A Central Limit Theorem for Repeating Patterns
Abstract
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 (2008) and Widom (2006). 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.
Fields of Study & Subjects
Bayesian Methods and Mixture Models
Fractal and DNA sequence analysis
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- The Electronic Journal of Combinatorics
- Volume
- 33
- Issue
- 2
- Publication date
- 18 June 2026
- Language
- EN