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Properties of Binomial Coefficients

  • Titu Andreescu
  • Zuming Feng

Abstract

[AIME 1987] A given sequence r 1, r 2, ..., r n of distinct real numbers can be put in ascending order by means of one or more “bubble passes.” A bubble pass through a given sequence consists in comparing the second term with the first term and exchanging them if and only if the second term is smaller, then comparing the third term with the current second term and exchanging them if and only if the third term is smaller, and so on, in order, through comparing the last term, r n , with its current predecessor and exchanging them if and only if the last term is smaller. Figure 3.1 shows how the sequence 1, 9, 8, 7 is transformed into the sequence 1, 8, 7, 9 by one bubble pass.

Keywords

Positive Integer Nonnegative Integer Arithmetic Progression License Plate Binomial Coefficient 
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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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Titu Andreescu
    • 1
  • Zuming Feng
    • 2
  1. 1.American Mathematics CompetitionsUniversity of NebraskaLincolnUSA
  2. 2.Department of MathematicsPhillips Exeter AcademyExeterUSA

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