Weighted Coxeter graphs and generalized geometric representations of\n Coxeter Groups

2013/04/02 by Vadim Bugaenko, Bugaenko, Vadim, Yonah Cherniavsky +5
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1304.0692

Abstract

We introduce the notion of weighted Coxeter graph and associate to it a\ncertain generalization of the standard geometric representation of a Coxeter\ngroup. We prove sufficient conditions for faithfulness and non-faithfulness of\nsuch a representation. In the case when the weighted Coxeter graph is balanced\nwe discuss how the generalized geometric representation is related to the\nnumbers game played on the Coxeter graph.\n

Citations

• A Contribution to the Theory of Chromatic Polynomials

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