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arXiv · 2509.01733

On Euclidean Algorithms for oriented linear Grassmanians

Maxim Arnold·Oleg Karpenkov
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Abstract

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 Pl\"ucker coordinates; the algorithm works only in $G(2,n)$. The second algorithm eliminates the Pl\"ucker 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.

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Maxim Arnold, Oleg Karpenkov. 2025-09-01. On Euclidean Algorithms for oriented linear Grassmanians. https://arxiv.org/abs/2509.01733

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