Covering triples by quadruples: an asymptotic solution
type: Item
instance of: scholarly article
title: Covering triples by quadruples: an asymptotic solution
zbMATH Open document ID: 0587.05022
DOI: 10.1016/0097-3165(86)90119-6
author: B. George
published in: Journal of Combinatorial Theory. Series A
publication date: 1986-01-01T00:00:00Z
review text: \textit{J. Schoenheim} [Pac. J. Math. 14, 1405--1411 (1964; Zbl 0128.24501)] showed that to cover all triples of an \(n\)-set by quadruples, at least \(\lceil \frac{1}{4}n\lceil \frac{1}{3}(n-1)\lceil \frac{1}{2}(n-2)\rceil \rceil \rceil\) quadruples are needed with equality e.g. when a Steiner quadruple system on n points exists. Using a construction of Mills for \(n=499\) and some recursive techniques it is shown that this number of quadruples suffices for all \(n\geq 52423\).
Mathematics Subject Classification ID: 05B40
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 3941562
zbMATH Keywords: Steiner quadruple system
MaRDI profile type: Publication
full work available at URL: 0097-3165(86)90119-6
OpenAlex ID: W1999217025
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description: scientific article; zbMATH DE number 3941562