Arithmetic properties of exceptional lattice paths

• Published in: Algebra and Discrete Mathematics
• Date: 2006
• Main Author: Rump, W.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2006
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/157386
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Arithmetic properties of exceptional lattice paths / W. Rump // Algebra and Discrete Mathematics. — 2006. — Vol. 5, № 3. — С. 101–118. — Бібліогр.: 16 назв. — англ.

For a fixed real number ρ > 0, let L be an affine line of slope ρ ⁻¹ in R ² . We show that the closest approximation of L by a path P in Z ² is unique, except in one case, up to integral translation. We study this exceptional case. For irrational ρ, the projection of P to L yields two q...