Coxeter polynomials of Salem trees

Abstract

Abstract. We compute the Coxeter polynomial of a family of Salem trees and also the limit of the spectral radius of their Coxeter transformations as the number of their vertices tends to infinity. We also prove that if z is a root of multiplicities m 1 , . . . , m k for the Coxeter polynomials of the trees T 1 , . . . , T k , then z is a root for the Coxeter polynomial of their join, of multiplicity at least min{m − m 1 , . . . , m − m k } where m = m 1 + . . . + m k .