of the Auslander-Reiten translation and the syzygy functor. We explore connections between t…