6 papers · 1 filter
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…
Flip Combinatorial Invariance and Weyl groups
Francesco Esposito, Mario Marietti, Salvatore Stella
In this work, we investigate the approach via flipclasses to the Combinatorial Invariance Conjecture for Kazhdan--Lusztig polynomials of all Coxeter groups. We prove the combinator…
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.
Dominance Regions for Rank Two Cluster Algebras
Dylan Rupel, Salvatore Stella
We study the polygons defining the dominance order on -vectors in cluster algebras of rank 2.