A Formula for Plücker Coordinates Associated with a Planar Network
نویسنده
چکیده
For a planar directed graph G, Postnikov’s boundary measurement map sends positive weight functions on the edges of G onto the appropriate totally nonnegative Grassmann cell. We establish an explicit formula for Postnikov’s map by expressing each Plücker coordinate as a ratio of two combinatorially defined polynomials in the edge weights, with positive integer coefficients. In the nonplanar setting, we show that a similar formula holds for special choices of Plücker coordinates.
منابع مشابه
On Plücker coordinates of a perfectly oriented planar network
Let G be a perfectly oriented planar graph. Postnikov’s boundary measurement construction provides a rational map from the set of positive weight functions on the edges of G onto the appropriate totally nonnegative Grassmann cell. We establish an explicit combinatorial formula for Postnikov’s map by expressing each Plücker coordinate of the image as a ratio of two polynomials in the edge weight...
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