Increasing and decreasing subsequences and their variants

@inproceedings{Stanley2006IncreasingAD,
  title={Increasing and decreasing subsequences and their variants},
  author={Richard P. Stanley},
  year={2006}
}
We survey the theory of increasing and decreasing subsequences of permutations. Enumeration problems in this area are closely related to the RSK algorithm. The asymptotic behavior of the expected value of the length is(w) of the longest increasing subsequence of a permutation w of 1, 2, . . . , n was obtained by Vershik–Kerov and (almost) by Logan–Shepp. The entire limiting distribution of is(w) was then determined by Baik, Deift, and Johansson. These techniques can be applied to other classes… CONTINUE READING
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