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On maximal Dynkin friezes
Abstract
The maximal entries of Dynkin friezes over the positive integers have recently been determined for all finite Dynkin types except Bn and Dn. In this note, we explicitly construct large positive integral points on affine cluster varieties of type Bn (resp. Dn), giving rise to friezes of types Bn (resp. Dn) over the positive integers with largest entries Fn+1 Fn+2 − 1 (resp. Fn Fn+1 − 1) where Fk is the k-th Fibonacci number. We conjecture that these are the maximal possible entries for their respective Dynkin types.
Versions
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BibTeX
@misc{zhang2026maximal,
title = {{On maximal Dynkin friezes}},
author = {Robin Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.02870},
eprint = {2606.02870},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.02870},
}
RIS
TY - UNPB
TI - On maximal Dynkin friezes
AU - Robin Zhang
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2606.02870
UR - https://arxiv.org/abs/2606.02870
AB - The maximal entries of Dynkin friezes over the positive integers have recently been determined for all finite Dynkin types except B_n and D_n. In this note, we explicitly construct large positive integral points on affine cluster varieties of type B_n (resp. D_n), giving rise to friezes of types B_n (resp. D_n) over the positive integers with largest entries F_n+1 F_n+2 − 1 (resp. F_n F_n+1 − 1) where F_k is the k-th Fibonacci number. We conjecture that these are the maximal possible entries for their respective Dynkin types.
ER -