Variations on the Monotone Subsequence Theme of Erdös and Szekeres

  • J. Michael Steele
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 72)


A review is given of the results on the length of the longest increasing subsequence and related problems. The review covers results on random and pseudorandom sequences as well as deterministic ones. Although most attention is given to previously published research, some new proofs and new results are given. In particular, some new phenomena are demonstrated for the monotonic subsequences of sections of sequences. A number of open problems from the literature are also surveyed.

Key words

Monotone subsequence unimodal subsequence partial ordering limit theory irrational numbers derandomization pseudo-random permutations 

AMS(MOS) subject classifications




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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • J. Michael Steele
    • 1
  1. 1.Department of StatisticsUniversity of Pennsylvania, The Wharton SchoolPhiladelphiaUSA

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