Continued fractions for $q$-deformed real numbers, $\{-1,0,1\}$-Hankel determinants, and Somos-Gale-Robinson sequences
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916401843798016 |
|---|---|
| author | Ovsienko, Valentin Pedon, Emmanuel |
| author_facet | Ovsienko, Valentin Pedon, Emmanuel |
| contents | $q$-deformed real numbers are power series with integer coefficients. We study Stieltjes and Jacobi type continued fraction expansions of $q$-deformed real numbers and find many new examples of such continued fractions. We also investigate the corresponding sequences of Hankel determinants and find an infinite family of power series for which several of the first sequences of Hankel determinants consist of $-1,0$ and $1$ only. These Hankel sequences satisfy Somos and Gale-Robinson recurrences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17009 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Continued fractions for $q$-deformed real numbers, $\{-1,0,1\}$-Hankel determinants, and Somos-Gale-Robinson sequences Ovsienko, Valentin Pedon, Emmanuel Combinatorics Number Theory 05A30, 11A55 (Primary) 11B37, 11C20, 37J70 (Secondary) $q$-deformed real numbers are power series with integer coefficients. We study Stieltjes and Jacobi type continued fraction expansions of $q$-deformed real numbers and find many new examples of such continued fractions. We also investigate the corresponding sequences of Hankel determinants and find an infinite family of power series for which several of the first sequences of Hankel determinants consist of $-1,0$ and $1$ only. These Hankel sequences satisfy Somos and Gale-Robinson recurrences. |
| title | Continued fractions for $q$-deformed real numbers, $\{-1,0,1\}$-Hankel determinants, and Somos-Gale-Robinson sequences |
| topic | Combinatorics Number Theory 05A30, 11A55 (Primary) 11B37, 11C20, 37J70 (Secondary) |
| url | https://arxiv.org/abs/2312.17009 |