Show that Delta_1 intersect Delta_2, Delta_1 union Delta_2 are both simplicial complexes too.
2. Show H_{Delta_1 union Delta_2} = H_{Delta_1} + H_{Delta_2} - H_{the intersection}.
3. Take the two simplicial complexes from the last homework. Compute their Hilbert series (meaning, that of the associated Stanley-Reisner ideals) using the formula we have for general monomial ideals. Confirm that it matches the answer we get from the formula specifically for SR ideals.
4. Let I be a homogeneous ideal. But let's homogenize it again, anyway! Relate H_I and H_{homog(I)}.
...more to come
