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Coxeter diagram

Coxeter diagram noun: a Coxeter-Dynkin diagram.

Noun

Coxeter diagram (plural Coxeter diagrams)

  1. A Coxeter-Dynkin diagram.
    • It suffices to make use of the tables above and observe that the Coxeter diagram of a direct sum of C-matrices is the disconnected union of the Coxeter diagrams of the summands.
    • For the description of C⁻-matrices satisfying condition (2) we shall use Coxeter diagrams with the additional stipulation that in case aᵢⱼ < −1 the vertices vᵢ and vⱼ are joined by a dotted line with index −aᵢⱼ. By the Coxeter diagram of a Coxeter polyhedron and a lattice generated by reflections...1991, Gregori A. Margulis, Discrete Subgroups of Semisimple Lie Groups, page 358

Examples of Coxeter diagram in a sentence

  • An automorphism of a Coxeter diagram M leads in a natural way to a Coxeter subgroup of the Coxeter group of type M.1993, B. Mühlherr, “Coxeter groups in Coxeter groups”, in Albrecht Beutelspacher, F. Buekenhout, J. Doyen, F. de Clerck, J. A. Thas, J. W....
  • One can see this by using the Dynkin diagram instead of the Coxeter diagram and noting that it does not have any nontrivial automorphisms.2008, Peter Abramenko, Kenneth S. Brown, Buildings: Theory and Applications, page 259:

Forms of Coxeter diagram

pluralCoxeter diagrams

Questions about Coxeter diagram

What does Coxeter diagram mean?
Coxeter diagram means a Coxeter-Dynkin diagram.
How do you use Coxeter diagram in a sentence?
An automorphism of a Coxeter diagram M leads in a natural way to a Coxeter subgroup of the Coxeter group of type M.
What part of speech is Coxeter diagram?
Coxeter diagram is a noun.
What is the plural of Coxeter diagram?
The plural of Coxeter diagram is Coxeter diagrams.

Words near Coxeter diagram in the dictionary

  1. coxcomically
  2. Coxe
  3. coxed
  4. coxes
  5. Coxeter
  6. Coxeter diagram
  7. Coxeter diagrams
  8. Coxeter graph
  9. Coxeter graphs
  10. Coxeter group
  11. Coxeter groups

Source and license

Adapted from Wiktionary: Coxeter 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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