Equable Parallelograms on the Eisenstein Lattice
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929212632334336 |
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| author | Aebi, Christian Cairns, Grant |
| author_facet | Aebi, Christian Cairns, Grant |
| contents | This paper studies equable parallelograms whose vertices lie on the Eisenstein lattice. Using Rosenberger's Theorem on generalised Markov equations, we show that the set of these parallelograms forms naturally an infinite tree, all of whose vertices have degree 4, bar the root which has degree 3. This study naturally complements the authors' previous study of equable parallelograms whose vertices lie on the integer lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08827 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equable Parallelograms on the Eisenstein Lattice Aebi, Christian Cairns, Grant Combinatorics 52C05, 11D25, 11H06 This paper studies equable parallelograms whose vertices lie on the Eisenstein lattice. Using Rosenberger's Theorem on generalised Markov equations, we show that the set of these parallelograms forms naturally an infinite tree, all of whose vertices have degree 4, bar the root which has degree 3. This study naturally complements the authors' previous study of equable parallelograms whose vertices lie on the integer lattice. |
| title | Equable Parallelograms on the Eisenstein Lattice |
| topic | Combinatorics 52C05, 11D25, 11H06 |
| url | https://arxiv.org/abs/2401.08827 |