On Euclidean algorithms for oriented linear Grassmannians
Volume 181 / 2026
Colloquium Mathematicum 181 (2026), 249-266
MSC: Primary 11J70; Secondary 11A05, 15A21
DOI: 10.4064/cm9726-4-2026
Published online: 25 October 2026
Abstract
We study Euclidean algorithms and the corresponding continued fractions for oriented linear Grassmannians $G(d,n)$. We propose two algorithms: Maximal Element Elimination and Minimal Element Elimination. 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 $G(d,n)$. We discuss basic features of these algorithms and formulate several natural open questions for further studies.
