Coxeter polynomials of Salem trees

Charalampos A. Evripidou. "Coxeter polynomials of Salem trees." Colloquium Mathematicae 141.2 (2015): 209-226. <http://eudml.org/doc/284045>.

@article{CharalamposA2015,
abstract = {We compute the Coxeter polynomial of a family of Salem trees, and also the limit of the spectral radii of their Coxeter transformations as the number of their vertices tends to infinity. We also prove that if z is a root of multiplicities $m₁,..., m_\{k\}$ for the Coxeter polynomials of the trees $₁,..., _\{k\}$ respectively, then z is a root for the Coxeter polynomial of their join, of multiplicity at least $min\{m-m₁,..., m-m_\{k\}\}$ where $m = m₁+ ⋯ +m_\{k\}$.},
author = {Charalampos A. Evripidou},
journal = {Colloquium Mathematicae},
keywords = {Coxeter polynomials; Coxeter transformations; spectral radii; Dynkin diagrams},
language = {eng},
number = {2},
pages = {209-226},
title = {Coxeter polynomials of Salem trees},
url = {http://eudml.org/doc/284045},
volume = {141},
year = {2015},
}

TY - JOUR
AU - Charalampos A. Evripidou
TI - Coxeter polynomials of Salem trees
JO - Colloquium Mathematicae
PY - 2015
VL - 141
IS - 2
SP - 209
EP - 226
AB - We compute the Coxeter polynomial of a family of Salem trees, and also the limit of the spectral radii of their Coxeter transformations as the number of their vertices tends to infinity. We also prove that if z is a root of multiplicities $m₁,..., m_{k}$ for the Coxeter polynomials of the trees $₁,..., _{k}$ respectively, then z is a root for the Coxeter polynomial of their join, of multiplicity at least $min{m-m₁,..., m-m_{k}}$ where $m = m₁+ ⋯ +m_{k}$.
LA - eng
KW - Coxeter polynomials; Coxeter transformations; spectral radii; Dynkin diagrams
UR - http://eudml.org/doc/284045
ER -