Lexicographic Configurations

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.