On Plücker coordinates of a perfectly oriented planar network

Abstract : 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 weights, with positive integer coefficients. These polynomials are weight generating functions for certain subsets of edges in $G$.
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Krattenthaler, Christian and Sagan, Bruce. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), pp.583-586, 2008, DMTCS Proceedings
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Kelli Talaska. On Plücker coordinates of a perfectly oriented planar network. Krattenthaler, Christian and Sagan, Bruce. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), pp.583-586, 2008, DMTCS Proceedings. 〈hal-01185150〉

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