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On the number of lines in planar spaces

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Abstract

SupposeS is a planar space withv>4 points and letq be the positive real number such thatv=q 3+q2+q+1. Assuming a weak non-degeneracy condition, we shall show thatS has at least (q2+1)(q2+q+1) lines with equality iffq is a prime power andS=PG(3,q).

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  1. Mathematisches Institut, Arndtstrasse 2, D-35392, Giessen, Germany

    Klaus Metsch

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  1. Klaus Metsch
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Metsch, K. On the number of lines in planar spaces. Combinatorica 15, 105–110 (1995). https://doi.org/10.1007/BF01294462

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  • DOI: https://doi.org/10.1007/BF01294462

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