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Maximizing the number of Pasch configurations in a Steiner triple system

Grannell, Mike and Lovegrove, Graham (2013). Maximizing the number of Pasch configurations in a Steiner triple system. Bulletin of the Institute of Combinatorics and its Applications, 69 pp. 23–35.

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Abstract

Let $P(v)$ denote the maximum number of Pasch configurations in any Steiner triple system on $v$ points. It is known that $P(v)\le M(v)=v(v-1)(v-3)/24$, with equality if and only if $v$ is of the form $2^n-1$. It is also known that $\displaystyle \limsup_{v\to\infty \atop v\ne 2^n-1} \frac{P(v)}{M(v)}=1$. We give a new proof of this result and improved lower bounds on $P(v)$ for certain values of $v$.

Item Type: Journal Item
Copyright Holders: 2013 Institute of Combinatorics and its Applications
ISSN: 1183-1278
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
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Item ID: 39212
Depositing User: Mike Grannell
Date Deposited: 06 Jan 2014 14:02
Last Modified: 07 Dec 2018 10:20
URI: http://oro.open.ac.uk/id/eprint/39212
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