From the 1 of 6 linked papers with an AI index.
6 papers
Neighboring seeds in affine type: Universal coefficients and finite mutation-type
Nathan Reading, Salvatore Stella
The paper studies seeds that lie closest to the boundary of the g‑vector fan in affine‑type cluster algebras, proving a conjecture about universal geometric cluster algebras and ch…
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…
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…
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…
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.