Methods to determine Coxeter polynomials Original Research Article

A reduction formula for the characteristic polynomials of the Coxeter matrices of certain split finite-dimensional algebras is proved. In the hereditary case, this yields explicit expressions for the Coxeter polynomials of large families of quivers. Moreover, a combinatorial interpretation of the entries of the Coxeter matrices of path algebras gives formulas for Coxeter polynomials of some quivers which cannot be treated by the above-mentioned reduction process.