13 citations · 28 across the 12 of their papers we have counts for
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Congruence invariants of matrix mutation
Ahmet Seven, İbrahim Ünal
Motivated by the recent work of R. Casals on binary invariants for matrix mutation, we study the matrix congruence relation on quasi-Cartan matrices. We obtain a classification and…
Cluster algebras and symmetrizable matrices
Ahmet Seven
In this paper, we study combinatorial properties of quasi-Cartan companions defined by the c-vectors of acyclic skew-symmetrizable cluster algebras. In particular, we show that the…
Maximal Green Sequences of Exceptional Finite Mutation Type Quivers
Ahmet I. Seven
Maximal green sequences are particular sequences of mutations of quivers which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecot…
Reflection group relations arising from cluster algebras
Ahmet Seven
In this paper, we obtain relations in the Weyl groups of Kac-Moody algebras that come from mutation classes of skew-symmetrizable matrices. These relations generalize those obtaine…
Maximal green sequences of skew-symmetrizable 3x3 matrices
Ahmet Seven
Maximal green sequences are particular sequences of mutations which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti-Cordova-…
Cluster algebras and symmetric matrices
Ahmet Seven
In this paper, we show that, for skew-symmetric cluster algebras, the c-vectors of any seed with respect to an acyclic initial seed define a quasi-Cartan companion of the correspon…
Mutation classes of finite type cluster algebras with principal coefficients
Ahmet Seven
In this paper, we prove Conjecture 4.8 of "Cluster algebras IV" by S. Fomin and A. Zelevinsky, stating that the mutation classes of rectangular matrices associated with cluster alg…
Mutation classes of skew-symmetrizable 3x3 matrices
Ahmet Seven
In this paper, we determine representatives for the mutation classes of skew-symmetrizable 3x3 matrices and associated graphs using a natural minimality condition, generalizing and…
Quivers of finite mutation type and skew-symmetric matrices
Ahmet Seven
In this paper, we study structural properties of finite mutation type quivers. In particular, we obtain a characterization of finite mutation type quivers that are associated with…
Cluster algebras and semipositive symmetrizable matrices
Ahmet Seven
In this paper, we give a description of the skew-symmetrizable matrices and their mutation classes which are determined by the generalized Cartan matrices of affine type.
Recognizing Cluster Algebras of Finite type
Ahmet Seven
We compute the list of all minimal 2-infinite diagrams, which are cluster algebraic analogues of extended Dynkin graphs.