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In a recent paper, Beniamini and Nisan gave a closed-form formula for theunique multilinear polynomial for the Boolean function determining whether agiven bipartite graph $G \subseteq K_{n,n}$ has a perfect matching, togetherwith an efficient algorithm for computing the coefficients of the monomials ofthis polynomial. We give the following generalization: Given an arbitrarynon-negative weight function $w$ on the edges of $K_{n,n}$, consider its set ofminimum weight perfect matchings. We give the real multilinear polynomial forthe Boolean function which determines if a graph $G \subseteq K_{n,n}$ containsone of these minimum weight perfect matchings.

A Real Polynomial for Bipartite Graph Minimum Weight Perfect Matchings