  Let R denote the reals, and let h: R^n --> R be a continuous,
piecewise-polynomial function. The Pierce-Birkhoff conjecture (1956) is that
any such h is representable in the form sup_i inf_j f_{ij}, for some finite
collection of polynomials f_{ij} in R[x_1,...,x_n]. (A simple example is h(x_1)
= |x_1| = sup{x_1, -x_1}.) In 1984, L. Mahe and, independently, G. Efroymson,
proved this for n < 3; it remains open for n > 2. In this paper we prove an
analogous result for "generalized polynomials" (also known as signomials),
i.e., where the exponents are allowed to be arbitrary real numbers, and not
just natural numbers; in this version, we restrict to the positive orthant,
where each x_i > 0. As before, our methods work only for n < 3.
