  We prove that the F-signature of an affine semigroup ring of positive
characteristic is always a rational number, and describe a method for computing
this number. We use this method to determine the F-signature of Segre products
of polynomial rings, and of Veronese subrings of polynomial rings. Our
technique involves expressing the F-signature of an affine semigroup ring as
the difference of the Hilbert-Kunz multiplicities of two monomial ideals, and
then using Watanabe's result that these Hilbert-Kunz multiplicities are
rational numbers.
