Hyperovals in Steiner triple systems
type: Item
instance of: scholarly article
title: Hyperovals in Steiner triple systems
zbMATH Open document ID: 0782.05013
DOI: 10.1007/BF01223811
author: Gaetano Quattrocchi
author: Herbert Zeitler
published in: Journal of Geometry
publication date: 1993-10-13T00:00:00Z
review text: A hyperoval in a Steiner triple system is the complement of a subsystem of maximum possible size, i.e. a hyperoval is a set of points met by each block in either two or zero points. For every \(v\equiv 1\) or \(3\pmod 6\) the authors define: \[ \text{HSTS}(v)=\bigl\{ h\in N:\;\text{there is an } \text{STS}(v)\text{ containing \(h\) hyperovals}\bigr\}\quad\text{and} \] \[ \text{H}(v)=\bigl\{2^ n-1: n\in N\text{ and } (v-2^ n+1)/2^ n\equiv 1\text{ or }3\pmod 6\bigr\}, \] and they show that \(\text{HSTS}(v)=\text{H}(v)\) for \(v>7\). The proof is by construction, relies on well-known results on Steiner triple systems, and uses standard techniques, like 1-factorizations of suitable complete graphs.
Mathematics Subject Classification ID: 05B07
Mathematics Subject Classification ID: 51E10
zbMATH DE Number: 428602
zbMATH Keywords: hyperoval
zbMATH Keywords: Steiner triple system
MaRDI profile type: Publication
cites work: Sur la structure de certains systèmes triples de Steiner
cites work: Systèmes triples de Steiner non engendrés par tous leurs triangles. (Steiner triple systems not surrounded by their triangles)
cites work: Q3963017
cites work: Hyperovale in Steiner-Tripel-Systemen
description: scientific article; zbMATH DE number 428602