PreprintCC BY 4.0arXiv
How large can Bn- and Dn-friezes be?
Abstract
We pin down the largest entries possible in positive integral friezes of types Dn for n≥ 4 and Bn for n≥ 2, addressing a conjecture of Robin Zhang. For type Dn, the sharp upper bound is FnFn+1−1, and for type Bn, it is Fn+1Fn+2−1, where Fk are the Virahanka--Fibonacci numbers.
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BibTeX
@misc{sprung2026large,
title = {{How large can $B_n$- and $D_n$-friezes be?}},
author = {Florian Ito Sprung},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31537},
eprint = {2609.31537},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31537},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - How large can B_n- and D_n-friezes be?
AU - Florian Ito Sprung
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31537
UR - https://arxiv.org/abs/2609.31537
AB - We pin down the largest entries possible in positive integral friezes of types D_n for n≥ 4 and B_n for n≥ 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+1F_n+2−1, where F_k are the Virahanka--Fibonacci numbers.
ER -