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

Abstract

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

arXiv comment10 pages, comments very welcome!