7 papers
Neighboring seeds in affine type: Universal coefficients and finite mutation-type
Nathan Reading, Salvatore Stella
Neighboring seeds in a cluster algebra of affine type are seeds that are as close as possible to the boundary of the g-vector fan. This short note highlights the characterization o…
Theta functions in acyclic affine type
Nathan Reading, Salvatore Stella
We characterize the theta functions for vectors in the imaginary wall in a cluster algebra of acyclic affine type and compute some of their structure constants. One of the structur…
Mutation of theta functions
Nathan Reading, Salvatore Stella
We give an account of mutation of theta functions in cluster scattering diagrams, starting with a notion of mutation that is related to, but different from, the notion of mutation…
Dominance regions for affine cluster algebras
Nathan Reading, Dylan Rupel, Salvatore Stella
We determine dominance regions associated to cluster algebras of affine type. In the most interesting cases, the dominance region is a line segment, which we describe explicitly. M…
Noncrossing arc diagrams of type B
Emily Barnard, Nathan Reading, Ashley M. Tharp
Noncrossing arc diagrams are combinatorial models for permutations that encode information about lattice congruences of the weak order and about the associated discrete geometry. I…
Cluster scattering coefficients in rank 2
Thomas Elgin, Nathan Reading, Salvatore Stella
We present conjectures on the scattering terms of cluster scattering diagrams of rank 2, supported by significant computational evidence.
Symmetric noncrossing partitions of an annulus with double points
Nathan Reading
For affine Coxeter groups of affine types and , we model the interval in the absolute order by symmetric noncrossing partitions of an annulus with on…