  We investigate the uncertainties of the heavy-quark parton distribution
functions in the variable flavor number scheme. Because the charm- and
bottom-quark parton distribution functions (PDFs) are constructed predominantly
from the gluon PDF, it is a common practice to assume that the heavy-quark and
gluon uncertainties are the same. We show that this approximation is a
reasonable first guess, but it is better for bottom quarks than charm quarks.
We calculate the PDF uncertainty for t-channel single-top-quark production
using the Hessian matrix method, and predict a cross section of 2.12+0.32-0.29
pb at run II of the Tevatron.
