Abstract
We introduce the notion of weighted Coxeter graph and associate to it a certain generalization of the standard geometric representation of a Coxeter group. We prove sufficient conditions for faithfulness and non-faithfulness of such a representation. In the case when the weighted Coxeter graph is balanced we discuss how the generalized geometric representation is related to the numbers game played on the Coxeter graph.
Original language | English |
---|---|
Pages (from-to) | 17-27 |
Number of pages | 11 |
Journal | Discrete Applied Mathematics |
Volume | 192 |
DOIs | |
State | Published - 10 Sep 2015 |
Keywords
- Balanced functions on graphs
- Coxeter graphs
- Coxeter groups
- Geometric representation
- Numbers game
- Signed graphs
- Weighted graphs
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics