Kelli Talaska

On Plücker coordinates of a perfectly oriented planar network
dmtcs:3616 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2008,
DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)

https://doi.org/10.46298/dmtcs.3616
On Plücker coordinates of a perfectly oriented planar network
Authors: Kelli Talaska ^{1}
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Kelli Talaska
1 Department of Mathematics  University of Michigan
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 $G$.
EMSW21RTG: Enhancing the Research Workforce in Algebraic Geometry and its Boundaries in the TwentyFirst Century; Funder: National Science Foundation; Code: 0502170