Year: 2024
Type: preprint
Abstract: A point set $M$ in Euclidean plane is called an integral point set in semi-general position if all the distances between the elements of $M$ are integers, and $M$ does not contain collinear triples. We improve the lower bound for diameter of such sets in the particular case when the characteristic of the set is of the form $4k+1$ or $4k+2$. To achieve that, we combine hyperbolae-based and grid-based toolsets.
Source: arXiv (Cornell University)
Authors: Avdeev, N. N., Lushina, E. A.
Institution: Voronezh State University
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4400611442