Switching sets in $\textrm {PG}(3, q)$
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- by A. Bruen and R. Silverman PDF
- Proc. Amer. Math. Soc. 43 (1974), 176-180 Request permission
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.References
- R. H. Bruck, Finite nets. II. Uniqueness and imbedding, Pacific J. Math. 13 (1963), 421–457. MR 154824
- A. Bruen, Unimbeddable nets of small deficiency, Pacific J. Math. 43 (1972), 51–54. MR 380614
- P. Dembowski, Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Springer-Verlag, Berlin-New York, 1968. MR 0233275
- David A. Foulser, Replaceable translation nets, Proc. London Math. Soc. (3) 22 (1971), 235–264. MR 291935, DOI 10.1112/plms/s3-22.2.235
- J. W. P. Hirschfeld, Classical configurations over finite fields. I. The double- six and the cubic surface with $27$ lines, Rend. Mat. e Appl. (5) 26 (1967), 115–152. MR 233272
- H. J. Ryser, Combinatorial configurations, SIAM J. Appl. Math. 17 (1969), 593–602. MR 256904, DOI 10.1137/0117056
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 43 (1974), 176-180
- MSC: Primary 50D30; Secondary 05BXX
- DOI: https://doi.org/10.1090/S0002-9939-1974-0333946-8
- MathSciNet review: 0333946