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Longest increasing subsequences in pattern-restricted permutations
The electronic journal of combinatorics, Permutation Patterns, Tome 9 (2002) no. 2
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Inspired by the results of Baik, Deift and Johansson on the limiting distribution of the lengths of the longest increasing subsequences in random permutations, we find those limiting distributions for pattern-restricted permutations in which the pattern is any one of the six patterns of length 3. We show that the (132)-avoiding case is identical to the distribution of heights of ordered trees, and that the (321)-avoiding case has interesting connections with a well known theorem of Erdős-Szekeres.
DOI : 10.37236/1684
Classification : 05A16, 05A05
Mots-clés : random permutations 
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     author = {Emeric Deutsch and A. J. Hildebrand and Herbert S. Wilf},
     title = {Longest increasing subsequences in pattern-restricted permutations},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     number = {2},
     doi = {10.37236/1684},
     zbl = {1011.05008},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1684/}
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Emeric Deutsch; A. J. Hildebrand; Herbert S. Wilf. Longest increasing subsequences in pattern-restricted permutations. The electronic journal of combinatorics, Permutation Patterns, Tome 9 (2002) no. 2. doi: 10.37236/1684

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