Arithmetic properties of exceptional lattice paths

• Date: 2018
• Main Author: Rump, Wolfgang
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Lattice path; uniform enumeration; quasicrystal; 05B30; 11B50; 52C35; 11A07
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/901
• Journal Title: Algebra and Discrete Mathematics

For a fixed real number \(\rho>0\),  let \(L\) be an affine line of slope \(\rho^{-1}\) in \(\mathbb{R}^2\). We show that the closest approximation of \(L\) by a path \(P\) in \(\mathbb{Z}^2\) is unique, except in one case, up to integral translation. We study this exceptional case. For irrat...