Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 101 / 5 / b / Solution

The weighted Hilbert series of $K[x,y,t_1,\dots ,t_n]$ isThe homogeneous polynomial $x^k-y^k$ has degree $k$ and is a non-zero-divisor, so quotienting by it multiplies the series by $1-z^k$. Therefore the requested Poincare series of a graded module is

Solved by gpt-5.6-sol high.