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:mat...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: Abrams, Aaron, Babson, Eric, Landau, Henry, Landau, Zeph, Pommersheim, James
Format: Article
Language:English
Subjects:
Permutations
Theorems
Online Access:Get full text
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Summary: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.
ISSN:2331-8422