Minimal nonstandard Coxeter trees
type: Item
instance of: scholarly article
title: Minimal nonstandard Coxeter trees
zbMATH Open document ID: 0795.05045
author: Luis Paris
published in: Journal of Algebra
publication date: 1994-08-29T00:00:00Z
review text: A Coxeter graph \(\Gamma\) consists of a set of vertices \(S\) and an associated matrix \(M\). The Witt form of \(\Gamma\) is a symmetric bilinear form \(B_ \Gamma\) defined over the real vector space \(V_ \Gamma\) of dimension \(| \Gamma |\) by \(B_ \Gamma = -\cos (\pi/m_{s,t})\) if \(m_{s,t} \neq+\infty\) and \(=-1\) if \(m_{s,t} = + \infty\). The signature of \(\Gamma\) is the \(l\)-tuple \((\varepsilon_ 1, \dots, \varepsilon_ l)\) where \(\varepsilon_ i\) is \(-1,0\) or 1 such that there exists \(P \in \text{GL} (V_ \Gamma)\) with \(PB_ \Gamma P^ t=\text{diag} (\varepsilon_ 1, \dots, \varepsilon_ l)\). A Coexter graph is nonstandard if its signature does not have 1's in all but the first position. The paper studies the structure of minimal nonstandard Coxeter trees, where minimal means not containing another Coxeter tree as a minor. A Coxeter graph is called ordinary if the weight of each edge is 3. The paper includes a complete list of ordinary minimal nonstandard Coxeter trees.
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 20F55
zbMATH DE Number: 495540
zbMATH Keywords: Coxeter graph
zbMATH Keywords: Witt form
zbMATH Keywords: Coxeter tree
reviewed by: Alan C. Tucker
MaRDI profile type: Publication
full work available at URL: jabr.1993.1064
OpenAlex ID: W2018981027
DOI: 10.1006/JABR.1993.1064
Recommended article: Minimal trees and monophonic convexity
Recommended article: Trees with minimal Laplacian coefficients
Recommended article: Minimum Level Nonplanar Patterns for Trees
Recommended article: Tree-width and planar minors
Recommended article: Some upper bounds for minimal trees
Recommended article: Trees with minimum F-coindex
Recommended article: Minimax trees and André polynomials
Recommended article: Trees having many minimal dominating sets
Recommended article: Q3970808
Recommended article: Minimal unimodal decomposition on trees
description: scientific article; zbMATH DE number 495540