11 papers
Noncrossing partitions of an annulus
Laura G. Brestensky, Nathan Reading
The noncrossing partition poset associated to a Coxeter group and Coxeter element is the interval in the absolute order on . We construct a new model of noncro…
Noncrossing partitions of a marked surface
Nathan Reading
We define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattic…
Cluster scattering diagrams of acyclic affine type
Nathan Reading, Salvatore Stella
We give an explicit construction of the cluster scattering diagram for any acyclic exchange matrix of affine type. We show that the corresponding cluster scattering fan coincides b…
The fundamental theorem of finite semidistributive lattices
Nathan Reading, David E Speyer, Hugh Thomas
We prove a Fundamental Theorem of Finite Semidistributive Lattices (FTFSDL), modelled on Birkhoff's Fundamental Theorem of Finite Distributive Lattices. Our FTFSDL is of the form "…
The action of a Coxeter element on an affine root system
Nathan Reading, Salvatore Stella
The characterization of orbits of roots under the action of a Coxeter element is a fundamental tool in the study of finite root systems and their reflection groups. This paper deve…
A combinatorial approach to scattering diagrams
Nathan Reading
Scattering diagrams arose in the context of mirror symmetry, but a special class of scattering diagrams (the cluster scattering diagrams) were recently developed to prove key struc…