Bounds on the Number of Pairs of Unjoined Points in a Partial Plane

  • David A. Drake
  • Paul Erdös
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 20)


We prove two theorems which bound the number of pairs of unjoined points in a partial plane ∑ defined on a finite number υ of points. The bounds are obtained under assumptions on the number of lines in ∑ together with the assumption that no line contains more than υ – 3 points.

Key words

linear space partial plane projective plane 


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  1. [1]
    A. Blokhuis, R. J. M. Schmitt and H. A. Wilbrink, On the number of lines in a linear space on p 2 + p + 1 points, Proceedings of Combinatorics ’88, Ravello, Italy (to appear) (1988).Google Scholar
  2. [2]
    N. G. de Bruijn and P. Erdös, On a combinatorial problem, Indagationes Math., 10 (1948), pp. 421–423.Google Scholar
  3. [3]
    P. Erdös, J. C. Fowler, V. T. Sòs and R. M. Wilson, On 2-designs, J. Combinatorial Theory, Series A, 38 (1985), pp. 131–142.zbMATHCrossRefGoogle Scholar
  4. [4]
    J. C. Fowler, A short proof of Totten’s classification of restricted linear spaces, Geometriae Dedicata, 15 (1984), pp. 413–422.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    J. Totten, Classification of restricted linear spaces, Canadian J. Math., 28 (1976), pp. 321–333.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1990

Authors and Affiliations

  • David A. Drake
    • 1
  • Paul Erdös
    • 2
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA
  2. 2.Mathematical InstituteHungarian Academy of SciencesBudapestHungary

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