Consider $\mathbb{C}[x_1, x_2, ..., x_n]^{S_n}$. I want to calculate the Hilbert series for this. To do this, I'm trying to find out the dimension of the space of homogeneous symmetric polynomials of degree $d$. I'm stuck on this part - I'm not sure how to go about this combinatorially. Any hint would be appreciated!
2026-04-01 00:44:04.1775004244
Hilbert series for symmetric polynomial ring
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