Longest Increasing and Decreasing Subsequences

  • C. Schensted
Part of the Modern Birkhäuser Classics book series (MBC)


This paper deals with finite sequences of integers. Typical of the problems we shall treat is the determination of the number of sequences of length n, consisting of the integers 1,2, ... , m, which have a longest increasing subsequence of length α. Throughout the first part of the paper we will deal only with sequences in which no numbers are repeated. In the second part we will extend the results to include the possibility of repetition. Our results will be stated in terms of standard Young tableaux.


Binary Sequence Column Form Standard Tableau Distinct Integer Hook Length 
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  1. 1.
    J. S. Frame, G. de B. Robinson, and R. M. Thrall, The hook graphs of the symmetric group, Can. J. Math., 6 (1954), 316.MATHMathSciNetGoogle Scholar
  2. 2.
    D. E. Rutherford, Substitutional analysis (Edinburgh University Press, 1948), p. 26.Google Scholar

Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • C. Schensted
    • 1
  1. 1.Institute for Defence AnalysisPrincetonUSA

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