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 networkArticle

Authors: Kelli Talaska 1

  • 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 $G$.


Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: boundary measurements,total positivity,totally nonnegative Grassmannian,perfectly oriented network,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • EMSW21-RTG: Enhancing the Research Workforce in Algebraic Geometry and its Boundaries in the Twenty-First Century; Funder: National Science Foundation; Code: 0502170

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