Fibonacci Designs

TL;DR

This paper explores Fibonacci-based parameters of quasi-residual Metis designs, discusses their existence, and examines related symmetric designs and automorphism fixed points.

Contribution

It introduces Fibonacci number expressions for parameters of certain Metis designs and analyzes their existence and automorphism properties.

Findings

Fibonacci numbers describe parameters of quasi-residual Metis designs

Nonexistence of certain difference sets is established

Connections to symmetric extensions and automorphisms are proposed

Abstract

A Metis design is one for which v=r+k+1. This paper deals with Metis designs that are quasi-residual. The parameters of such designs and the corresponding symmetric designs can be expressed by Fibonacci numbers. Although the question of existence seems intractable because of the size of the designs, the nonexistence of corresponding difference sets can be dealt with in a substantive way. We also recall some inequalities for the number of fixed points of an automorphism of a symmetric design and suggest possible connections to the designs that would be the symmetric extensions of Metis designs.