A Central Limit Theorem for Repeating Patterns
  We prove a central limit theorem for the length of the longest subsequence of a random permutation which follows one of a class of repeating patterns. This class includes every fixed pattern of ups and downs having at least one of each, such as the alternating case considered by Stanley in arXiv:math/0511419 and Widom in arXiv:math/0511533. In every case considered the convergence in the limit of long permutations is to normal with mean and variance linear in the length of the permutation. 
Aaron Abrams, Eric Babson, Henry Landau, Zeph Landau, James   Pommersheim
math.CO math.PR