On resolvable Steiner 2-designs and maximal arcs in projective planes

TL;DR

This paper provides a combinatorial characterization of resolvable Steiner 2-designs that can be embedded as maximal arcs in projective planes, generalizing a conjecture by Brouwer and expanding understanding of these geometric structures.

Contribution

It introduces a new combinatorial characterization for resolvable Steiner 2-designs embeddable as maximal arcs and generalizes Brouwer's conjecture on these configurations.

Findings

Characterization of resolvable Steiner 2-designs as maximal arcs

Formulation of a generalized conjecture by Brouwer

Insights into the embedding of combinatorial designs in projective planes

Abstract

A combinatorial characterization of resolvable Steiner 2-$(v,k,1)$ designs embeddable as maximal arcs in a projective plane of order $(v-k)/(k-1)$ is proved, and a generalization of a conjecture by Andries Brouwer \cite{Br} is formulated.