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Pasch trades with a negative block

Drizen, A.L.; Grannell, Mike and Griggs, Terry (2011). Pasch trades with a negative block. Discrete Mathematics, 311(21) pp. 2411–2416.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1016/j.disc.2011.06.023
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Abstract

A Steiner triple system of order $v$, STS($v$), may be called \emph{equivalent} to another STS($v$) if one can be converted to the other by a sequence of three simple operations involving Pasch trades with a single negative block. It is conjectured that any two STS($v$)s on the same base set are equivalent in this sense. We prove that the equivalence class containing a given system $S$ on a base set $V$ contains all the systems that can be obtained from $S$ by any sequence of well over one hundred distinct trades, and that this equivalence class contains all isomorphic copies of $S$ on $V$. We also show that there are trades which cannot be effected by means of Pasch trades with a single negative block.

Item Type: Journal Article
Copyright Holders: 2011 Elsevier B.V.
ISSN: 0012-365X
Keywords: Pasch configuration; Steiner triple system; trade
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 29520
Depositing User: Mike Grannell
Date Deposited: 19 Sep 2011 07:39
Last Modified: 30 Nov 2012 10:37
URI: http://oro.open.ac.uk/id/eprint/29520
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