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Structure of braid graphs in simply-laced Coxeter systems

Cadman, Quentin D (2021) Structure of braid graphs in simply-laced Coxeter systems. Masters thesis, Northern Arizona University.

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Abstract

Any two reduced expressions for the same Coxeter group element are related by a sequence of commutation and braid moves. We say that two reduced expressions are braid equivalent if they are related via a sequence of braid moves,and the corresponding equivalence classes are called braid classes. Each braid class can be encoded in terms of a braid graph in a natural way. In this thesis, we study the structure of braid graphs in simply-laced Coxeter systems. In a recent paper, Awik et al. proved that every reduced expression has a unique factorization as a product of so-called links, which in turn induces a decomposition of the braid graph into a box product of the braid graphs for each link factor. For a special class of links, called Fibonacci links, they showed that the corresponding braid graph is isomorphic to a Fibonacci cube graph. In this thesis, we prove that every Fibonacci cube occurs as the braid graph for a link in any simply-laced triangle-free Coxeter System whose corresponding braid graph contains the Coxeter graph of the Coxeter system of type ÇD 4 as a subgraph.

Item Type: Thesis (Masters)
Publisher’s Statement: © Copyright is held by the author. Digital access to this material is made possible by the Cline Library, Northern Arizona University. Further transmission, reproduction or presentation of protected items is prohibited except with permission of the author.
Keywords: Braid graphs; Coxeter graphs; Coxeter system; Fibonacci cubes; root systems; simply-laced
Subjects: Q Science > QA Mathematics
NAU Depositing Author Academic Status: Student
Department/Unit: Graduate College > Theses and Dissertations
College of the Environment, Forestry, and Natural Sciences > Mathematics and Statistics
Date Deposited: 07 Feb 2022 16:56
Last Modified: 07 Feb 2022 16:56
URI: https://openknowledge.nau.edu/id/eprint/5668

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