vix.ing · top · new · best · stats · spec

On the characteristic and diameter of planar integral point sets

2024/07/11 by N. N. Avdeev, Avdeev, N. N., E. A. Lushina +1
Mathematics · Engineering · #Fixed Point Theorems Analysis #Mathematical Approximation and Integration #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.2407.08121

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.

Related