Kelli Talaska - Combinatorial formulas for ⅃-coordinates in a totally nonnegative Grassmannian, extended abstract, extended abstract

dmtcs:2706 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2706
Combinatorial formulas for ⅃-coordinates in a totally nonnegative Grassmannian, extended abstract, extended abstractArticle

Authors: Kelli Talaska 1

  • 1 Department of Mathematics - University of Michigan

Postnikov constructed a decomposition of a totally nonnegative Grassmannian $(Gr _{kn})_≥0$ into positroid cells. We provide combinatorial formulas that allow one to decide which cell a given point in $(Gr _{kn})_≥0$ belongs to and to determine affine coordinates of the point within this cell. This simplifies Postnikov's description of the inverse boundary measurement map and generalizes formulas for the top cell given by Speyer and Williams. In addition, we identify a particular subset of Plücker coordinates as a totally positive base for the set of non-vanishing Plücker coordinates for a given positroid cell.


Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: positroid,totally nonnegative Grassmannian,Le-diagram,[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
  • Algebraic Combinatorics; Funder: National Science Foundation; Code: 0555880

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