On Euclidean Algorithms for oriented linear Grassmanians
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915485471211520 |
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| author | Arnold, Maxim Karpenkov, Oleg |
| author_facet | Arnold, Maxim Karpenkov, Oleg |
| contents | In this paper we study Euclidean algorithms and the corresponding continued fractions for oriented linear Grassmanians $G(k,n)$. We propose two algorithms: Maximal Element Elimination algorithm and Minimal Element Elimination algorithm. The first algorithm reduces the absolute maximal value of the Plücker coordinates; the algorithm works only in $G(2,n)$. The second algorithm eliminates the Plücker coordinate with the smallest absolute values, while all other coordinates may increase; the algorithm works for arbitrary $G(2,n)$. We discuss basic features of these algorithms and formulate several natural open questions for further studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01733 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Euclidean Algorithms for oriented linear Grassmanians Arnold, Maxim Karpenkov, Oleg Number Theory 11J70, 11A05, 15A21 In this paper we study Euclidean algorithms and the corresponding continued fractions for oriented linear Grassmanians $G(k,n)$. We propose two algorithms: Maximal Element Elimination algorithm and Minimal Element Elimination algorithm. The first algorithm reduces the absolute maximal value of the Plücker coordinates; the algorithm works only in $G(2,n)$. The second algorithm eliminates the Plücker coordinate with the smallest absolute values, while all other coordinates may increase; the algorithm works for arbitrary $G(2,n)$. We discuss basic features of these algorithms and formulate several natural open questions for further studies. |
| title | On Euclidean Algorithms for oriented linear Grassmanians |
| topic | Number Theory 11J70, 11A05, 15A21 |
| url | https://arxiv.org/abs/2509.01733 |