  If, for a subset S of Z^k, we compare the conditions of being parametrizable
(a) by a single k-tuple of polynomials with integer coefficients, (b) by a
single k-tuple of integer-valued polynomials and, (c) by finitely many k-tuples
of polynomials with integer coefficients (variables ranging through the
integers in each case) then (a) implies (b) (obviously), (b) implies (c), and
neither converse holds. Condition (b) is equivalent to the set S being the set
of integer values taken by some k-tuple of polynomials with rational
coefficients as the variables range through the integers. We also show that
every co-finite subset of Z^k is parametrizable a single k-tuple of polynomials
with integer coefficients.
