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A paper of the first author and Zilke proposed seven combinatorial problemsaround formulas for the characteristic polynomial and the exponents of anisolated quasihomogeneous singularity. The most important of them was aconjecture on the characteristic polynomial. Here the conjecture is proved, andsome of the other problems are solved, too. In the cases where also an oldconjecture of Orlik on the integral monodromy holds, this has implications onthe automorphism group of the Milnor lattice. The combinatorics used in theproof of the conjecture consists of tuples of orders on sets $\{0,1,...,n\}$with special properties and may be of independent interest.

The combinatorics of weight systems and characteristic polynomials of isolated quasihomogeneous singularities