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So we can restrict our attention to multilinear polynomials. … Proof: We first show that the polynomials are linearly independent. Suppose that $f = \sum_S c_S \prod_{i \in S} x_i = 0$ for all $(x_1,\ldots,x_n) \in \{0,1\}^n$. …
answered Feb 21 '14 by Yuval Filmus