A Coxeter diagram is a graphical representation of a Coxeter group, which encodes the group's abstract structure by illustrating the relations between its generating reflections. Each node in the diagram represents a generator, and edges, often labeled with integers, denote the order of the product of the reflections corresponding to the connected nodes.

Coxeter Diagram

Graphical representation is a visual method of presenting data or information, allowing for easier interpretation and analysis by highlighting patterns, trends, and relationships. It encompasses various forms such as charts, graphs, and diagrams, each suited to different types of data and analytical needs.

Graphical Representation

A Coxeter group is an abstract group defined by a set of generators subject to specific relations, primarily involving products of pairs of generators that are involutions. These groups are fundamental in the study of symmetries and have applications in various fields, including geometry, algebra, and combinatorics.

Coxeter Group

Abstract structure

Generating reflections

Each node

Edges represent the boundaries or limits where two different areas, surfaces, or entities meet, playing a crucial role in defining shapes and structures in both physical and abstract spaces. They are fundamental in various fields, from computer science and mathematics to art and geography, serving as critical components in graph theory, image processing, and network analysis.

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