Saved in:
Bibliographic Details
Main Authors: Bazier-Matte, Veronique, Bourgie, Marie-Anne, Felikson, Anna, Tumarkin, Pavel
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2512.18810
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • An $SL_2$-tiling is a bi-infinite matrix in which all adjacent $2 \times 2$ minors are equal to $1$. Positive integral $SL_2$-tilings were introduced by Assem, Reutenauer and Smith as generalisations of classical Conway--Coxeter frieze patterns. We show that positive integral $SL_2$-tilings with translational symmetry are in bijection with triangulations of annuli. We use this correspondence to study the properties of periodic positive integral $SL_2$-tilings.