Methods to Determine Coxeterpolynomials

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