Richard P. Stanley Seminar in Combinatorics: Leafy trees, wall-crossing, and m-Tamari intervals

Trees appear in several approaches to wall-crossing. I will present a new plane-tree model for the central wall in rank-2 cluster scattering diagrams, inspired by the recently introduced tight gradings on Dyck paths. These trees turn out to be in bijection with intervals in the m-Tamari lattice, a lattice on m-ballot paths. I will explain this correspondence and show how the tree perspective leads to algebraic functional equations for enumerating these intervals and a new combinatorial proof of the central wall formula. No prior knowledge of wall-crossing or cluster algebras will be assumed. This talk is based on joint work with Amanda Burcroff and Kyungyong Lee.

For information about the Richard P. Stanley Seminar in Combinatorics, visit… https://math.mit.edu/combin/