Further results on transitive Kirkman triple systems
type: Item
instance of: scholarly article
title: Further results on transitive Kirkman triple systems
zbMATH Open document ID: 0855.05023
DOI: 10.1016/0378-3758(95)00083-6
published in: Journal of Statistical Planning and Inference
publication date: 1996-09-05T00:00:00Z
review text: Let \(X\) be a finite set of cardinality \(v\). A Kirkman triple system \((X, {\mathcal B})\) is called transitive and denoted by \(\text{TKTS}(v)\) if there exists a sharply transitive group \(G\) on \(X\) under which the set of blocks \(\mathcal B\) is invariant, i.e. for any \(\{x, y, z\}\in {\mathcal B}\) and any \(\alpha\in G\), we have \(\alpha(\{x, y, z\})= \{\alpha(x), \alpha(y), \alpha(z)\}\in {\mathcal B}\). This paper contains a new construction for transitive Kirkman triple systems. One of the main results is to show that if there exists a \(\text{TKTS}(3p)\) for any prime \(p\equiv 5\pmod 6\), then for any \(v\equiv 3\pmod 6\) there exists a \(\text{TKTS}(v)\).
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 906657
zbMATH Keywords: Kirkman triple system
author: Jianguo Lei
reviewed by: Esther R. Lamken
MaRDI profile type: Publication
full work available at URL: 0378-3758(95)00083-6
OpenAlex ID: W2019794650
cites work: Q3903014
cites work: Further cases of double resolvability
cites work: Q3974835
description: scientific article; zbMATH DE number 906657