On particular diameter bounds for integral point sets in higher dimensions
N.N. Avdeev, R.E. Zvolinsky, E.A. Momot
TL;DR
This paper explores classifications of planar integral point sets and provides bounds on their minimal diameter in higher dimensions using constructions and machine search techniques.
Contribution
It introduces a classification approach for planar integral point sets and offers new upper bounds for their minimal diameter in higher dimensions.
Findings
Constructed bounds for minimal diameter in higher dimensions.
Provided examples of planar integral point sets through machine search.
Developed a classification framework for integral point sets.
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.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Analytic Number Theory Research · Point processes and geometric inequalities