Constructions of Large m-Distance Sets on Triangular Lattice

2025/08/31 by Bao, Li-Ren, Yu, Wei-Hsuan
#Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2509.00880

Abstract

An m-distance set is a collection of points such that the distances between any two points have m possible values. We use two different methods to construct large m-distance sets on the triangular lattices. One is to use the first m smallest distances and find the largest cliques, and the other is using the notions of hexagons. Multiplicities of the distances were observed for comparison for the two methods.

Citations

• Lattice Configurations Determining Few Distances
• Constructions of maximum few-distance sets in Euclidean spaces
• Maximal m-distance sets containing the representation of the Hamming graph H(n,m)

Related

• Constructions of maximum few-distance sets in Euclidean spaces
• Nearly k-distance sets
• Maximal m-distance sets containing the representation of the Hamming graph H(n,m)
• Lattice Configurations Determining Few Distances
• A proof of a Dodecahedron conjecture for distance sets