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Coxeter-Dynkin diagram

Coxeter-Dynkin diagram noun: a graph with numerically labelled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).

coxeter-dynkin diagram: a graph with numerically labelled edges (called branches) representing the spatial relations...
Image: Rgugliel, CC BY-SA 3.0, via Wikimedia Commons

Noun

Coxeter-Dynkin diagram (plural Coxeter-Dynkin diagrams)

  1. A graph with numerically labelled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).
    • A Coxeter-Dynkin diagram encodes the information in a Coxeter matrix, which in turn encodes the presentation of a Coxeter group.
    • Vertices of a Coxeter-Dynkin diagram represent generators of the corresponding Coxeter group. The generators (algebraic) in turn correspond to the reflecting hyperplanes (geometric). A pair of vertices which are not linked by an edge correspond to a pair of commuting generators. An unnumbered edge...

Examples of Coxeter-Dynkin diagram in a sentence

  • Let 𝒬 be an indecomposable root lattice and let Γ denote the Coxeter-Dynkin diagram of the underlying root system Δ.1995 June, R. V. Moody, J. Patera, “Voronoi Domains and Dual Cells in the Generalized Kaleidoscope with Applications to Root and Weight...
  • There is a deep and only partially understood connection between the classification and structure of singularities and the Coxeter-Dynkin diagrams introduced by H.2000, Andrei Gabrielov, “Coxeter-Dynkin diagrams and singularities”, in Evgeniĭ Borisovich Dynkin, A. A. Yushkevich, Gary M. Seitz, A. L....
  • For 3 ≤ n ≤ 5, we will use Eₙ to denote the Coxeter-Dynkin diagrams of types A₁ + A₂(N = 3), A₄(N = 4) and D₅(N = 5).2012, Igor V. Dolgachev, Classical Algebraic Geometry: A Modern View, page 363:

Synonyms of Coxeter-Dynkin diagram

Forms of Coxeter-Dynkin diagram

pluralCoxeter-Dynkin diagrams

Origin of Coxeter-Dynkin diagram

After mathematicians H. S. M. Coxeter and Eugene Dynkin.

Questions about Coxeter-Dynkin diagram

What does Coxeter-Dynkin diagram mean?
Coxeter-Dynkin diagram means a graph with numerically labelled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).
How do you use Coxeter-Dynkin diagram in a sentence?
Let 𝒬 be an indecomposable root lattice and let Γ denote the Coxeter-Dynkin diagram of the underlying root system Δ.
What part of speech is Coxeter-Dynkin diagram?
Coxeter-Dynkin diagram is a noun.
What is the plural of Coxeter-Dynkin diagram?
The plural of Coxeter-Dynkin diagram is Coxeter-Dynkin diagrams.

Words near Coxeter-Dynkin diagram in the dictionary

  1. Coxeter graphs
  2. Coxeter group
  3. Coxeter groups
  4. Coxeter matrix
  5. Coxeter matrixes
  6. Coxeter-Dynkin diagram
  7. Coxeter-Dynkin diagrams
  8. Coxeters
  9. Coxey
  10. Coxhead
  11. Coxheads

Source and license

Adapted from Wiktionary: Coxeter-Dynkin diagram (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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