Diamond Determinants and Somos Sequences
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917299895664640 |
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| author | Beluhov, Nikolai |
| author_facet | Beluhov, Nikolai |
| contents | A Somos sequence of order $n$ is defined by a quadratic recurrence of width $n + 1$. Some of the remarkable properties of these sequences for small $n$ are tied to certain matrices built out of them being of finite rank. We give an elementary proof of the finite-rank property for order $6$, previously only established with the help of advanced machinery from the theory of hyperelliptic functions. Our method also yields a new finite-rank property for the Somos sequences of order $7$. In addition, we conjecture generalisations of these results to higher orders, for the subclass of Gale-Robinson sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_24239 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Diamond Determinants and Somos Sequences Beluhov, Nikolai Number Theory 11B37, 11C20 A Somos sequence of order $n$ is defined by a quadratic recurrence of width $n + 1$. Some of the remarkable properties of these sequences for small $n$ are tied to certain matrices built out of them being of finite rank. We give an elementary proof of the finite-rank property for order $6$, previously only established with the help of advanced machinery from the theory of hyperelliptic functions. Our method also yields a new finite-rank property for the Somos sequences of order $7$. In addition, we conjecture generalisations of these results to higher orders, for the subclass of Gale-Robinson sequences. |
| title | Diamond Determinants and Somos Sequences |
| topic | Number Theory 11B37, 11C20 |
| url | https://arxiv.org/abs/2602.24239 |