On particular diameter bounds for integral point sets in higher dimensions

2019/09/23 by N. N. Avdeev, Avdeev, N. N., R. E. Zvolinsky +4
Mathematics · #52C10 #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Point processes and geometric inequalities #math.CO #msc:52C10

paper · pdf · doi:10.48550/arxiv.1909.10386

openalex publication_date 2019/09/23 · arxiv created 2021/11/22 · arxiv updated 2021/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an attempt to build a classification of planar integral point sets. For two obtained classes, we provide general constructions of upper bounds for minimal diameter of integral point sets in higher dimensions of certain cardinality. Employing machine search, we give the examples of planar integral point sets to build such bounds.

Citations

• Maximal integral point sets over ℤ²
• On the characteristic of integral point sets in 𝔼^m

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