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3) with equally many point and line classes. Such a decomposition, if line-tactical, must also be point-tactical. (This holds more generally in any 2-design.) We conjecture that such a tactical decomposition with more than one class has either a singleton point class, or just two point classes, one of which is a hyperplane. Using the previously mentioned result, we reduce the conjecture to the case 
doi:10.1006/eujc.1998.0265 
Copyright © 1999 Academic Press. All rights reserved.
Regular Article
On a Conjecture of Cameron and Liebler
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K. Drudge
Received 8 May 1997;
Abstract
Cameron–Liebler line classes arose from an attempt by Cameron and Liebler to classify those collineation groups ofPG(n, q) which have the same number of orbits on points as on lines. They satisfy several equivalent properties; among them, constant intersection with spreads. Cameron and Liebler conjectured that, apart from some ‘obvious’ examples, no sets of lines of this type exist inPG(3, q). This paper introduces a connection between Cameron–Liebler line classes inPG(3, q) and blocking sets inPG(2, q), and uses it to provide the strongest results to date concerning the non-existence of certain of these sets. In addition, a complete classification of Cameron–Liebler line classes inPG(3, 3) is obtained, with the main result being that there is, essentially, a unique counterexample to Cameron and Liebler's conjecture in this space.
f1 k.drudge@qmw.ac.uk
