We show that the mesh mutations are the minimal relations among the g-vectors with respect to any initial seed in any finite type cluster algebra. We then use this algebraic result to derive… Expand

An enumeration algorithm for arrangements with a given support is provided, based on the properties of certain greedy pseudoline arrangements and on their connection with sorting networks, which leads to a natural definition of multipseudotriangulations, which generalizes both.Expand

We generalize the brick polytope of V. Pilaud and F. Santos to spherical subword complexes for nite Coxeter groups. This construction pro- vides polytopal realizations for a certain class of subword… Expand

We explore lattice structures on integer binary relations (i.e. binary relations on the set $\{1, 2, \dots, n\}$ for a fixed integer $n$) and on integer posets (i.e. partial orders on the set $\{1,… Expand

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… Expand