Further results on overlarge sets of Kirkman triple systems
type: Item
instance of: scholarly article
title: Further results on overlarge sets of Kirkman triple systems
zbMATH Open document ID: 1188.05036
publication date: 2009-11-11T00:00:00Z
review text: An overlarge set of Steiner triple systems on \(v\) vertices, \(\text{OLSTS}(v)\), is a collection \(\{(X-x,\mathcal{B}_{x}),x\in X,\left| X\right| =v+1\}\) of \(v+1\) Steiner triple systems on \(v\) vertices, \(\text{STS}(v),\) where \(\{\mathcal{ B}_{x},x\in X\}\) constitutes a partition of all triples on \(X.\) The spectrum of \(\text{OLSTS}(v)\) has been completely determined by M. J. Sharry and A. P. Street. If we substitute \(STS(v)\) by the Kirkman triple system then we get the notion of the overlarge set of Kirkman triple systems, \(\text{OLKTS}(v).\) The spectrum of \(\text{OLKTS}(v)\) is not known yet. In the paper the authors provide new constructions of \(\text{OLKTS}(v)\) for some specific values of \(v.\)
reviewed by: Peter Horák
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 5629510
zbMATH Keywords: Kirkman triple system
zbMATH Keywords: overlarge set
author: Lan-dang Yuan
author: Qingde Kang
MaRDI profile type: Publication
full work available at URL: s10114-008-6615-4
OpenAlex ID: W2010810236
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DOI: 10.1007/S10114-008-6615-4
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5629510