Some determinants and relations in Heronian friezes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912372982022144 |
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| author | Šneperger, Anja |
| author_facet | Šneperger, Anja |
| contents | 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 $4$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_08015 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some determinants and relations in Heronian friezes Šneperger, Anja Combinatorics Metric Geometry 13F60, 51K99, 52C25, 05E99 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 $4$. |
| title | Some determinants and relations in Heronian friezes |
| topic | Combinatorics Metric Geometry 13F60, 51K99, 52C25, 05E99 |
| url | https://arxiv.org/abs/2505.08015 |