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arXiv · 2609.31537

How large can $B_n$- and $D_n$-friezes be?

Florian Ito Sprung
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Abstract

We pin down the largest entries possible in positive integral friezes of types $D_n$ for $n\geq 4$ and $B_n$ for $n\geq 2$, addressing a conjecture of Robin Zhang. For type $D_n$, the sharp upper bound is $F_nF_{n+1}-1$, and for type $B_n$, it is $F_{n+1}F_{n+2}-1$, where $F_k$ are the Virahanka--Fibonacci numbers.

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Florian Ito Sprung. 2026-09-25. How large can $B_n$- and $D_n$-friezes be?. https://arxiv.org/abs/2609.31537

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