2019/07/22 by N. N. Avdeev, Avdeev, N. N.
Computer Science · Engineering · Mathematics · #52C10 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Point processes and geometric inequalities #Structural Analysis and Optimization #math.CO #msc:52C10
paper · pdf · doi:10.48550/arxiv.1907.09331
arxiv created 2019/07/22 · openalex publication_date 2019/07/22 · arxiv updated 2019/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A point set M in the Euclidean plane is called a planar integral point set if all the distances between the elements of M are integers, and M is not situated on a straight line. A planar integral point set is called to be in semi-general position, if it does not contain collinear triples. The existing lower bound for mininum diameter of planar integral point sets is linear. We prove a new lower bound for mininum diameter of planar integral point sets in semi-general position that is better than linear.