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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Switching sets in $\textrm {PG}(3, q)$

Authors: A. Bruen and R. Silverman
Journal: Proc. Amer. Math. Soc. 43 (1974), 176-180
MSC: Primary 50D30; Secondary 05BXX
MathSciNet review: 0333946
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Abstract: In this note, we are mainly concerned with partial spreads $U,V$ of $PG(3,q)$ which cover the same points and have no line in common. Setting $|U| = |V| = t$, we show that if $t > q + 1$ then $t \geqq \max (q + 2,2q - 2)$. Certain applications of this result to (0, 1) matrices and to translation planes are then discussed.

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Keywords: Partial spread, replaceable net, embeddable net, regulus, double-six, translation plane, <IMG WIDTH="50" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$(0,1)$"> matrix
Article copyright: © Copyright 1974 American Mathematical Society