Asymptotic bounds on the equilateral dimension of hypercubes

TL;DR

This paper investigates the asymptotic behavior of the maximum size of equilateral subsets within hypercubes, considering how this size scales with increasing dimension and fixed distances.

Contribution

It provides new asymptotic bounds on the equilateral dimension of hypercubes as functions of dimension and distance, advancing understanding of geometric properties in high-dimensional spaces.

Findings

Derived asymptotic bounds for equilateral dimensions

Analyzed the relationship between dimension and fixed distances

Extended known results on hypercube geometry

Abstract

A subset of the finite dimensional hypercube is said to be equilateral if the distance of any two distinct points equals a fixed value. The equilateral dimension of the hypercube is defined as the maximal size of its equilateral subsets. We study asymptotic bounds on the latter quantity considered as a function of two variables, namely dimension and distance.