Neighboring seeds in affine type: Universal coefficients and finite mutation-type

Nathan Reading; Salvatore Stella

Neighboring seeds in affine type: Universal coefficients and finite mutation-type

Combinatorics 2026-07-28 v1 Representation Theory

Authors: Nathan Reading , Salvatore Stella

Abstract

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 of neighboring seeds given in a recent paper of Reading, Rupel, and Stella and applies that characterization in two ways. We prove a conjecture on the construction of universal geometric cluster algebras of affine type. We also characterize extended exchange matrices of affine type that are mutation-finite.

Keywords

cluster algebras affine type neighboring seeds universal geometric cluster algebras mutation-finite g-vector fan

Cite

@article{arxiv.2607.26130,
  title  = {Neighboring seeds in affine type: Universal coefficients and finite mutation-type},
  author = {Nathan Reading and Salvatore Stella},
  journal= {arXiv preprint arXiv:2607.26130},
  year   = {2026}
}

Comments

12 pages