Cluster algebras of type D: pseudotriangulations approach

Understand

We present a combinatorial model for cluster algebras of type $D_n$ in terms of centrally symmetric pseudotriangulations of a regular $2n$-gon with a small disk in the centre.

• This model provides convenient and uniform interpretations for clusters, cluster variables and their exchange relations, as well as for quivers and their mutations.
• We also present a new combinatorial interpretation of cluster variables in terms of perfect matchings of a graph after deleting two of its vertices.
• This interpretation differs from known interpretations in the literature.