2006/01/27 by Jon McCammond, McCammond, Jon · 1 citation
Computer Science · Mathematics · #05E15 #20F36 #46L54 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.math/0601687
openalex publication_date 2006/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Certain mathematical structures make a habit of reoccuring in the most diverse list of settings. Some obvious examples exhibiting this intrusive type of behavior include the Fibonacci numbers, the Catalan numbers, the quaternions, and the modular group. In this article, the focus is on a lesser known example: the noncrossing partition lattice. The focus of the article is a gentle introduction to the lattice itself in three of its many guises: as a way to encode parking functions, as a key part of the foundations of noncommutative probability, and as a building block for a contractible space acted on by a braid group. Since this article is aimed primarily at nonspecialists, each area is briefly introduced along the way.