Lower bounds on the independence numbers of distance graphs with vertices in $\{-1, 0, 1\}^n$

TL;DR

This paper investigates lower bounds on the independence numbers of distance graphs with vertices in -1,0,1^n, providing new asymptotic results and numerical insights into their properties.

Contribution

It introduces novel lower bounds for independence numbers of these graphs, expanding understanding over a broad parameter range and analyzing their asymptotic behavior.

Findings

New asymptotic lower bounds established

Numerical results reveal complex relationships between bounds

Discussion on potential suboptimality of known upper bounds

Abstract

This work is devoted to lower bounds on independence numbers of distance graphs with vertices in $\{-1,0,1\}^n$. The asymptotic case is studied, yielding new results over a broad range of parameters. Numerical results are presented, highlighting nontrivial relationships between the obtained bounds. Known upper bounds and their potential suboptimality are discussed separately.