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arXiv · 2505.08015

Some determinants and relations in Heronian friezes

Anja Šneperger
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Abstract

In this article, we give algebraic relations and determinant vanishing equalities that hold for the entries of a single Heronian diamond of a Heronian frieze arising from a cyclic $n$-gon. We also give algebraic relations that hold between entries of multiple adjacent diamonds of such a frieze. Furthermore, we define a plane Heronian frieze, and establish some more determinant vanishing equalities for the entries of a plane Heronian frieze arising from a cyclic $n$-gon, where $n$ is a positive integer divisible by $4$.

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Anja Šneperger. 2025-05-12. Some determinants and relations in Heronian friezes. https://arxiv.org/abs/2505.08015

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