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{\bf Ghassan Firro, Toufik Mansour and Mark C. Wilson}
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{\bf Longest Alternating Subsequences in Pattern-Restricted Permutations}
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Inspired by the results of Stanley and Widom concerning the limiting
distribution of the lengths of longest alternating subsequences in
random permutations, and results of Deutsch, Hildebrand and Wilf on the
limiting distribution of the longest increasing subsequence for
pattern-restricted permutations, we find the limiting distribution of
the longest alternating subsequence for pattern-restricted permutations
in which the pattern is any one of the six patterns of length three. Our
methodology uses recurrences, generating functions, and complex
analysis, and also yields more detailed information. Several ideas for
future research are listed.
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