Maximum line-free set geometry in ℤd 3

Abstract:

Let ℤ^d <inf>3</inf> be the affine space of dimension d on the ℤ<inf>3</inf> field. The main goal of this paper is the geometric representation of the maximum linefree set E in ℤ^d <inf>3</inf>. Therefore the complement T of E is the minimum size set in ℤ ^d <inf>3</inf> intersecting all the affine lines in ℤ^d <inf>3</inf>. We describe, from an affine point of view, the geometric structure for d = 2,3 of set E producing the maximal cardinality. The case d = 4 is partly obtained from these structures.

Año de publicación:

2007

Keywords:

• Hyperplane
• Line-free
• Affine space
• Plane
• Zero-sum
• Line

Fuente:

scopus

google