Math 515 homework #16 Due date: 19980408 D. J. Bernstein 19980401 Exercise 46. Eisenbud 10.3. Exercise 47. Eisenbud 10.11. (In this exercise, k is a field; S is the subring k[x, y^{2}] of the polynomial ring k[x, y]; S_{n} is the set of homogeneous degree-n polynomials in S; and H_{S}(n) is the length of S_{n} over k. For example, S_{3} = kx^{3} + kxy^{2}.)