On the Connectedness of Rational Arithmetic Discrete Hyperplanes

Abstract

While connected arithmetic discrete lines are entirely characterized by their arithmetic thickness, only partial results exist for arithmetic discrete hyperplanes in any dimension In the present paper, we focus on 0-connected rational arithmetic discrete planes in ℤ3 Thanks to an arithmetic reduction on a given integer vector n, we provide an algorithm which computes the thickness of the thinnest 0-connected arithmetic plane with normal vector n.