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Coxeter polynomials of Salem trees

Charalampos A. Evripidou (2015)

Colloquium Mathematicae

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 m , . . . , m k for the Coxeter polynomials of the trees , . . . , k respectively, then z is a root for the Coxeter polynomial of their join, of multiplicity at least m i n m - m , . . . , m - m k where m = m + + m k .

Cycle-finite algebras of semiregular type

Jerzy Białkowski, Andrzej Skowroński, Adam Skowyrski, Paweł Wiśniewski (2012)

Colloquium Mathematicae

We describe the structure of artin algebras for which all cycles of indecomposable finitely generated modules are finite and all Auslander-Reiten components are semiregular.

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