English

Growth of infinite frieze patterns of affine type

Combinatorics 2026-03-24 v1 Representation Theory

Abstract

We analyse the growth coefficients of infinite frieze patterns arising from cluster algebras using cluster modular groups and cluster categories. For a fixed cluster category of affine type, we prove that the collection of infinite frieze patterns given by both the homogeneous and non-homogeneous stable tubes all have the same growth coefficients. We also derive and verify an explicit formula for the kk-th growth coefficient, expressed directly in terms of data from homogeneous tubes, or, alternatively, from appropriate elements of the corresponding cluster algebra.

Keywords

Cite

@article{arxiv.2603.21157,
  title  = {Growth of infinite frieze patterns of affine type},
  author = {Karin Baur and Anna Felikson and Deepanshu Prasad and Pavel Tumarkin and Emine Yıldırım},
  journal= {arXiv preprint arXiv:2603.21157},
  year   = {2026}
}