Longest Alternating Subsequences in Pattern-Restricted Permutations

We determine the limiting distributions of the longest alternating subsequence for pattern-restricted permutations in which the pattern is any one of the six patterns of length three. This work is inspired by results of Stanley concerning limiting distributions of the lengths of the longest alternating subsequences in random permutations, results of Widom on the limiting distribution of longest alternating subsequence in random permutations, and results of Deutsch, Hildebrand and Wilf on the limiting distribution of the longest increasing subsequences for pattern-restricted permutations, 2000 Mathematics Subject Classification: 05A05, 05A15, 05A16 Key words: limiting distributions, alternating sequences, functional equations, kernel methods, restricted permutations.

• Type: Journal
• Year: 2007
• Where: COMBINATORICS
• Authors: Ghassan Firro, Toufik Mansour, Mark C. Wilson
• Keywords: COMBINATORICS 2007, Pattern-restricted Permutations, Permutations, Random Permutations