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