Polynesian Journal of Mathematics

Volume 4, Issue 12
Special volume AJAX in honor of René Schoof

On maximal Dynkin friezes

Robin Zhang

Abstract:

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.

Citation:

Robin Zhang. On maximal Dynkin friezes. Polynesian Journal of Mathematics, Volume 4, Issue 12, Pages 1–17. (Sept. 2026) DOI: 10.69763/polyjmath.4.12

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Milestones:

Received 27 Feb 2026
Revised 29 May 2026
Accepted 29 May 2026
Published 28 Sep 2026
Communicated by Samuele Anni

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