A Central Limit Theorem for Repeating Patterns
Combinatorics
2024-09-25 v2 Probability
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 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.
Cite
@article{arxiv.1204.2872,
title = {A Central Limit Theorem for Repeating Patterns},
author = {Aaron Abrams and Eric Babson and Henry Landau and Zeph Landau and James Pommersheim},
journal= {arXiv preprint arXiv:1204.2872},
year = {2024}
}
Comments
19 pages, 1 figure, 11 references