2019/06/27 by N. N. Avdeev, Avdeev, Nikolai
Mathematics · #52C10 #Analytic and geometric function theory #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.1906.11926
openalex publication_date 2019/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A point set M in m-dimensional Euclidean space is called an integral point set if all the distances between the elements of M are integers, and M is not situated on an (m-1)-dimensional hyperplane. We improve the linear lower bound for diameter of planar integral point sets. This improvement takes into account some results related to the Point Packing in a Square problem. Then for arbitrary integers m ≥ 2, n ≥ m+1, d ≥ 1 we give a construction of an integral point set M of n points in m-dimensional Euclidean space, where M contains points M1 and M2 such that distance between M1 and M2 is exactly d.