Lexicographic Configurations
Christoph Hering, Andreas Krebs, Thomas Edgar

TL;DR
This paper introduces a simple, purely geometric method for constructing finite symmetric configurations with specific properties, providing a constructive existence proof and generating interesting periodic matrices.
Contribution
It presents a novel geometric approach to constructing symmetric configurations E(k-1) with k points on a line, including a constructive proof of their existence.
Findings
Constructed symmetric configurations E(k-1) with k points on a line.
Produced interesting periodic matrices through the geometric method.
Provided a simple, purely geometric constructive existence proof.
Abstract
We describe a new way to construct finite geometric objects. For every k we obtain a symmetric configuration E(k-1) with k points on a line. In particular, we have a constructive existence proof for such configurations. The method is very simple and purely geometric. It also produces interesting periodic matrices.
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Taxonomy
Topicsgraph theory and CDMA systems · Mathematics and Applications · Computational Geometry and Mesh Generation
