Linear independence in finite spaces View Full Text


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Article Info

DATE

1987-05

AUTHORS

J. W. P. Hirschfeld, J. A. Thas

ABSTRACT

The maximum number m2(n, q) of points in PG(n, q), n⩾2, such that no three are collinear is known precisely for (n, q)=(n,2), (2,q), (3,q), (4, 3), (5,3). In this paper an improved upper bound of order qn−1−1/2qn−2 is obtained for q even when n⩾4 and q>2. A necessary preliminary is an improved upper bound for m′2(3, q), the maximum size of a k-cap not contained in an ovoid. It is shown that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$m'_2 (3,q){\text{ }} \leqslant q^2 - \tfrac{1}{2}{\text{q}} - \tfrac{1}{2}\sqrt {\text{q}} {\text{ + 2}}$$ \end{document} and that m′2(3, 4)=14. More... »

PAGES

15-31

References to SciGraph publications

  • 1985-06. A characterization of Baer cones in finite projective spaces in GEOMETRIAE DEDICATA
  • 1980-12. Blocking sets and partial spreads in finite projective spaces in GEOMETRIAE DEDICATA
  • 1959-12. Le geometrie di Galois in ANNALI DI MATEMATICA PURA ED APPLICATA (1923 -)
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    http://scigraph.springernature.com/pub.10.1007/bf00147388

    DOI

    http://dx.doi.org/10.1007/bf00147388

    DIMENSIONS

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