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arXiv · 0801.4822

A formula for Plücker coordinates associated with a planar network

Kelli Talaska
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Abstract

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 Pluecker coordinate as a ratio of two combinatorially defined polynomials in the edge weights, with positive integer coefficients. In the non-planar setting, we show that a similar formula holds for special choices of Pluecker coordinates.

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Kelli Talaska. 2008-04-15. A formula for Plücker coordinates associated with a planar network. https://doi.org/10.1093/imrn%2Frnn081

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