Bipartite Perfect Matching as a Real Polynomial

We obtain a description of the Bipartite Perfect Matching decision problem as a multi-linear polynomial over the Reals. We show that it has full degree and has $(1-o(1))\cdot 2^{n^2}$ monomials with non-zero coefficients. In contrast, we show that in the dual representation (switching the roles of 0 and 1) there are only $2^{\theta(n \l...More