Support sizes of indecomposable threefold triple systems
type: Item
instance of: scholarly article
zbMATH Open document ID: 0978.05012
author: Giovanni Lo Faro
author: Hao Shen
publication date: 2002-01-21T00:00:00Z
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 1612941
zbMATH Keywords: Steiner triple system
zbMATH Keywords: support size
MaRDI profile type: Publication
title: Support sizes of indecomposable threefold triple systems
published in: JCMCC. The Journal of Combinatorial Mathematics and Combinatorial Computing
review text: A \(\lambda\)-fold triple system is a pair \(T=(V,\text{QTR}{\mathcal B})\), \(\text{QTR}{\mathcal B}\) being a collection of 3-subsets of \(V,\) so that each \(2-\)subset of \(V\) occurs in exactly \(\lambda \) block of \(\text{QTR} {\mathcal B}\). If there is no \(\text{QTR}{\mathcal B}'\subset \text{QTR}{\mathcal B}\) so that \((V,\text{QTR}{\mathcal B}')\) is a \(\lambda '\)-fold triple system, \(\lambda '<\lambda ,\) then \(T\) is called indecomposable. Further, the support size of \(T\) is the number of distinct blocks in \(\text{QTR}{\mathcal B}\). In the paper the spectrum of support sizes of indecomposable \(3\)-fold triple systems of order \(v>15\) is determined.
reviewed by: Peter Horák
description: scientific article; zbMATH DE number 1612941