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Longest Increasing and Decreasing Subsequences

Published online by Cambridge University Press:  20 November 2018

C. Schensted
C. Schensted*
Affiliation:
Institute for Defence Analysis, Princeton
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Extract

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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 179 - 191
Copyright
Copyright © Canadian Mathematical Society 1961

References

1. Frame, J. S., Robinson, G. de B., and Thrall, R. M., The hook graphs of the symmetric group, Can. J. Math., 6 (1954), 316.Google Scholar
2. Rutherford, D. E., Substitutional analysis (Edinburgh University Press, 1948) p. 26.Google Scholar