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A Balanced Interval of Two Sets of Points on a Line

  • Atsushi Kaneko
  • M. Kano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3330)

Abstract

Let n,m,k,h be positive integers such that 1 ≤ nm, 1≤ kn and 1≤ hm. Then we give a necessary and sufficient condition for a configuration with n red points and m blue points on a line to have an interval containing precisely k red points and h blue points.

Keywords

Positive Integer General Position Point Change Parallel Line Half Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bárány, I., Matoušek, J.: Simultaneous partitions of measures by k-fans. Discrete Comput. Geom. 25, 317–334 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Goodman, J., O’Rourke, J.: Handbook of Discrete and Computational Geometry. CRC Press, Boca Raton (1997)zbMATHGoogle Scholar
  3. 3.
    Kaneko, A., Kano, M.: Discrete geometry on red and blue points in the plane — A survey. In: Discrete and Computational GeometryE The Goodman-Pollack Festschrift, pp. 551–570. Springer, Heidelberg (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Atsushi Kaneko
    • 1
  • M. Kano
    • 2
  1. 1.Department of Computer Science and Communication EngineeringKogakuin UniversityTokyoJapan
  2. 2.Department of Computer and Information SciencesIbaraki UniversityHitachi, IbarakiJapan

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