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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2408.06902 |
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| _version_ | 1866909286238519296 |
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| author | Burcroff, Amanda Ovenhouse, Nicholas Schiffler, Ralf Zhang, Sylvester W. |
| author_facet | Burcroff, Amanda Ovenhouse, Nicholas Schiffler, Ralf Zhang, Sylvester W. |
| contents | We introduce a $q$-analog of the higher continued fractions introduced by the last three authors in a previous work (together with Gregg Musiker), which are simultaneously a generalization of the $q$-rational numbers of Morier-Genoud and Ovsienko. They are defined as ratios of generating functions for $P$-partitions on certain posets. We give matrix formulas for computing them, which generalize previous results in the $q=1$ case. We also show that certain properties enjoyed by the $q$-rationals are also satisfied by our higher versions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06902 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher $q$-Continued Fractions Burcroff, Amanda Ovenhouse, Nicholas Schiffler, Ralf Zhang, Sylvester W. Combinatorics We introduce a $q$-analog of the higher continued fractions introduced by the last three authors in a previous work (together with Gregg Musiker), which are simultaneously a generalization of the $q$-rational numbers of Morier-Genoud and Ovsienko. They are defined as ratios of generating functions for $P$-partitions on certain posets. We give matrix formulas for computing them, which generalize previous results in the $q=1$ case. We also show that certain properties enjoyed by the $q$-rationals are also satisfied by our higher versions. |
| title | Higher $q$-Continued Fractions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.06902 |