17. Vandermonde determinants
Vandermonde matrix all the top row entries have total degree 0, all the second row entries have total degree 1, and so on. Thus, in this permutation-wise sum for a Vandermonde determinant, each summand has total degree 0 + 1 + 2 + :::+ (n 1) = 1 2 n(n 1) so the total degree of the determinant is the total degree of the product X 1 i<j n 1 = X 1 ... ................
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